2tan (problem 3.3.2)

Time bar (total: 19.3s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze58.0ms (0.3%)

Memory
7.2MiB live, 46.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.1s (31.6%)

Memory
-138.8MiB live, 8 291.7MiB allocated
Samples
3.4s26 109×0invalid
736.0ms5 495×0valid
496.0ms2 761×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.3s
ival-tan: 903.0ms (27.3% of total)
const: 709.0ms (21.4% of total)
ival-add: 281.0ms (8.5% of total)
ival-mult: 276.0ms (8.3% of total)
ival-<=: 253.0ms (7.6% of total)
ival-sub: 251.0ms (7.6% of total)
ival-fabs: 228.0ms (6.9% of total)
ival-<: 167.0ms (5% of total)
ival-and: 101.0ms (3.1% of total)
adjust: 83.0ms (2.5% of total)
exact: 48.0ms (1.4% of total)
ival-assert: 13.0ms (0.4% of total)
Bogosity

preprocess32.0ms (0.2%)

Memory
-18.9MiB live, 53.2MiB allocated
Algorithm
egg-herbie
Rules
102×sub-neg
80×lower-fma.f64
80×lower-fma.f32
68×cancel-sign-sub-inv
64×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13835
28635
316935
431035
536735
644535
748235
849135
067
0107
1137
2187
3247
4327
5477
6807
71077
81517
91667
101747
01747
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Outputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

explain94.0ms (0.5%)

Memory
15.2MiB live, 178.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2171(-1.633612713922059e-185 7.491851022733448e-189)4(-2.4091249698043953e-76 2.856240789299352e-78)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20-0-(tan.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))cancellation2149
tan.f64(tan.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2134
-138
Precision
0.9953271028037384
Recall
0.9815668202764977
Confusion?
Predicted +Predicted MaybePredicted -
+21340
-1533
Precision?
0.9730941704035875
Recall?
1.0
Freqs
test
numberfreq
042
1212
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
21.0ms330×0valid
19.0ms174×1valid
4.0ms2valid
1.0ms3valid
Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-tan: 17.0ms (58.3% of total)
adjust: 4.0ms (13.7% of total)
ival-add: 4.0ms (13.7% of total)
ival-sub: 3.0ms (10.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.6%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify15.0ms (0.1%)

Memory
-38.3MiB live, 15.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Rules
80×lower-fma.f64
80×lower-fma.f32
48×lower-*.f64
48×lower-*.f32
36×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11318
21818
32418
43218
54718
68018
710718
815118
916618
1017418
017418
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
Outputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)

localize26.0ms (0.1%)

Memory
29.5MiB live, 29.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(tan.f64 x)
accuracy99.8%
(tan.f64 (+.f64 x eps))
accuracy63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Samples
8.0ms87×1valid
8.0ms165×0valid
2.0ms2valid
0.0ms3valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-tan: 6.0ms (51.7% of total)
adjust: 2.0ms (17.2% of total)
ival-add: 2.0ms (17.2% of total)
ival-sub: 2.0ms (17.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series24.0ms (0.1%)

Memory
-21.3MiB live, 17.1MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#<alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))>
#<alt (tan.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (tan.f64 x)>
Outputs
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
Calls

21 calls:

TimeVariablePointExpression
7.0ms
eps
@0
(- (tan (+ x eps)) (tan x))
4.0ms
x
@0
(- (tan (+ x eps)) (tan x))
2.0ms
x
@-inf
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@inf
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@0
(+ x eps)

simplify372.0ms (1.9%)

Memory
46.2MiB live, 509.5MiB allocated
Algorithm
egg-herbie
Rules
14 592×lower-fma.f64
14 592×lower-fma.f32
5 316×lower-*.f64
5 316×lower-*.f32
2 664×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01571351
14641285
215341274
359491242
085341195
Stop Event
iter limit
node limit
Counts
84 → 77
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite364.0ms (1.9%)

Memory
-3.0MiB live, 394.2MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 404×lower-*.f64
4 404×lower-*.f32
3 318×lower-/.f64
3 318×lower-/.f32
3 264×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15016
240216
3611716
0809516
Stop Event
iter limit
node limit
iter limit
Counts
4 → 259
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(tan.f64 x)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
(+.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(+.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (tan.f64 x) #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(fma.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 (+.f64 x eps)))
(fma.f64 (neg.f64 (sin.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 x eps)))) (neg.f64 (tan.f64 x)))
(fma.f64 (neg.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (tan.f64 x) (tan.f64 (+.f64 x eps)))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (-.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (+.f64 x eps) x))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(neg.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (*.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (*.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 9 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) (*.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 6 binary64)))))
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(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (*.f64 eps eps)) (-.f64 x eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(tan.f64 x)
(neg.f64 (neg.f64 (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

eval44.0ms (0.2%)

Memory
3.2MiB live, 87.4MiB allocated
Compiler

Compiled 8 701 to 983 computations (88.7% saved)

prune56.0ms (0.3%)

Memory
-4.1MiB live, 117.0MiB allocated
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New31818336
Fresh000
Picked011
Done000
Total31819337
Accuracy
100.0%
Counts
337 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
35.2%
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (+.f64 x eps) x))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
63.8%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
63.6%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
63.6%
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
62.8%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
63.6%
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
63.8%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
22.9%
(-.f64 (tan.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
63.6%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
62.8%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
62.9%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
62.7%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
35.8%
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
62.5%
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
Compiler

Compiled 1 129 to 486 computations (57% saved)

simplify478.0ms (2.5%)

