2tan (problem 3.3.2)

Time bar (total: 16.3s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze43.0ms (0.3%)

Memory
8.3MiB live, 54.1MiB 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)

sample8.5s (51.9%)

Memory
142.5MiB live, 7 494.9MiB allocated
Samples
4.2s26 142×0invalid
1.2s2 806×1valid
940.0ms5 450×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.8s
ival-tan: 1.1s (22.3% of total)
const: 954.0ms (19.8% of total)
ival-add: 936.0ms (19.4% of total)
ival-<=: 531.0ms (11% of total)
ival-mult: 387.0ms (8% of total)
ival-<: 271.0ms (5.6% of total)
ival-fabs: 220.0ms (4.6% of total)
ival-sub: 197.0ms (4.1% of total)
ival-and: 109.0ms (2.3% of total)
adjust: 78.0ms (1.6% of total)
exact: 49.0ms (1% of total)
ival-assert: 12.0ms (0.2% of total)
Bogosity

explain117.0ms (0.7%)

Memory
-0.6MiB live, 125.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2303(-2.0889617513847496e-164 1.3356537702641282e-166)3(9.631292575085681e-45 1.0816492021419804e-46)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10-0-(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))cancellation2306
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+2273
-323
Precision
0.9869565217391304
Recall
0.9869565217391304
Confusion?
Predicted +Predicted MaybePredicted -
+22730
-3320
Precision?
0.9745762711864406
Recall?
1.0
Freqs
test
numberfreq
026
1229
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
49.0ms192×1valid
16.0ms318×0valid
3.0ms2valid
Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-tan: 34.0ms (65.9% of total)
ival-add: 9.0ms (17.5% of total)
adjust: 4.0ms (7.8% of total)
ival-sub: 3.0ms (5.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess47.0ms (0.3%)

Memory
-17.5MiB live, 19.6MiB 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
0.7MiB live, 0.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory
6.3MiB live, 6.3MiB 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)

localize49.0ms (0.3%)

Memory
-0.4MiB live, 36.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(tan.f64 x)
accuracy0.059303802495346905
(tan.f64 (+.f64 x eps))
accuracy25.002841220992565
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Samples
32.0ms159×0valid
10.0ms96×1valid
1.0ms2valid
Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-tan: 6.0ms (54% of total)
adjust: 2.0ms (18% of total)
ival-add: 2.0ms (18% of total)
ival-sub: 2.0ms (18% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory
-17.0MiB live, 24.4MiB 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
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
x
@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))

simplify182.0ms (1.1%)

Memory
34.0MiB live, 228.4MiB 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)

rewrite169.0ms (1%)

Memory
9.4MiB live, 201.5MiB 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)))
(/.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64)) (cos.f64 (+.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))))
(/.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)))

eval122.0ms (0.7%)

Memory
-34.3MiB live, 80.5MiB allocated
Compiler

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

prune25.0ms (0.2%)

Memory
-21.0MiB live, 56.5MiB allocated
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New25521276
Fresh000
Picked011
Done000
Total25522277
Accuracy
100.0%
Counts
277 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
60.8%
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
60.8%
(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)))
60.9%
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
59.8%
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)))
59.9%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
60.9%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
60.9%
(-.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))
60.8%
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
60.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
59.9%
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
60.2%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
60.9%
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
99.2%
#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))))
99.2%
#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))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
99.9%
#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))
100.0%
#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))
99.7%
#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 1 187 to 612 computations (48.4% saved)

simplify195.0ms (1.2%)

Memory
24.5MiB live, 138.1MiB 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)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
cost-diff0
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
cost-diff0
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
cost-diff0
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff0
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
cost-diff0
#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))
cost-diff0
(+.f64 eps x)
cost-diff0
(sin.f64 (+.f64 eps x))
cost-diff0
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
cost-diff0
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 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
(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-diff1
(*.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)
cost-diff14
(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-diff15
(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)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0581147
01111147
11941147
24671147
316311110
46301936
08240915
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 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(cos.f64 (+.f64 eps x))
(tan.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))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
eps
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 (tan.f64 eps) (tan.f64 x))
#s(literal 2 binary64)
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (tan.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)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)))))
(*.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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))))
(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) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #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 (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 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 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 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 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))))))
(fma.f64 (*.f64 #s(literal -1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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 (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)) #s(literal -1 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 (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 -2/3 binary64) (neg.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 3 binary64))))) (sin.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)))
(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 -2/3 binary64) (neg.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 3 binary64)))))
(/.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 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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)))) (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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.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 (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 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(cos.f64 (+.f64 eps x))
(tan.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))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
eps
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 (tan.f64 eps) (tan.f64 x))
#s(literal 2 binary64)
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (tan.f64 x))

localize322.0ms (2%)

