2tan (problem 3.3.2)

Time bar (total: 12.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze315.0ms (2.6%)

Memory
-12.0MiB live, 62.7MiB 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)

sample6.3s (52.8%)

Memory
102.2MiB live, 6 839.7MiB allocated
Samples
3.6s26 232×0invalid
650.0ms5 481×0valid
538.0ms2 775×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.3s
const: 803.0ms (24.3% of total)
ival-tan: 714.0ms (21.6% of total)
ival-add: 383.0ms (11.6% of total)
ival-<=: 318.0ms (9.6% of total)
ival-<: 236.0ms (7.1% of total)
ival-mult: 222.0ms (6.7% of total)
ival-fabs: 208.0ms (6.3% of total)
ival-sub: 189.0ms (5.7% of total)
ival-and: 105.0ms (3.2% of total)
adjust: 76.0ms (2.3% of total)
exact: 40.0ms (1.2% of total)
ival-assert: 11.0ms (0.3% of total)
Bogosity

explain102.0ms (0.8%)

Memory
37.6MiB live, 76.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2231(-1.1250245095404491e-234 9.388785750458769e-237)2(-5.91046744799245e-23 8.546941406357813e-25)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
30-0-(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))cancellation2226
tan.f64(tan.f64 (+.f64 x eps))sensitivity30
Confusion
Predicted +Predicted -
+2223
-130
Precision
0.9955156950672646
Recall
0.9866666666666667
Confusion?
Predicted +Predicted MaybePredicted -
+22221
-1426
Precision?
0.9781659388646288
Recall?
0.9955555555555555
Freqs
test
numberfreq
033
1221
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
37.0ms308×0valid
20.0ms204×1valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
ival-sub: 25.0ms (59.4% of total)
ival-tan: 9.0ms (21.4% of total)
adjust: 4.0ms (9.5% of total)
ival-add: 3.0ms (7.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess63.0ms (0.5%)

Memory
-28.5MiB live, 16.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13835
28635
316935
431235
538335
646935
750935
852135
067
0107
1137
2187
3247
4327
5477
6807
71107
81597
91757
101837
01837
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))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory
3.9MiB live, 3.9MiB 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))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11318
21818
32418
43218
54718
68018
711018
815918
917518
1018318
018318
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))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(tan.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(tan.f64 x)

localize22.0ms (0.2%)

Memory
19.2MiB live, 19.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(tan.f64 x)
accuracy0.12667603662424365
(tan.f64 (+.f64 x eps))
accuracy25.6243997000046
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Samples
10.0ms102×1valid
7.0ms154×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-tan: 4.0ms (41.2% of total)
adjust: 2.0ms (20.6% of total)
ival-add: 2.0ms (20.6% of total)
ival-sub: 1.0ms (10.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory
-28.1MiB live, 9.9MiB allocated
Counts
4 → 31
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
(/ (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)))
(+ (* 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)))
eps
(+ eps x)
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 (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ 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))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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)))))
(+ (* 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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
x
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms
eps
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms
x
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms
eps
@inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms
eps
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify173.0ms (1.4%)

Memory
28.5MiB live, 102.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157950
1464884
21539873
36077710
08335686
Stop Event
iter limit
node limit
Counts
31 → 29
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)))
(+ (* 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)))
eps
(+ eps x)
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 (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ 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))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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)))))
(+ (* 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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.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 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.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 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.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 (+.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64))) #s(literal 1/2 binary64))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps)) #s(literal 1 binary64))) x (/.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 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.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 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/3 binary64))) x) x (*.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps)) #s(literal 1 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) 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)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(/ (sin x) (cos 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))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* 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)))))
(*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 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)))))
(*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 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)))))
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 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)))
(fma.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps (/.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 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ x eps)))
(+.f64 eps 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))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite255.0ms (2.1%)