Memory
-18.8MiB live, 536.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (tan.f64 x) (tan.f64 eps))
cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
cost-diff320
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff320
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
cost-diff0
(tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))
cost-diff0
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
cost-diff1728
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
cost-diff0
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
cost-diff192
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
cost-diff26816
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
cost-diff39808
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))
cost-diff79744
(fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))))
Rules
20 726×lower-fma.f32
20 706×lower-fma.f64
3 554×lower-+.f32
3 544×lower-+.f64
3 206×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0631247
01221217
12331035
2616892
32007848
47625848
08093821
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
eps
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))
(fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(literal 1/3 binary64)
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(sin.f64 x)
x
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
(*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
#s(literal 1/6 binary64)
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (sin.f64 x) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
#s(literal 1/3 binary64)
(*.f64 x x)
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
#s(literal 1 binary64)
(-.f64 x eps)
x
eps
(*.f64 (+.f64 x eps) (-.f64 x eps))
(+.f64 x eps)
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 (+.f64 x eps))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
x
(tan.f64 eps)
eps
(+.f64 (tan.f64 x) (tan.f64 eps))
(neg.f64 (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps eps) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps eps) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
eps
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps eps) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps eps) eps)))
(fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))))
(fma.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64)) (/.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x))))
(fma.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
#s(literal 1/3 binary64)
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(sin.f64 x)
x
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
(*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))
#s(literal 1/6 binary64)
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (sin.f64 x) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
#s(literal 1/3 binary64)
(*.f64 x x)
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))
(tan.f64 (+.f64 x eps))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(+.f64 x eps)
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
#s(literal 1 binary64)
(-.f64 x eps)
x
eps
(*.f64 (+.f64 x eps) (-.f64 x eps))
(+.f64 x eps)
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 (+.f64 x eps))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
x
(tan.f64 eps)
eps
(+.f64 (tan.f64 x) (tan.f64 eps))
(neg.f64 (tan.f64 x))

localize512.0ms (2.6%)

Memory
-11.3MiB live, 568.7MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy64.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
accuracy99.9%
(sin.f64 (+.f64 x eps))
accuracy99.9%
(cos.f64 (+.f64 x eps))
accuracy63.9%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
accuracy99.9%
(tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
accuracy63.9%
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
accuracy56.6%
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
accuracy99.9%
(tan.f64 (+.f64 x eps))
accuracy99.7%
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
accuracy98.6%
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))
accuracy63.9%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
accuracy99.9%
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
accuracy99.8%
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy99.5%
(*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy98.5%
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
Samples
175.0ms12×5exit
146.0ms92×1valid
76.0ms152×0valid
Compiler

Compiled 1 129 to 69 computations (93.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 331.0ms
ival-tan: 167.0ms (50.4% of total)
ival-mult: 41.0ms (12.4% of total)
ival-add: 28.0ms (8.5% of total)
adjust: 23.0ms (6.9% of total)
ival-div: 20.0ms (6% of total)
ival-pow: 11.0ms (3.3% of total)
ival-sin: 9.0ms (2.7% of total)
const: 8.0ms (2.4% of total)
ival-sub: 8.0ms (2.4% of total)
ival-cos: 8.0ms (2.4% of total)
ival-pow2: 6.0ms (1.8% of total)
ival-neg: 1.0ms (0.3% of total)
exact: 1.0ms (0.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series529.0ms (2.7%)

Memory
2.7MiB live, 238.9MiB allocated
Counts
25 → 528
Calls
Call 1
Inputs
#<alt (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))))>
#<alt (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))>
#<alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))>
#<alt (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))>
#<alt (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))>
#<alt (tan.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))>
#<alt (-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))>
#<alt (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 x eps))>
#<alt (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))>
#<alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))>
#<alt (cos.f64 (+.f64 x eps))>
#<alt (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))>
#<alt (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))>
#<alt (*.f64 (tan.f64 x) (tan.f64 eps))>
#<alt (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))>
#<alt (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))>
#<alt (pow.f64 (sin.f64 x) #s(literal 4 binary64))>
#<alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (+.f64 (tan.f64 x) (tan.f64 eps))>
Outputs
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))>
#<alt (* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
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#<alt 1/3>
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#<alt (* 1/3 eps)>
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#<alt (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))>
#<alt (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))>
#<alt (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))>
#<alt (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))>
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (+ 1 (* -2/3 (pow x 2))))>
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))>
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (pow (sin x) 4)>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ x (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
Calls

132 calls:

TimeVariablePointExpression
272.0ms
x
@inf
(sin (+ x eps))
45.0ms
x
@inf
(+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))
26.0ms
x
@inf
(* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x)))
13.0ms
x
@inf
(/ 1 (- 1 (* (tan x) (tan eps))))
8.0ms
eps
@inf
(/ 1 (cos (+ x eps)))

simplify584.0ms (3%)

Memory
-3.6MiB live, 394.7MiB allocated
Algorithm
egg-herbie
Rules
10 234×lower-fma.f64
10 234×lower-fma.f32
6 412×lower-*.f64
6 412×lower-*.f32
5 134×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078513713
1250213423
0824212892
Stop Event
iter limit
node limit
Counts
528 → 515
Calls
Call 1
Inputs
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* 1/3 eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 4)
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(/ (sin eps) (cos eps))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
Outputs
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))
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(* 1/3 eps)
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(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(* 1/3 (pow x 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 x (fma.f64 (sin.f64 eps) (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (cos.f64 eps) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (cos.f64 eps)) (sin.f64 eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ x (/ (sin eps) (cos eps)))
(+.f64 x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
(+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(fma.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

rewrite425.0ms (2.2%)