Memory
17.0MiB live, 331.0MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy0.015625
(*.f64 (tan.f64 eps) (tan.f64 x))
accuracy0.1328125
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
accuracy24.994935743541635
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
accuracy0.00390625
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy0.01171875
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy0.01953125
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy0.5366878961861644
#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))
accuracy0.0234375
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
accuracy0.025722509768442016
(sin.f64 (+.f64 eps x))
accuracy0.05424472348973429
(cos.f64 (+.f64 eps x))
accuracy25.002841220992565
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
accuracy0.0
(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy0.0
(sin.f64 eps)
accuracy0.0
(cos.f64 eps)
accuracy0.9975955860967971
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy0.01953125
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy0.024101269536884032
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
accuracy0.31640625
(*.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)
accuracy0.32421875
(*.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))))
Samples
137.0ms100×1valid
88.0ms153×0valid
7.0ms3valid
3.0ms2valid
Compiler

Compiled 2 232 to 122 computations (94.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 170.0ms
ival-mult: 54.0ms (31.8% of total)
ival-div: 23.0ms (13.5% of total)
ival-add: 19.0ms (11.2% of total)
ival-tan: 14.0ms (8.2% of total)
adjust: 14.0ms (8.2% of total)
ival-pow2: 10.0ms (5.9% of total)
ival-cos: 7.0ms (4.1% of total)
ival-sin: 7.0ms (4.1% of total)
ival-neg: 6.0ms (3.5% of total)
ival-sub: 5.0ms (2.9% of total)
const: 5.0ms (2.9% of total)
ival-pow: 5.0ms (2.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series129.0ms (0.8%)

Memory
-1.4MiB live, 160.4MiB allocated
Counts
27 → 171
Calls
Call 1
Inputs
(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 (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 (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)
(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)))))))
#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 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps 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))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(*.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 (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 (sin.f64 x) #s(literal 4 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 (+.f64 eps x))
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 (tan.f64 eps) (tan.f64 x))
Outputs
-2/3
(- (* -2 (pow x 2)) 2/3)
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3)
-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)
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
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))))
(/ (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)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (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)))
(* -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 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)))))))
(pow x 4)
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
1
(+ 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))))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(+ (* -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 (* (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 eps 2) (+ (* -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))) (+ 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)))) (* 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 (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (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 (* 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 (sin x) 4)
(pow (cos x) 2)
(cos (+ eps x))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos (- 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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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 (* (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)))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (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))))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (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 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (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)))))))
(* 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 (+ 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)))))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (- (+ (* -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)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(cos (- x (* -1 eps)))
Calls

6 calls:

TimeVariablePointExpression
56.0ms
x
@-inf
((+ (* (/ (+ (* (/ (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))) (+ (* (* (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))))) (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (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)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (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)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
22.0ms
x
@inf
((+ (* (/ (+ (* (/ (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))) (+ (* (* (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))))) (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (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)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (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)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
12.0ms
eps
@inf
((+ (* (/ (+ (* (/ (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))) (+ (* (* (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))))) (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (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)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (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)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
12.0ms
x
@0
((+ (* (/ (+ (* (/ (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))) (+ (* (* (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))))) (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (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)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (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)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
11.0ms
eps
@0
((+ (* (/ (+ (* (/ (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))) (+ (* (* (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))))) (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (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)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (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)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))

simplify176.0ms (1.1%)