Memory
-15.0MiB live, 100.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15016
240216
3613716
0816616
Stop Event
iter limit
node limit
iter limit
Counts
4 → 255
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
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #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 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))))
(*.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))))
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal -1 binary64))
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
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(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sin.f64 (+.f64 eps x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 1 binary64))
(/.f64 (+.f64 (tan.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (tan.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (tan.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #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 (neg.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (+.f64 eps x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 eps x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #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))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))))
(/.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #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 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (neg.f64 (cos.f64 (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(neg.f64 (tan.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps))))
(neg.f64 (tan.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(neg.f64 (tan.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))))
(neg.f64 (tan.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (cos.f64 (+.f64 eps x))))
(neg.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 (+.f64 eps x)))))
(tan.f64 (+.f64 eps x))
(exp.f64 (*.f64 (log.f64 (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 (+.f64 eps x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 x (/.f64 x (-.f64 x eps)))) (*.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 x (/.f64 x (-.f64 x eps))) (fma.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.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 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(neg.f64 (neg.f64 (tan.f64 x)))
(tan.f64 x)
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))

eval96.0ms (0.8%)

Memory
2.5MiB live, 39.9MiB allocated
Compiler

Compiled 7 565 to 1 005 computations (86.7% saved)

prune17.0ms (0.1%)

Memory
26.1MiB live, 26.1MiB allocated
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New25818276
Fresh000
Picked011
Done000
Total25819277
Accuracy
100.0%
Counts
277 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
24.0%
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))))
59.7%
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
60.0%
(fma.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) (neg.f64 (tan.f64 x)))
59.7%
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x)))
60.0%
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
59.9%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
34.7%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
59.8%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
60.0%
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
59.2%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
59.7%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.1%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))))
98.6%
#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))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps))
Compiler

Compiled 1 099 to 548 computations (50.1% saved)

simplify311.0ms (2.6%)

Memory
-14.7MiB live, 186.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff0
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
cost-diff2
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
cost-diff9
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
cost-diff2
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff14
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
cost-diff0
(+.f64 eps x)
cost-diff0
(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff0
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff4
(-.f64 (+.f64 eps x) x)
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 eps)
cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 eps))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
cost-diff1
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
cost-diff1
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
cost-diff3
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
cost-diff4
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0631207
01211183
12301181
25751156
320491117
087741097
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)
(fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps)
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
(sin.f64 x)
x
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal -1/3 binary64)
(/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 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 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
eps
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
x
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(cos.f64 x)
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
(sin.f64 x)
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (+.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (sin.f64 x) (cos.f64 x))) eps)) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)))) eps))
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)
(*.f64 (fma.f64 (*.f64 eps eps) (+.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (sin.f64 x) (cos.f64 x))) eps)) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)))) eps)
(fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))))
(fma.f64 (*.f64 eps eps) (+.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (sin.f64 x) (cos.f64 x))) eps)) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps)
(*.f64 (+.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (sin.f64 x) (cos.f64 x))) eps)) eps)
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (sin.f64 x) (cos.f64 x))) eps))
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 #s(literal -1/3 binary64) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))) (fma.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(sin.f64 x)
x
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1/3 binary64) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal -1/3 binary64)
(/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 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 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
eps
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(sin.f64 eps)
(-.f64 (+.f64 eps x) x)
eps
(+.f64 eps x)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
x
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (tan.f64 (+.f64 eps x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(cos.f64 x)
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (sin.f64 x))
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
(sin.f64 x)
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (cos.f64 x))

localize238.0ms (2%)

Memory
17.5MiB live, 329.6MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.01953125
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
accuracy0.021816259768442016
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
accuracy0.02734375
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
accuracy25.611369453282492
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
accuracy0.1875
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy0.21875
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
accuracy26.181621164799637
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
accuracy28.317254210816326
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
accuracy0.015625
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy0.03125
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy0.10011884073013777
(cos.f64 (+.f64 eps x))
accuracy25.748357568802987
(-.f64 (+.f64 eps x) x)
accuracy0.0
(sin.f64 eps)
accuracy0.0
(cos.f64 eps)
accuracy0.00390625
(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy1.7367886639738366
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy0.037441259768442016
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy0.3046875
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps)
accuracy0.33203125
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
accuracy0.44856167886737885
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
Samples
106.0ms104×1valid
66.0ms151×0valid
2.0ms2valid
Compiler