Memory
22.4MiB live, 734.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 654×lower-fma.f32
5 636×lower-fma.f64
5 016×lower-*.f32
5 004×lower-*.f64
2 254×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058653
0114623
1522425
25165425
08203402
Stop Event
iter limit
node limit
iter limit
Counts
25 → 783
Calls
Call 1
Inputs
(fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(sin.f64 (+.f64 x eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
Outputs
(+.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))))))
(+.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x)))))
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(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64))
(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (*.f64 #s(literal 1 binary64) (tan.f64 eps)) (tan.f64 x))
(+.f64 (*.f64 (tan.f64 x) #s(literal 1 binary64)) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(+.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (*.f64 (tan.f64 x) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (tan.f64 eps))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 #s(literal 1 binary64) (tan.f64 eps) (tan.f64 x))
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(fma.f64 (tan.f64 eps) #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x))
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 eps))
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (tan.f64 eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (sin.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 eps) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps)))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 eps)))
(/.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (cos.f64 eps) #s(literal 1 binary64))) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (fma.f64 (sin.f64 eps) (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 eps) (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 eps) (tan.f64 x)))
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 x) (tan.f64 eps))))

eval300.0ms (1.6%)

Memory
3.6MiB live, 468.6MiB allocated
Compiler

Compiled 100 468 to 4 465 computations (95.6% saved)

prune170.0ms (0.9%)

Memory
28.8MiB live, 347.5MiB allocated
Pruning

22 alts after pruning (19 fresh and 3 done)

PrunedKeptTotal
New1 553151 568
Fresh9413
Picked325
Done011
Total1 565221 587
Accuracy
100.0%
Counts
1 587 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
63.6%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
63.1%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
63.6%
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
63.6%
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
63.8%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
35.4%
(-.f64 (tan.f64 (/.f64 (*.f64 (/.f64 (+.f64 eps x) (-.f64 x eps)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 eps x))) (tan.f64 x))
63.6%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
35.8%
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
63.1%
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64))) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) x)))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 eps (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
99.8%
#s(approx (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x))) (*.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))))
Compiler

Compiled 1 362 to 599 computations (56% saved)

simplify347.0ms (1.8%)

Memory
-21.9MiB live, 389.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff0
(fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff320
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff320
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
cost-diff896
(fma.f64 eps (/.f64 x eps) eps)
cost-diff0
#s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))
cost-diff0
(tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps)))
cost-diff0
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
cost-diff896
(fma.f64 eps (/.f64 x eps) eps)
cost-diff0
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
cost-diff0
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
cost-diff0
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
cost-diff6272
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
cost-diff6848
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
cost-diff13312
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
cost-diff41152
(-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
Rules
11 596×lower-fma.f32
11 566×lower-fma.f64
3 486×lower-*.f32
3 472×lower-*.f64
3 366×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01062392
01792427
13552102
29201833
332361588
084001508
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
(fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps)
eps
(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))))
(pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
(*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))
(fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))
(-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
(fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))
(cos.f64 (+.f64 x x))
(+.f64 x x)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))
(*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)))
#s(literal 1/3 binary64)
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
eps
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
(tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps)))
#s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))
(fma.f64 eps (/.f64 x eps) eps)
eps
(/.f64 x eps)
x
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps)))
#s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))
(fma.f64 eps (/.f64 x eps) eps)
(/.f64 x eps)
(neg.f64 (tan.f64 x))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
eps
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps)))
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))
x
(fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal 2/3 binary64))
#s(literal 2/3 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 1/3 binary64) eps)
#s(literal 1/3 binary64)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/3 binary64))) (*.f64 eps (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/3 binary64))) (*.f64 eps (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
eps
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eps
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#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
(-.f64 (tan.f64 #s(approx (+ x eps) (+.f64 x eps))) (tan.f64 x))
(tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps)))
(tan.f64 #s(approx (+ x eps) (+.f64 x eps)))
#s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))
#s(approx (+ x eps) (+.f64 x eps))
(fma.f64 eps (/.f64 x eps) eps)
(+.f64 x eps)
eps
(/.f64 x eps)
x
(tan.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 #s(approx (+ x eps) (+.f64 x eps))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps)))
(sin.f64 #s(approx (+ x eps) (+.f64 x eps)))
#s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))
#s(approx (+ x eps) (+.f64 x eps))
(fma.f64 eps (/.f64 x eps) eps)
(+.f64 x eps)
(/.f64 x eps)
(neg.f64 (tan.f64 x))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps (fma.f64 x (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps (fma.f64 x (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
eps
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps (fma.f64 x (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps)))
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps (fma.f64 x (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) x))
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))
(fma.f64 eps (fma.f64 x (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) x)
x
(fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal 2/3 binary64))
#s(literal 2/3 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 1/3 binary64) eps)
(*.f64 eps #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)

localize997.0ms (5.2%)

Memory
-159.1MiB live, 907.7MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy99.5%
(*.f64 eps #s(literal 2/3 binary64))
accuracy99.5%
(*.f64 #s(literal 1/3 binary64) eps)
accuracy97.8%
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps)))
accuracy99.9%
(cos.f64 (+.f64 x eps))
accuracy99.6%
(fma.f64 eps (/.f64 x eps) eps)
accuracy99.6%
#s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))
accuracy63.9%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
accuracy99.9%
(tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps)))
accuracy99.6%
(fma.f64 eps (/.f64 x eps) eps)
accuracy99.6%
#s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))
accuracy63.9%
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
accuracy100.0%
(*.f64 eps eps)
accuracy100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
accuracy99.7%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
accuracy56.1%
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
accuracy99.8%
(*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))
accuracy99.8%
(fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
accuracy99.5%
(*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)))
accuracy56.5%
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
Samples
442.0ms230×1valid
118.0ms12×5exit
10.0ms14×0valid
Compiler