Memory
17.0MiB live, 243.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07475061
124184868
080104589
Stop Event
iter limit
node limit
Counts
171 → 169
Calls
Call 1
Inputs
-2/3
(- (* -2 (pow x 2)) 2/3)
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3)
-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)
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
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))))
(/ (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)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (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)))
(* -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 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)))))))
(pow x 4)
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
1
(+ 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))))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(+ (* -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 (* (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 eps 2) (+ (* -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))) (+ 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)))) (* 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 (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (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 (* 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 (sin x) 4)
(pow (cos x) 2)
(cos (+ eps x))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos (- 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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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 (* (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)))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (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))))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (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 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (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)))))))
(* 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 (+ 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)))))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (- (+ (* -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)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(cos (- x (* -1 eps)))
Outputs
-2/3
#s(literal -2/3 binary64)
(- (* -2 (pow x 2)) 2/3)
(fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -2/3 binary64))
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3)
(fma.f64 (fma.f64 #s(literal -37/12 binary64) (*.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal -2/3 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal -154/45 binary64) (*.f64 x x) #s(literal -37/12 binary64)) (*.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal -2/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* -2/3 (* eps x)) 1/3)
(fma.f64 (*.f64 #s(literal -2/3 binary64) x) eps #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))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 5/6 binary64) eps (*.f64 #s(literal 17/9 binary64) (pow.f64 eps #s(literal 3 binary64))))) x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps)) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/3 (* eps x)))
(fma.f64 (*.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x)) x #s(literal 1/3 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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (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)) (sin.f64 eps)) (/.f64 x (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) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.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)) (/.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)))
(+ (* 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 (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)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (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)))
(+ (* 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 (fma.f64 (neg.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.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)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (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)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
(+ eps (* eps (pow x 2)))
(fma.f64 (*.f64 eps x) x eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 eps x) x) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 x x) #s(literal 2/45 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (/.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)))
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (fma.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)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.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)))) 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 (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x)
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64)) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) x #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -2/3 x)
(*.f64 #s(literal -2/3 binary64) x)
(* x (- (* -17/9 (pow x 2)) 2/3))
(*.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #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))
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(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* -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)))))))))
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x
(* x (+ 1 (/ eps x)))
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(pow (sin x) 2)
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(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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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)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (sin.f64 x) (neg.f64 eps) (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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps (cos.f64 x))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps eps))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 17/45 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(/ (* eps (sin x)) (cos x))
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(*.f64 (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x)) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 2/15 binary64)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (sin.f64 x) (/.f64 eps (cos.f64 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))))))
(*.f64 (*.f64 (sin.f64 x) eps) (-.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)))))
(* 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))))))))
(*.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)) 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)))) eps)
(* -1 (* (pow eps 4) (* (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 (*.f64 (neg.f64 (pow.f64 eps #s(literal 4 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 -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)))))
(* (pow eps 4) (+ (* -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))))
(*.f64 (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(*.f64 (fma.f64 (neg.f64 (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 -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)))) (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps)) (/.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))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(*.f64 (fma.f64 (neg.f64 (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 -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)))) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps))) (/.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))) (pow.f64 eps #s(literal 4 binary64)))
(* -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)))))))
(*.f64 (*.f64 (sin.f64 x) (neg.f64 eps)) (-.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)))))
(* 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)))))))
(*.f64 (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))) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps 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)))))))
(*.f64 (*.f64 (*.f64 eps eps) (neg.f64 (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 -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)))))
(* (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))))
(*.f64 (*.f64 (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))) eps) 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)))))
(*.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)) (/.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)))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(*.f64 (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 (-.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)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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))))
(*.f64 (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 (-.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)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -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 (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)))) (neg.f64 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 (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 eps) eps)
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))

rewrite245.0ms (1.5%)

Memory
-12.2MiB live, 351.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057665
0110649
1485546
24365526
08147515
Stop Event
iter limit
node limit
iter limit
Counts
27 → 642
Calls
Call 1
Inputs
(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 (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 (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)
(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)))))))
#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 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps 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))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(*.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 (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 (sin.f64 x) #s(literal 4 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 (+.f64 eps x))
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 (tan.f64 eps) (tan.f64 x))
Outputs
(*.f64 (-.f64 (pow.f64 (/.f64 (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 (/.f64 (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)))) #s(literal -2 binary64))) (pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (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 -1 binary64)))
(*.f64 (fma.f64 (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal -3 binary64)) #s(literal -1/27 binary64) (pow.f64 (/.f64 (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)))) #s(literal -3 binary64))) (pow.f64 (fma.f64 (/.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)) (-.f64 (/.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)) (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x))) (pow.f64 (/.f64 (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))) #s(literal -1 binary64)))
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(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
(exp.f64 (+.f64 (-.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))) (*.f64 (log.f64 (tan.f64 eps)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64) (*.f64 (log.f64 (tan.f64 eps)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 eps)) #s(literal 2 binary64) (-.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 eps)) #s(literal 2 binary64) (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 eps) #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (tan.f64 x)) #s(literal 1 binary64)))
(*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (pow.f64 (cos.f64 eps) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))))
(*.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 (tan.f64 eps) (pow.f64 (*.f64 (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (tan.f64 eps) (*.f64 (tan.f64 x) #s(literal 1 binary64)))
(*.f64 (tan.f64 eps) (tan.f64 x))
(*.f64 (tan.f64 x) (pow.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (tan.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 (sin.f64 eps) (*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (tan.f64 x)))
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x)))
(pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (tan.f64 x)) (neg.f64 (cos.f64 eps)))
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (tan.f64 x) (neg.f64 (sin.f64 eps))) (neg.f64 (cos.f64 eps)))
(/.f64 (*.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 eps) #s(literal -1 binary64)))
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
(/.f64 (*.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (tan.f64 eps) #s(literal -1 binary64)))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 eps)) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 x) (neg.f64 (cos.f64 eps))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (pow.f64 (tan.f64 eps) #s(literal -1 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64)) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(/.f64 (tan.f64 x) (pow.f64 (tan.f64 eps) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)))

eval399.0ms (2.4%)