Compiled 1 160 to 69 computations (94.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 136.0ms
ival-mult: 36.0ms (26.5% of total)
ival-div: 24.0ms (17.6% of total)
ival-add: 16.0ms (11.8% of total)
adjust: 14.0ms (10.3% of total)
ival-tan: 9.0ms (6.6% of total)
ival-sub: 7.0ms (5.1% of total)
ival-cos: 6.0ms (4.4% of total)
ival-neg: 6.0ms (4.4% of total)
const: 5.0ms (3.7% of total)
ival-pow: 5.0ms (3.7% of total)
ival-sin: 5.0ms (3.7% of total)
ival-pow2: 3.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series116.0ms (1%)

Memory
-1.2MiB live, 153.4MiB allocated
Counts
28 → 182
Calls
Call 1
Inputs
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
(+.f64 (tan.f64 eps) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 (+.f64 eps x))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
Outputs
-1/3
(- (* -2/3 (* eps x)) 1/3)
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3)
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3)
(* -2/3 x)
(* x (- (* -17/9 (pow x 2)) 2/3))
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
1
(+ 1 (* eps x))
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps))))))
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))
(/ (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)))
eps
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ eps x)
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos eps) (sin eps))
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(/ (cos eps) (* x (sin eps)))
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 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)))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x)
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x)
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x)
x
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6))))))
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))
(* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))
(+ 1 (/ (* eps (sin x)) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* x (+ 1 (/ eps x)))
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (cos x) (sin x))
(/ (cos (+ eps x)) (sin (+ eps x)))
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))))
(pow (cos x) 2)
(cos (+ eps x))
(* (cos x) (cos (+ eps x)))
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 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)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(/ (pow (cos x) 2) (pow (sin x) 2))
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (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)))
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))))
(* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))
(* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* eps (+ 1 (/ x eps)))
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))
(* -1 (* eps (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
(cos (- x (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
Calls

6 calls:

TimeVariablePointExpression
23.0ms
x
@-inf
((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (tan (+ x eps)) (tan x)) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
22.0ms
x
@inf
((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (tan (+ x eps)) (tan x)) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
20.0ms
eps
@0
((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (tan (+ x eps)) (tan x)) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
17.0ms
eps
@-inf
((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (tan (+ x eps)) (tan x)) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
16.0ms
x
@0
((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (tan (+ x eps)) (tan x)) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))

simplify192.0ms (1.6%)

Memory
-7.7MiB live, 222.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09638537
131447981
085077715
Stop Event
iter limit
node limit
Counts
182 → 180
Calls
Call 1
Inputs
-1/3
(- (* -2/3 (* eps x)) 1/3)
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3)
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3)
(* -2/3 x)
(* x (- (* -17/9 (pow x 2)) 2/3))
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
1
(+ 1 (* eps x))
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps))))))
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))
(/ (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)))
eps
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ eps x)
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos eps) (sin eps))
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(/ (cos eps) (* x (sin eps)))
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 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)))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x)
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x)
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x)
x
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6))))))
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))
(* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))
(+ 1 (/ (* eps (sin x)) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* x (+ 1 (/ eps x)))
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (cos x) (sin x))
(/ (cos (+ eps x)) (sin (+ eps x)))
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))))
(pow (cos x) 2)
(cos (+ eps x))
(* (cos x) (cos (+ eps x)))
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 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)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(/ (pow (cos x) 2) (pow (sin x) 2))
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (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)))
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))))
(* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))
(* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* eps (+ 1 (/ x eps)))
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))
(* -1 (* eps (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
(cos (- x (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
Outputs
-1/3
#s(literal -1/3 binary64)
(- (* -2/3 (* eps x)) 1/3)
(fma.f64 (*.f64 eps x) #s(literal -2/3 binary64) #s(literal -1/3 binary64))
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3)
(fma.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64))
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 eps x) #s(literal -4/3 binary64)) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64))
(* -2/3 x)
(*.f64 #s(literal -2/3 binary64) x)
(* x (- (* -17/9 (pow x 2)) 2/3))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -17/9 binary64) #s(literal -2/3 binary64)) x)
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))
(*.f64 (fma.f64 (fma.f64 #s(literal -124/45 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) x)
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2764/945 binary64) (*.f64 x x) #s(literal -124/45 binary64)) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/3 (* eps x)))
(fma.f64 #s(literal 2/3 binary64) (*.f64 eps x) #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* eps x))
(fma.f64 eps x #s(literal 1 binary64))
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 x x) eps) x #s(literal 1 binary64))
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) eps) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps))) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 binary64))
(/ (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 x (/.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 (* (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 (fma.f64 x (/.f64 (*.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)))) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.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 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.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)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) #s(literal 1/2 binary64))) (/.f64 (*.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)))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 #s(literal 2/3 binary64) (cos.f64 eps)) (/.f64 (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ eps x)
(+.f64 eps x)
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(*.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x)))))))
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64))) (*.f64 eps eps) (cos.f64 x)) eps (sin.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
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(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
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(cos x)
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(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
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(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
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(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
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(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
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(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))
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(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
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(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
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(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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)))) eps))))
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))
(*.f64 (neg.f64 eps) (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 3 binary64)))) (sin.f64 x) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) eps) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps)))
(- (/ (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 (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps)
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
(*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))))