Compiled 1 925 to 105 computations (94.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 509.0ms
ival-tan: 86.0ms (16.9% of total)
ival-mult: 81.0ms (15.9% of total)
adjust: 73.0ms (14.3% of total)
ival-add: 57.0ms (11.2% of total)
ival-pow2: 47.0ms (9.2% of total)
ival-cos: 47.0ms (9.2% of total)
ival-div: 45.0ms (8.8% of total)
const: 23.0ms (4.5% of total)
ival-sub: 15.0ms (2.9% of total)
ival-pow: 15.0ms (2.9% of total)
ival-sin: 14.0ms (2.8% of total)
ival-neg: 4.0ms (0.8% of total)
exact: 1.0ms (0.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series347.0ms (1.8%)

Memory
-7.8MiB live, 351.8MiB allocated
Counts
28 → 564
Calls
Call 1
Inputs
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#<alt (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))>
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#<alt (*.f64 eps eps)>
#<alt #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))>
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#<alt (*.f64 #s(literal 1/3 binary64) eps)>
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Outputs
#<alt (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))>
#<alt (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))>
#<alt (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))>
#<alt (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))>
#<alt (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))>
#<alt (* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))>
#<alt (* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))>
#<alt (* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))>
#<alt (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))>
#<alt (* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))>
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#<alt 1/3>
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#<alt 1/3>
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#<alt (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))>
#<alt (pow x 2)>
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#<alt (- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt x>
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#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))>
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#<alt (/ (sin eps) (cos eps))>
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#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
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#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
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#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
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#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
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#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))>
#<alt (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))>
#<alt (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))>
#<alt (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))>
#<alt (* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))>
#<alt (* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))>
#<alt (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 1/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
#<alt (* 2/3 eps)>
Calls

141 calls:

TimeVariablePointExpression
56.0ms
x
@-inf
(+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
50.0ms
x
@inf
(+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
8.0ms
x
@-inf
(- (+ (* eps (+ (* (- (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (tan x)) (/ (* 1/3 (+ (* (sin x) (pow (tan x) 2)) (sin x))) (cos x)))) (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))))) (+ (* (pow (tan x) 2) -1/3) -1/3))
8.0ms
x
@inf
(- (+ (* eps (+ (* (- (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (tan x)) (/ (* 1/3 (+ (* (sin x) (pow (tan x) 2)) (sin x))) (cos x)))) (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))))) (+ (* (pow (tan x) 2) -1/3) -1/3))
7.0ms
x
@-inf
(+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)

simplify530.0ms (2.7%)

Memory
21.8MiB live, 722.3MiB allocated
Algorithm
egg-herbie
Rules
10 618×lower-fma.f64
10 618×lower-fma.f32
6 012×lower-*.f64
6 012×lower-*.f32
5 722×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070826056
1242424772
0823123313
Stop Event
iter limit
node limit
Counts
564 → 544
Calls
Call 1
Inputs
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (pow (cos x) 2))) (* 1/2 (cos (* 2 x))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (pow (cos x) 2))) (* 1/2 (cos (* 2 x))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (pow (cos x) 2))) (* 1/2 (cos (* 2 x))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (pow (cos x) 2))) (* 1/2 (cos (* 2 x))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x)))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x)))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x)))))
(- (+ 1/2 (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x)))))
x
(* x (+ 1 (* 5/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(+ eps (* 1/3 (pow eps 3)))
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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x
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(+ eps (* 1/3 (pow eps 3)))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(* 1/3 x)
(* x (+ 1/3 (* 5/18 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 5/18 (* 61/360 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 5/18 (* (pow x 2) (+ 61/360 (* 277/3024 (pow x 2))))))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(* 1/3 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))))
(- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
(- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
(- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
(- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))) eps)))))
(* 2/3 (* eps x))
(* x (+ x (* 2/3 eps)))
(* x (+ (* 2/3 eps) (* x (+ 1 (* 17/9 (* eps x))))))
(* x (+ (* 2/3 eps) (* x (+ 1 (* x (+ (* 5/3 x) (* 17/9 eps)))))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 3) (* eps (pow (cos x) 3))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 3) (* eps (pow (cos x) 3))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* 1/3 eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
Outputs
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
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(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
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(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps)))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps)))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps eps)))))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps)))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps)))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps eps)))))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
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(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
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(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))) eps)))))
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))) eps)))))
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(- (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1/3 binary64) (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1/3 binary64) (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1/3 binary64) (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (/ 1/2 (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* eps (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 3) (* eps (pow (cos x) 3))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) eps)))))
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(* 1/3 (pow eps 2))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (* 2 x))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (cos x)))) (/ (* (pow (sin x) 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* 1/3 eps)
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(* 1/3 eps)
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(* 1/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
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(* 2/3 eps)
(*.f64 eps #s(literal 2/3 binary64))

rewrite505.0ms (2.6%)