rewrite184.0ms (1.5%)

Memory
21.3MiB live, 172.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063674
0121629
1527523
24769505
08218494
Stop Event
iter limit
node limit
iter limit
Counts
28 → 857
Calls
Call 1
Inputs
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
(+.f64 (tan.f64 eps) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 (+.f64 eps x))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
Outputs
(*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 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 2 binary64))) (pow.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (neg.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 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 binary64)))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (neg.f64 (tan.f64 (+.f64 eps x))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 eps x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (tan.f64 x) #s(literal -1 binary64))) (*.f64 (tan.f64 x) (neg.f64 (tan.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))) (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))
(fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
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(+.f64 (*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (*.f64 (sin.f64 x) #s(literal 1 binary64)))
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eval224.0ms (1.9%)

Memory
-15.2MiB live, 238.2MiB allocated
Compiler

Compiled 73 245 to 5 279 computations (92.8% saved)

prune31.0ms (0.3%)

Memory
-13.7MiB live, 64.4MiB allocated
Pruning

22 alts after pruning (20 fresh and 2 done)

PrunedKeptTotal
New96917986
Fresh10313
Picked415
Done011
Total983221 005
Accuracy
100.0%
Counts
1 005 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
99.8%
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
59.9%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
34.7%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
35.0%
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
99.5%
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
99.4%
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
60.0%
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
59.2%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
99.8%
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
98.5%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 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 (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
Compiler

Compiled 1 217 to 705 computations (42.1% saved)

simplify150.0ms (1.3%)

Memory
32.3MiB live, 110.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 eps)
cost-diff0
(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff0
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
cost-diff0
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
cost-diff0
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff0
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
cost-diff0
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
cost-diff0
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff0
(sin.f64 eps)
cost-diff0
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
cost-diff0
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
cost-diff2
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
cost-diff0
(sin.f64 eps)
cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 x))
cost-diff0
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
cost-diff0
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047255
072247
1107243
2165243
3413240
42125240
53430240
65705240
77792240
08080237
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
eps
(cos.f64 x)
x
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(sin.f64 eps)
eps
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
eps
(cos.f64 x)
x
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
#s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(sin.f64 eps)
eps
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(sin.f64 eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
(cos.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 eps)
eps
(tan.f64 x)
x
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)

localize113.0ms (0.9%)

Memory
5.3MiB live, 118.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
accuracy0.015625
(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy0.021816259768442016
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
accuracy25.6243997000046
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
accuracy0.0
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
accuracy0.0
(cos.f64 x)
accuracy0.03125
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy0.10011884073013777
(cos.f64 (+.f64 eps x))
accuracy0.0
(sin.f64 eps)
accuracy0.00390625
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy0.33152299922042383
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy1.7367886639738366
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
accuracy0.0
(*.f64 eps eps)
accuracy0.0078125
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
accuracy0.38405655789567417
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
accuracy1.7367886639738366
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
accuracy0.0
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
accuracy0.0078125
(/.f64 (sin.f64 eps) (cos.f64 x))
accuracy0.0234375
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
accuracy0.10011884073013777
(cos.f64 (+.f64 eps x))
Samples
46.0ms102×1valid
40.0ms153×0valid
1.0ms2valid
Compiler

Compiled 201 to 41 computations (79.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-div: 10.0ms (15.7% of total)
adjust: 9.0ms (14.1% of total)
ival-add: 9.0ms (14.1% of total)
ival-mult: 9.0ms (14.1% of total)
ival-tan: 8.0ms (12.5% of total)
ival-cos: 5.0ms (7.8% of total)
ival-sin: 5.0ms (7.8% of total)
ival-sub: 4.0ms (6.3% of total)
const: 4.0ms (6.3% of total)
ival-neg: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series52.0ms (0.4%)

Memory
2.5MiB live, 46.6MiB allocated
Counts
23 → 97
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(cos.f64 (+.f64 eps x))
(*.f64 eps eps)
(cos.f64 x)
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(+ (* 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)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (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 (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (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)))
(+ 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (+ eps x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(cos (+ eps x))
(cos x)
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 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)))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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)))
(+ 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)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(cos (- x (* -1 eps)))
Calls

6 calls:

TimeVariablePointExpression
20.0ms
eps
@0
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1))
9.0ms
x
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1))
6.0ms
eps
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1))
6.0ms
eps
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1))
5.0ms
x
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1))

simplify194.0ms (1.6%)

Memory
1.6MiB live, 154.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05232556
116302383
253662254
081622135
Stop Event
iter limit
node limit
Counts
97 → 96
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(+ (* 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)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (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 (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (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)))
(+ 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (+ eps x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(cos (+ eps x))
(cos x)
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 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)))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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)))
(+ 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)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(cos (- x (* -1 eps)))
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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (*.f64 (sin.f64 eps) (-.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(fma.f64 (neg.f64 (*.f64 (sin.f64 eps) (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 x x) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 x) x) (*.f64 (sin.f64 eps) #s(literal -61/720 binary64)) (*.f64 #s(literal 5/24 binary64) (sin.f64 eps))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.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 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.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 (fma.f64 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (*.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (-.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (*.f64 (sin.f64 eps) (/.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)) (neg.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)) (neg.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)))))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -4/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64))) (pow.f64 (cos.f64 eps) #s(literal 4 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
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eps
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(fma.f64 (*.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x)))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x)))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal -1/3 binary64) (fma.f64 (/.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 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (*.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/3 binary64)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(/ (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)))
(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 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)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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 (fma.f64 (fma.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ eps (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(pow eps 2)
(*.f64 eps eps)
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
(fma.f64 (neg.f64 eps) (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(fma.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64))) eps #s(literal 1 binary64))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(fma.f64 (neg.f64 eps) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 #s(literal -2/15 binary64) (*.f64 eps eps) #s(literal -1/3 binary64))) #s(literal 1 binary64)))
(* 1/3 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(* 1/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (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 (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))

rewrite420.0ms (3.5%)