Memory
8.8MiB live, 739.1MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 324×lower-fma.f32
5 298×lower-fma.f64
4 132×lower-*.f32
4 118×lower-*.f64
3 110×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0991653
01631642
17901073
085301070
Stop Event
iter limit
node limit
iter limit
Counts
28 → 538
Calls
Call 1
Inputs
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(fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))
(*.f64 eps eps)
#s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps)))
(*.f64 #s(literal 1/3 binary64) eps)
(*.f64 eps #s(literal 2/3 binary64))
Outputs
(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64) (*.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))))))
(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64))))
(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (-.f64 (*.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
(+.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64)))
(+.f64 (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))))
(+.f64 (*.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64)) (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 eps (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (fma.f64 (tan.f64 x) (*.f64 eps (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))))
(+.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (tan.f64 x) eps)) (fma.f64 eps (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))))
(+.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal 1/3 binary64))
(+.f64 (+.f64 (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 eps (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))) (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (tan.f64 x) eps)))
(-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (*.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))))))
(-.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
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eval275.0ms (1.4%)

Memory
18.8MiB live, 411.2MiB allocated
Compiler

Compiled 124 354 to 5 642 computations (95.5% saved)

prune301.0ms (1.6%)

Memory
-12.1MiB live, 396.5MiB allocated
Pruning

20 alts after pruning (16 fresh and 4 done)

PrunedKeptTotal
New1 33691 345
Fresh7714
Picked325
Done123
Total1 347201 367
Accuracy
100.0%
Counts
1 367 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
63.6%
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
63.8%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
63.6%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
35.8%
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
63.1%
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps #s(approx (- (+ (* eps (+ (* (- (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (tan x)) (/ (* 1/3 (+ (* (sin x) (pow (tan x) 2)) (sin x))) (cos x)))) (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) (*.f64 eps #s(literal 2/3 binary64))) #s(literal 1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps #s(approx (- (+ (* eps (+ (* (- (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (tan x)) (/ (* 1/3 (+ (* (sin x) (pow (tan x) 2)) (sin x))) (cos x)))) (/ (+ (* (- 1/2 (* 1/2 (cos (+ x x)))) (pow (tan x) 2)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64))) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 eps (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
51.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps)))))
Compiler

Compiled 1 137 to 554 computations (51.3% saved)

simplify371.0ms (1.9%)

Memory
21.7MiB live, 488.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(+.f64 (tan.f64 x) (tan.f64 eps))
cost-diff0
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))
cost-diff0
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff320
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
cost-diff0
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
cost-diff0
(fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff320
(fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))
cost-diff0
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))))
cost-diff0
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
cost-diff640
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))
cost-diff12928
(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
cost-diff13248
(-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
cost-diff13248
(fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))
cost-diff14656
(fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
Rules
11 938×lower-fma.f32
11 900×lower-fma.f64
3 652×lower-*.f32
3 632×lower-*.f64
3 404×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01062229
01862215
13731923
29531596
331871583
082631506
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
(fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps)
eps
(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
(pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
(*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
(fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))
(tan.f64 x)
(-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 x x))
(+.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))
(/.f64 #s(literal 1/3 binary64) (cos.f64 x))
#s(literal 1/3 binary64)
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps)
eps
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))
x
(fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)
(*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))
#s(literal 2/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
eps
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x)))
(fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))
#s(literal 1/3 binary64)
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x)
(*.f64 eps eps)
(*.f64 #s(literal 2/3 binary64) x)
#s(literal 2/3 binary64)
x
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))
(*.f64 eps eps)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(fma.f64 eps (-.f64 eps x) (*.f64 x x))
(-.f64 eps x)
(neg.f64 (tan.f64 x))
(tan.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
x
(tan.f64 eps)
eps
(fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 eps eps) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x))))) eps))
(fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps)
(fma.f64 eps (fma.f64 (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 eps eps) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x))))) eps)
eps
(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
(fma.f64 (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 eps eps) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x)))))
(pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
(*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))
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(fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) x)
(*.f64 eps eps)
(*.f64 #s(literal 2/3 binary64) x)
(*.f64 x #s(literal 2/3 binary64))
#s(literal 2/3 binary64)
x
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))
(fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))
(*.f64 eps eps)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(fma.f64 eps (-.f64 eps x) (*.f64 x x))
(fma.f64 x x (*.f64 eps (-.f64 eps x)))
(-.f64 eps x)
(neg.f64 (tan.f64 x))
(tan.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
x
(tan.f64 eps)
eps
(fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)

localize848.0ms (4.4%)

Memory
-17.5MiB live, 1 255.2MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(neg.f64 (tan.f64 eps))
accuracy100.0%
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))
accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy63.8%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
accuracy99.8%
(*.f64 x (*.f64 x x))
accuracy99.7%
(fma.f64 eps (-.f64 eps x) (*.f64 x x))
accuracy63.8%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
accuracy36.6%
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
accuracy100.0%
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy99.8%
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
accuracy99.5%
(*.f64 #s(literal 2/3 binary64) x)
accuracy97.8%
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x)))
accuracy100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
accuracy99.8%
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))
accuracy99.7%
(*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))
accuracy52.4%
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))))
accuracy99.8%
(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
accuracy99.8%
(*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)
accuracy99.5%
(*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))
accuracy53.9%
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
Samples
396.0ms152×2valid
196.0ms85×1valid
52.0ms3valid
11.0ms14×0valid
Compiler