Memory
-350.6MiB live, 152.3MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047213
072193
1293165
22500165
08201165
Stop Event
iter limit
node limit
iter limit
Counts
23 → 847
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(cos.f64 (+.f64 eps x))
(*.f64 eps eps)
(cos.f64 x)
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))) (sin.f64 eps))
(*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.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))) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)))
(*.f64 (sin.f64 eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))))
(pow.f64 (/.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.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)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (tan.f64 eps) (tan.f64 x)) (*.f64 (cos.f64 x) (*.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))))) (*.f64 (cos.f64 x) (-.f64 (tan.f64 eps) (tan.f64 x))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))))) (*.f64 (cos.f64 x) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (neg.f64 (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) (*.f64 (cos.f64 x) (neg.f64 (neg.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))))) (*.f64 (cos.f64 x) (neg.f64 (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 (+.f64 x eps))))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (*.f64 (-.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (*.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (*.f64 (cos.f64 x) (*.f64 (-.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))
(fma.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64)) (tan.f64 x))
(fma.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps) (tan.f64 x))
(fma.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (neg.f64 (cos.f64 eps)) #s(literal -1 binary64)) (tan.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 eps))
(fma.f64 #s(literal 1 binary64) (tan.f64 eps) (tan.f64 x))
(fma.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (tan.f64 x))
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(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (tan.f64 eps) (tan.f64 x))
(*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (neg.f64 (cos.f64 eps)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (tan.f64 eps))
(*.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(/.f64 (+.f64 (tan.f64 (neg.f64 x)) (tan.f64 (+.f64 x eps))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (neg.f64 x)) (tan.f64 (+.f64 x eps)))))
(/.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (neg.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (neg.f64 x)))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 (-.f64 eps x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 (-.f64 eps x)))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 eps))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (neg.f64 (cos.f64 eps))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal -1 binary64)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(neg.f64 (neg.f64 (tan.f64 eps)))
(tan.f64 eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (*.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps)))
(-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(-.f64 (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 (+.f64 #s(literal 0 binary64) x))) (*.f64 (sin.f64 eps) (sin.f64 (+.f64 #s(literal 0 binary64) x))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 (pow.f64 (*.f64 (+.f64 (+.f64 x eps) x) eps) #s(literal 2 binary64)) (pow.f64 (pow.f64 (+.f64 (+.f64 x eps) x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps (-.f64 eps #s(literal 0 binary64)))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) eps) (neg.f64 eps))
(/.f64 (*.f64 eps (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 eps (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 4 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 0 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps eps)))))
(/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 eps #s(literal 4 binary64)))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (*.f64 (+.f64 (+.f64 x eps) x) eps) #s(literal 2 binary64)) (pow.f64 (pow.f64 (+.f64 (+.f64 x eps) x) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 eps) (neg.f64 eps) #s(literal 0 binary64))
(fma.f64 eps (-.f64 eps #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 eps eps #s(literal 0 binary64))
(-.f64 (*.f64 eps eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(*.f64 (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))))
(fma.f64 (*.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 eps) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 (tan.f64 eps)) (*.f64 (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(fma.f64 (tan.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64))
(fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(+.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)))

eval93.0ms (0.8%)

Memory
19.7MiB live, 131.7MiB allocated
Compiler

Compiled 24 350 to 3 263 computations (86.6% saved)

prune37.0ms (0.3%)

Memory
-6.8MiB live, 72.2MiB allocated
Pruning

29 alts after pruning (24 fresh and 5 done)

PrunedKeptTotal
New74317760
Fresh8715
Picked145
Done112
Total75329782
Accuracy
100.0%
Counts
782 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
35.0%
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
90.9%
(/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
99.8%
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
99.6%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x))
34.7%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
99.8%
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x))
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
60.0%
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
100.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
100.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
99.3%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)))))
98.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
99.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
98.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
98.5%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
32.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
6.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
Compiler

Compiled 1 308 to 861 computations (34.2% saved)

simplify124.0ms (1%)

Memory
-5.2MiB live, 114.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
cost-diff2
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff14
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
cost-diff0
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff0
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
cost-diff1
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
cost-diff1
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))))
cost-diff2
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
cost-diff0
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)
cost-diff0
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
cost-diff0
(sin.f64 eps)
cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 x))
cost-diff0
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
cost-diff0
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063431
097419
1169411
2283400
3561393
41836387
55863387
08380373
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
eps
(cos.f64 x)
x
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(cos.f64 eps)
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
(neg.f64 (sin.f64 eps))
(sin.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
#s(literal 1/9 binary64)
(pow.f64 eps #s(literal 4 binary64))
eps
#s(literal 4 binary64)
(-.f64 #s(literal 1 binary64) (*.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 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
x
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (/.f64 (sin.f64 eps) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
eps
(cos.f64 x)
x
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(cos.f64 eps)
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
(*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))
(neg.f64 (sin.f64 eps))
(sin.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (/ (sin eps) (cos eps)) (/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))))
(fma.f64 #s(literal -1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64))
#s(literal 1/9 binary64)
(pow.f64 eps #s(literal 4 binary64))
eps
#s(literal 4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
(cos.f64 x)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
x
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))
(tan.f64 (+.f64 eps x))
(tan.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
eps
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))

localize197.0ms (1.6%)

Memory
-9.1MiB live, 227.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.1328125
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
accuracy0.21875
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
accuracy26.181621164799637
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
accuracy28.317254210816326
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
accuracy0.0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy0.015625
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy0.03125
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy0.10011884073013777
(cos.f64 (+.f64 eps x))
accuracy0.0859375
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
accuracy0.2109375
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
accuracy0.38405655789567417
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
accuracy1.7367886639738366
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
accuracy0.2109375
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
accuracy0.38405655789567417
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
accuracy1.7367886639738366
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
accuracy61.2632633060152
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
accuracy0.00390625
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
accuracy0.00390625
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
accuracy0.0078125
(/.f64 (sin.f64 eps) (cos.f64 x))
accuracy0.0234375
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
Samples
82.0ms102×1valid
66.0ms154×0valid
Compiler

Compiled 319 to 49 computations (84.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 96.0ms
ival-div: 25.0ms (26.2% of total)
ival-mult: 18.0ms (18.8% of total)
adjust: 9.0ms (9.4% of total)
ival-sub: 9.0ms (9.4% of total)
ival-tan: 7.0ms (7.3% of total)
ival-cos: 6.0ms (6.3% of total)
const: 6.0ms (6.3% of total)
ival-add: 6.0ms (6.3% of total)
ival-sin: 5.0ms (5.2% of total)
ival-pow: 3.0ms (3.1% of total)
ival-neg: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series39.0ms (0.3%)

Memory
16.3MiB live, 53.6MiB allocated
Counts
28 → 129
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
(cos.f64 (+.f64 eps x))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(+ (* 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos eps) (sin eps))
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x)
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x)
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x)
(* -1 (* x (sin eps)))
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps)))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps))))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps)))))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(/ (cos eps) (* x (sin eps)))
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin eps) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (cos x) (cos (+ eps x)))
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (cos x) (sin x))
(/ (cos (+ eps x)) (sin (+ eps x)))
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))
(* -1 (* (sin eps) (sin x)))
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))
(cos (+ eps x))
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* (cos x) (cos (- eps (* -1 x))))
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* 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)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
1
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* -1/9 (pow eps 4)))
(+ 1 (* -1/3 (pow eps 2)))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x))))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x)))))))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
(* 1/3 (pow eps 2))
(* 1/9 (pow eps 4))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(/ (pow (cos x) 2) (pow (sin x) 2))
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(* -1/9 (pow eps 4))
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9))
(* -1/3 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
(cos (- x (* -1 eps)))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
eps
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x))))
7.0ms
eps
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x))))
5.0ms
x
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x))))
5.0ms
x
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x))))
4.0ms
eps
@0
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x))))

simplify215.0ms (1.8%)

Memory
6.1MiB live, 210.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07076465
123115981
084065816
Stop Event
iter limit
node limit
Counts
129 → 128
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(+ (* 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos eps) (sin eps))
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x)
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x)
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x)
(* -1 (* x (sin eps)))
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps)))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps))))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps)))))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(/ (cos eps) (* x (sin eps)))
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x)
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin eps) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (cos x) (cos (+ eps x)))
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (cos x) (sin x))
(/ (cos (+ eps x)) (sin (+ eps x)))
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))
(* -1 (* (sin eps) (sin x)))
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))
(cos (+ eps x))
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* (cos x) (cos (- eps (* -1 x))))
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* 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)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
1
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* -1/9 (pow eps 4)))
(+ 1 (* -1/3 (pow eps 2)))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x))))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x)))))))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
(* 1/3 (pow eps 2))
(* 1/9 (pow eps 4))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(/ (pow (cos x) 2) (pow (sin x) 2))
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(* -1/9 (pow eps 4))
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9))
(* -1/3 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
(cos (- x (* -1 eps)))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
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 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 #s(literal 2/3 binary64) (cos.f64 eps)) (/.f64 (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal 5/24 binary64)) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
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(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) (*.f64 eps eps) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal 1/5040 binary64) (*.f64 eps eps) #s(literal -1/120 binary64))) (*.f64 eps eps) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps) (neg.f64 (sin.f64 x))) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(* 1/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
(* 1/9 (pow eps 4))
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(/ (pow (cos x) 2) (pow (sin x) 2))
(/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(fma.f64 (neg.f64 eps) (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(fma.f64 (neg.f64 (fma.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.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)))) #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))) (/.f64 (*.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 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)))) (cos.f64 x))) (sin.f64 x))) eps (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (*.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)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(* 1/3 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(* -1/9 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/9 binary64))
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/9 binary64)) (pow.f64 eps #s(literal 4 binary64)))
(* -1/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/3 binary64))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3))
(fma.f64 (*.f64 eps eps) #s(literal -1/3 binary64) #s(literal 1 binary64))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(- (/ (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 (neg (* -1 eps)))
(sin.f64 eps)
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps))))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps))))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps)))))
(*.f64 (/.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x)))