Compiled 1 803 to 117 computations (93.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 557.0ms
ival-mult: 141.0ms (25.3% of total)
adjust: 104.0ms (18.7% of total)
ival-add: 69.0ms (12.4% of total)
ival-cos: 53.0ms (9.5% of total)
ival-tan: 48.0ms (8.6% of total)
ival-div: 40.0ms (7.2% of total)
const: 34.0ms (6.1% of total)
ival-pow2: 24.0ms (4.3% of total)
ival-pow: 14.0ms (2.5% of total)
ival-sub: 11.0ms (2% of total)
ival-sin: 11.0ms (2% of total)
ival-neg: 6.0ms (1.1% of total)
exact: 1.0ms (0.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series386.0ms (2%)

Memory
21.5MiB live, 266.2MiB allocated
Counts
31 → 624
Calls
Call 1
Inputs
#<alt (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))>
#<alt (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))>
#<alt (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))>
#<alt (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))>
#<alt (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))>
#<alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))>
#<alt (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps)>
#<alt #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))))>
#<alt (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))>
#<alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))>
#<alt (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)>
#<alt (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))>
#<alt (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))>
#<alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))>
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#<alt (+.f64 x eps)>
#<alt (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))>
#<alt (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))>
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#<alt (tan.f64 x)>
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#<alt (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))>
#<alt (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)>
#<alt (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))>
#<alt #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x)))>
#<alt (*.f64 #s(literal 2/3 binary64) x)>
#<alt (pow.f64 (tan.f64 x) #s(literal 2 binary64))>
#<alt (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))>
#<alt (fma.f64 eps (-.f64 eps x) (*.f64 x x))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (neg.f64 (tan.f64 eps))>
Outputs
#<alt (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))>
#<alt (* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))>
#<alt (* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 2/3 (* eps x)))>
#<alt (+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))>
#<alt (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 17/9 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 17/9 (* 124/45 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 17/9 (* (pow x 2) (+ 124/45 (* 2764/945 (pow x 2))))))))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))>
#<alt 1/3>
#<alt (+ 1/3 (* 4/3 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))>
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#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))>
#<alt (* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))>
#<alt (* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))>
#<alt (pow x 2)>
#<alt (+ (* -1 (* eps x)) (pow x 2))>
#<alt (+ (* eps (+ eps (* -1 x))) (pow x 2))>
#<alt (+ (* eps (+ eps (* -1 x))) (pow x 2))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ x eps))))>
#<alt (* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))>
#<alt (* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))>
#<alt (pow eps 2)>
#<alt (+ (* -1 (* eps x)) (pow eps 2))>
#<alt (+ (* x (+ x (* -1 eps))) (pow eps 2))>
#<alt (+ (* x (+ x (* -1 eps))) (pow eps 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -1 eps)>
#<alt (* eps (- (* -1/3 (pow eps 2)) 1))>
#<alt (* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))>
#<alt (* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
#<alt (* -1 (/ (sin eps) (cos eps)))>
Calls

156 calls:

TimeVariablePointExpression
47.0ms
x
@-inf
(+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
41.0ms
x
@inf
(+ (* (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (pow (tan x) 2)) eps) eps)
33.0ms
x
@inf
(- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))
17.0ms
x
@inf
(+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
10.0ms
eps
@-inf
(+ (* (/ 1 (cos (+ x eps))) (sin (/ (+ (* eps (* eps eps)) (* x (* x x))) (+ (* eps (- eps x)) (* x x))))) (neg (tan x)))

simplify720.0ms (3.7%)

Memory
-13.9MiB live, 492.0MiB allocated
Algorithm
egg-herbie
Rules
8 922×lower-fma.f64
8 922×lower-fma.f32
6 972×lower-+.f64
6 972×lower-+.f32
5 086×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097125990
1326525599
0824924453
Stop Event
iter limit
node limit
Counts
624 → 610
Calls
Call 1
Inputs
(- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
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1/3
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* eps x)
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* 2/3 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (- (* -2/3 x) (* 1/3 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))
(* x (+ eps (* 2/3 (pow eps 3))))
(* x (+ eps (+ (* 1/3 (/ (pow eps 2) x)) (* 2/3 (pow eps 3)))))
(* x (+ eps (+ (* 1/3 (/ (pow eps 2) x)) (* 2/3 (pow eps 3)))))
(* x (+ eps (+ (* 1/3 (/ (pow eps 2) x)) (* 2/3 (pow eps 3)))))
(* x (+ eps (* 2/3 (pow eps 3))))
(* -1 (* x (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1/3 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1/3 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1/3 (/ (pow eps 2) x)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
x
(+ x (* 1/3 eps))
(+ x (* eps (+ 1/3 (* 2/3 (* eps x)))))
(+ x (* eps (+ 1/3 (* 2/3 (* eps x)))))
(* 2/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))
(* (pow eps 2) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* 2/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/3) eps)) (* 2/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/3) eps)) (* 2/3 x)))
(* 1/3 eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(* x (+ 1 (* 2/3 (pow eps 2))))
(* x (+ 1 (+ (* 1/3 (/ eps x)) (* 2/3 (pow eps 2)))))
(* x (+ 1 (+ (* 1/3 (/ eps x)) (* 2/3 (pow eps 2)))))
(* x (+ 1 (+ (* 1/3 (/ eps x)) (* 2/3 (pow eps 2)))))
(* -1 (* x (- (* -2/3 (pow eps 2)) 1)))
(* -1 (* x (- (+ (* -2/3 (pow eps 2)) (* -1/3 (/ eps x))) 1)))
(* -1 (* x (- (+ (* -2/3 (pow eps 2)) (* -1/3 (/ eps x))) 1)))
(* -1 (* x (- (+ (* -2/3 (pow eps 2)) (* -1/3 (/ eps x))) 1)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(* 1/3 (pow eps 2))
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(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ (* eps (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* 1/3 eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
(* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
(pow x 2)
(+ (* -1 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
Outputs
(- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) #s(literal 1/3 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) #s(literal 1/3 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) #s(literal 1/3 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))))
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 eps (+.f64 (fma.f64 (sin.f64 x) (/.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) eps)) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))))
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
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1/3
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (* 2 x)))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (/ (* (+ 1/2 (* -1/2 (cos (neg (* -2 x))))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(fma.f64 eps (+.f64 (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
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(* 2/3 x)
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(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(*.f64 eps (+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
(*.f64 eps (fma.f64 x (/.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps)
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps)
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (-.f64 (/.f64 (fma.f64 x (/.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64)) eps) x) eps) eps)
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
(*.f64 x (+.f64 (/.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 eps x))))
(* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 eps x))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x)
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 (-.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 0 binary64) x) #s(literal 0 binary64)) x) eps) x) x)
(pow x 2)
(*.f64 x x)
(+ (* -1 (* eps x)) (pow x 2))
(*.f64 x (-.f64 x eps))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(fma.f64 x (-.f64 x eps) (*.f64 eps eps))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(fma.f64 x (-.f64 x eps) (*.f64 eps eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) eps)))
(pow eps 2)
(*.f64 eps eps)
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(fma.f64 x (-.f64 x eps) (*.f64 eps eps))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(fma.f64 x (-.f64 x eps) (*.f64 eps eps))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 eps x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (/.f64 (*.f64 eps eps) x)) x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (/.f64 (*.f64 eps eps) x)) x)))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(* -1 eps)
(neg.f64 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(*.f64 eps (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -2/15 binary64) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -17/315 binary64) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))