rewrite181.0ms (1.5%)

Memory
10.1MiB live, 202.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063357
097340
1372275
22827273
08825264
Stop Event
iter limit
node limit
iter limit
Counts
28 → 465
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))
(cos.f64 (+.f64 eps x))
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x)))) (cos.f64 (-.f64 eps x)))
(*.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 x)))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)))
(*.f64 (sin.f64 eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))))
(pow.f64 (/.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 eps) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) (cos.f64 x))
(/.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps)))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)))
(/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(neg.f64 (/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 eps))
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eval93.0ms (0.8%)

Memory
-1.0MiB live, 167.5MiB allocated
Compiler

Compiled 21 174 to 2 358 computations (88.9% saved)

prune71.0ms (0.6%)

Memory
-13.8MiB live, 62.1MiB allocated
Pruning

30 alts after pruning (24 fresh and 6 done)

PrunedKeptTotal
New5148522
Fresh31619
Picked415
Done055
Total52130551
Accuracy
100.0%
Counts
551 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
35.0%
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
90.9%
(/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
99.8%
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
99.6%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x))
34.7%
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
99.8%
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x))
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
60.0%
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
59.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))))
99.3%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
98.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
99.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
98.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
98.5%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
100.0%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
97.3%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
32.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
97.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
Compiler

Compiled 2 588 to 895 computations (65.4% saved)

regimes54.0ms (0.5%)

Memory
4.3MiB live, 84.2MiB allocated
Counts
61 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x))
#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))
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) (neg.f64 (tan.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))))
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.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 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 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 (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
Calls

3 calls:

19.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms
x
14.0ms
eps
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.3%)

Memory
13.4MiB live, 52.0MiB allocated
Counts
49 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x))
#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))
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) (neg.f64 (tan.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
Calls

3 calls:

13.0ms
eps
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.3%)

Memory
6.9MiB live, 45.8MiB allocated
Counts
47 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x))
#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))
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) (neg.f64 (tan.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
Calls

3 calls:

12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
eps
11.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory
-21.9MiB live, 27.1MiB allocated
Counts
25 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
Calls

3 calls:

8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory
-16.2MiB live, 22.5MiB allocated
Counts
22 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
Calls

3 calls:

8.0ms
x
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
99.0%1x
99.0%1eps
99.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory
19.3MiB live, 19.3MiB allocated
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
Calls

3 calls:

5.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory
-19.8MiB live, 19.3MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
Calls

3 calls:

4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
97.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
6.5MiB live, 6.5MiB allocated
Accuracy

Total -58.3b remaining (-3447%)

Threshold costs -58.3b (-3447%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
Calls

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
97.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify84.0ms (0.7%)

Memory
11.8MiB live, 50.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068223
199210
2139198
3226198
4638198
54464198
67913198
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps)))

soundness899.0ms (7.5%)

Memory
-15.9MiB live, 622.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157950
1464884
21539873
36077710
08335686
05232556
116302383
253662254
081622135
047213
072193
1293165
22500165
08201165
0616
01016
15016
240216
3613716
0816616
07076465
123115981
084065816
09638537
131447981
085077715
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 482 to 259 computations (46.3% saved)

preprocess121.0ms (1%)

Memory
26.7MiB live, 145.7MiB allocated
Compiler

Compiled 478 to 164 computations (65.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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