rewrite506.0ms (2.6%)

Memory
40.6MiB live, 1 023.9MiB allocated
Algorithm
batch-egg-rewrite
Rules
7 156×lower-fma.f32
7 120×lower-fma.f64
5 392×lower-*.f32
5 372×lower-*.f64
3 548×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01041682
01821604
18901190
086421128
Stop Event
iter limit
node limit
iter limit
Counts
31 → 643
Calls
Call 1
Inputs
(fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
(fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))
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(fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps)
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps))))
(fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))
(*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)
(*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))
#s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x)))
(*.f64 #s(literal 2/3 binary64) x)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(fma.f64 eps (-.f64 eps x) (*.f64 x x))
(*.f64 x (*.f64 x x))
(neg.f64 (tan.f64 eps))
Outputs
(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64) (*.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))))))
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(+.f64 (*.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))))
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(+.f64 (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (tan.f64 x) eps)) (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))) eps) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))))
(+.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))
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(*.f64 (exp.f64 (log.f64 (tan.f64 x))) (exp.f64 (log.f64 (tan.f64 x))))
(*.f64 (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))) (neg.f64 (sin.f64 x)))
(*.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64)) (tan.f64 x))
(+.f64 eps x)
(+.f64 x eps)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(neg.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))))
(/.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 eps eps (*.f64 x (+.f64 eps x))) (-.f64 eps x))) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 eps eps (*.f64 x (+.f64 eps x))) (-.f64 eps x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))))
(/.f64 (*.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 eps eps (*.f64 x (+.f64 eps x))) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (*.f64 (fma.f64 eps eps (*.f64 x (+.f64 eps x))) (-.f64 eps x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(*.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))
(*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))
(+.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x))
(-.f64 (/.f64 (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))))
(-.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 x eps))
(fma.f64 eps (-.f64 eps x) (*.f64 x x))
(fma.f64 x x (*.f64 eps (-.f64 eps x)))
(fma.f64 (-.f64 eps x) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 eps (-.f64 eps x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x)) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x)))))
(/.f64 (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(/.f64 (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))))
(/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (-.f64 (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (*.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))))
(*.f64 (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 (neg.f64 x) x))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(+.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 eps)))
(-.f64 #s(literal 0 binary64) (tan.f64 eps))
(neg.f64 (tan.f64 eps))
(/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps)))
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (tan.f64 eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (tan.f64 eps)))
(/.f64 (*.f64 #s(literal -1 binary64) (sin.f64 eps)) (cos.f64 eps))
(*.f64 #s(literal -1 binary64) (tan.f64 eps))

eval455.0ms (2.4%)

Memory
-10.3MiB live, 828.4MiB allocated
Compiler

Compiled 158 496 to 7 612 computations (95.2% saved)

prune418.0ms (2.2%)

Memory
-22.9MiB live, 659.1MiB allocated
Pruning

20 alts after pruning (17 fresh and 3 done)

PrunedKeptTotal
New2 027162 043
Fresh10111
Picked415
Done224
Total2 043202 063
Accuracy
100.0%
Counts
2 063 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
63.8%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) #s(approx (neg (tan eps)) (*.f64 eps (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))) #s(literal 1 binary64))) (tan.f64 x))
63.6%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (*.f64 #s(literal 1/3 binary64) eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (fma.f64 #s(literal 1/3 binary64) eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (*.f64 x (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* (tan x) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (* (* (+ (pow (tan x) 2) 1) (sin x)) (/ 1/3 (cos x))))) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) (*.f64 eps #s(literal 2/3 binary64))) #s(literal 1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* (tan x) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (* (* (+ (pow (tan x) 2) 1) (sin x)) (/ 1/3 (cos x))))) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
97.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
51.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps)))))
Compiler

Compiled 2 668 to 644 computations (75.9% saved)

regimes50.0ms (0.3%)

Memory
34.2MiB live, 71.9MiB allocated
Counts
59 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (-.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (/.f64 (*.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (cos.f64 x))) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps))
Calls

3 calls:

16.0ms
eps
14.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes49.0ms (0.3%)

Memory
-20.9MiB live, 63.5MiB allocated
Counts
53 → 1
Calls
Call 1
Inputs
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(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* (tan x) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (* (* (+ (pow (tan x) 2) 1) (sin x)) (/ 1/3 (cos x))))) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) (*.f64 eps #s(literal 2/3 binary64))) #s(literal 1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
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Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
Calls

3 calls:

18.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
x
13.0ms
eps
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.2%)

Memory
-2.0MiB live, 73.7MiB allocated
Counts
52 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
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Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* (tan x) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (* (* (+ (pow (tan x) 2) 1) (sin x)) (/ 1/3 (cos x))))) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
Calls

3 calls:

15.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms
eps
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes40.0ms (0.2%)

Memory
15.1MiB live, 56.3MiB allocated
Counts
44 → 1
Calls
Call 1
Inputs
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(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
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Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
Calls

3 calls:

14.0ms
eps
11.0ms
x
11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.2%)

Memory
-19.4MiB live, 57.9MiB allocated
Counts
43 → 1
Calls
Call 1
Inputs
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(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
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(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
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#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (*.f64 (/.f64 (+.f64 eps x) (-.f64 x eps)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 eps x))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))))) eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 eps (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 2/3 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))))) eps))
Calls

3 calls:

12.0ms
x
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
eps
Results
AccuracySegmentsBranch
99.4%1x
99.4%1eps
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.1%)

Memory
32.3MiB live, 32.3MiB allocated
Counts
31 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (*.f64 #s(literal 1/3 binary64) eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (fma.f64 #s(literal 1/3 binary64) eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (tan.f64 #s(approx (* (/ 1 (- x eps)) (* (+ x eps) (- x eps))) (fma.f64 eps (/.f64 x eps) eps))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (*.f64 x (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (*.f64 (/.f64 (+.f64 eps x) (-.f64 x eps)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 eps x))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps #s(literal 4/3 binary64))) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) (*.f64 #s(literal 1/3 binary64) eps))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) (neg.f64 (tan.f64 x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (fma.f64 #s(literal 1/3 binary64) eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
Calls

3 calls:

8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms
x
8.0ms
eps
Results
AccuracySegmentsBranch
99.4%1x
99.4%1eps
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory
-20.6MiB live, 17.6MiB allocated
Counts
18 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64))) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (*.f64 #s(literal 1/3 binary64) eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (*.f64 #s(literal 1/3 binary64) eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
Calls

3 calls:

24.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
99.3%1x
99.3%1eps
99.3%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory
16.9MiB live, 16.9MiB allocated
Counts
17 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
Calls

3 calls:

5.0ms
eps
5.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
x
Results
AccuracySegmentsBranch
99.0%1eps
99.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.0%1x
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory
-22.8MiB live, 18.2MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
Calls

3 calls:

8.0ms
eps
4.0ms
x
4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.0%1x
99.0%1eps
99.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
19.8MiB live, 19.8MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (neg.f64 eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64))) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64))) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
Calls

3 calls:

3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory
-22.6MiB live, 15.4MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
Calls

3 calls:

4.0ms
eps
3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
98.8%1eps
98.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.8%1x
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0%)

Memory
14.5MiB live, 14.5MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) eps)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
98.6%1x
98.6%1eps
98.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory
12.4MiB live, 12.4MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) eps)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
97.9%1x
97.9%1eps
97.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory
8.9MiB live, 8.9MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
Calls

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
97.9%1eps
97.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.9%1x
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify23.0ms (0.1%)

Memory
-4.6MiB live, 34.0MiB allocated
Algorithm
egg-herbie
Rules
38×*-commutative_binary64
10×+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01962275
12222275
22272275
32302275
42312275
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (tan.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/3 binary64)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* (tan x) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (* (* (+ (pow (tan x) 2) 1) (sin x)) (/ 1/3 (cos x))))) (- (/ (* (+ (pow (tan x) 2) 1) (+ (* (cos (+ x x)) -1/2) 1/2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) #s(approx (+ (* eps 1/3) (+ (* (* eps eps) (* 2/3 x)) x)) (fma.f64 #s(literal 1/3 binary64) eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (*.f64 #s(literal 1/3 binary64) eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) (pow.f64 #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))
Outputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 x #s(literal 2/3 binary64)) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 x #s(literal 2/3 binary64)) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 x #s(literal 2/3 binary64)) x))) #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 2/3 binary64) x) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (*.f64 x #s(literal 2/3 binary64)) x))) #s(approx (pow (tan x) 2) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))) (/ (sin x) (cos x))))) (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (* 2/3 (* eps eps))) eps))) (*.f64 x eps))) eps))

soundness1.6s (8.2%)

Memory
1.3MiB live, 948.5MiB allocated
Rules
14 592×lower-fma.f64
14 592×lower-fma.f32
10 618×lower-fma.f64
10 618×lower-fma.f32
10 234×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058653
0114623
1522425
25165425
08203402
01571351
14641285
215341274
359491242
085341195
070826056
1242424772
0823123313
078513713
1250213423
0824212892
097125990
1326525599
0824924453
01041682
01821604
18901190
086421128
0991653
01631642
17901073
085301070
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 800 to 299 computations (62.6% saved)

preprocess164.0ms (0.8%)

Memory
6.6MiB live, 171.0MiB allocated
Compiler

Compiled 1 082 to 262 computations (75.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...