Memory
-15.2MiB live, 294.1MiB allocated
Compiler

Compiled 81 153 to 6 140 computations (92.4% saved)

prune194.0ms (1.2%)

Memory
13.4MiB live, 92.3MiB allocated
Pruning

26 alts after pruning (23 fresh and 3 done)

PrunedKeptTotal
New1 023161 039
Fresh9716
Picked325
Done011
Total1 035261 061
Accuracy
100.0%
Counts
1 061 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
60.8%
(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)))
35.0%
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (tan.f64 x)))
60.9%
(-.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))
60.8%
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
60.5%
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (tan.f64 x))
60.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
60.2%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 #s(approx (* (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)))) (*.f64 #s(literal -2/3 binary64) 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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) #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))
100.0%
#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))
99.7%
#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))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (fma.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)))) (neg.f64 eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
24.1%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (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 (-.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)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))))
Compiler

Compiled 3 144 to 1 332 computations (57.6% saved)

simplify206.0ms (1.3%)

Memory
14.8MiB live, 125.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))))
cost-diff0
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))
cost-diff1
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
cost-diff0
(sin.f64 (+.f64 eps x))
cost-diff0
(neg.f64 (sin.f64 (+.f64 eps x)))
cost-diff1
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))
cost-diff3
(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)))
cost-diff0
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff0
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
cost-diff1
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
cost-diff1
(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)))
cost-diff2
(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)))))
cost-diff16
(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))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0961465
01721455
13191442
28511421
336101298
082001265
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#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))
(*.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)
(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))))
(*.f64 eps 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)))))
(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 eps (sin.f64 x))
(sin.f64 x)
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 -1/3 binary64)
(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(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)))
(neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
(pow.f64 (cos.f64 x) #s(literal -2 binary64))
#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)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(*.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))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
#s(literal 1/3 binary64)
(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)))
(neg.f64 (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))
#s(literal 1 binary64)
(neg.f64 (cos.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
#s(literal 2/3 binary64)
eps
(*.f64 #s(literal 4/3 binary64) x)
#s(literal 4/3 binary64)
x
#s(literal 1/3 binary64)
(*.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 (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)))
(sin.f64 x)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#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)
Outputs
#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 (fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 #s(literal -1 binary64) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)))) (*.f64 eps eps) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps))
(*.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)
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 #s(literal -1 binary64) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)))) (*.f64 eps eps) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)
(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))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 #s(literal -1 binary64) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)))) (*.f64 eps eps) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
(*.f64 eps 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)))))
(fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 #s(literal -1 binary64) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))))
(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))))
(neg.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 #s(literal -1 binary64) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x))) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)))))
(*.f64 eps (sin.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
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 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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 -1/3 binary64)
(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(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))
(/.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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)))
(fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (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)))
(neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
(pow.f64 (cos.f64 x) #s(literal -2 binary64))
#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)))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (tan.f64 x))
(*.f64 (tan.f64 x) (sin.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))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64))
(fma.f64 (tan.f64 x) eps #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(-.f64 (tan.f64 (+.f64 eps x)) #s(approx (tan x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(tan.f64 (+.f64 x eps))
(tan.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
#s(approx (tan x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
#s(literal 1/3 binary64)
(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 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(neg.f64 (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x)))
#s(literal 1 binary64)
(neg.f64 (cos.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (fma.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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))))
(fma.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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
#s(literal 2/3 binary64)
eps
(*.f64 #s(literal 4/3 binary64) x)
#s(literal 4/3 binary64)
x
#s(literal 1/3 binary64)
(*.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)))
(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)))
(sin.f64 x)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#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)

localize429.0ms (2.6%)

Memory
13.0MiB live, 453.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.23046875
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
accuracy0.3125
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
accuracy0.3203125
(*.f64 #s(literal 4/3 binary64) x)
accuracy0.6014202425464805
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
accuracy0.0
(neg.f64 (cos.f64 (+.f64 eps x)))
accuracy0.021816259768442016
(sin.f64 (+.f64 eps x))
accuracy0.05424472348973429
(cos.f64 (+.f64 eps x))
accuracy24.95173741332391
(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)))
accuracy0.0
(+.f64 x eps)
accuracy0.055397552495346905
(tan.f64 (+.f64 x eps))
accuracy0.5297447882557296
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
accuracy24.964996493222515
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
accuracy0.0
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
accuracy0.0
(*.f64 x x)
accuracy0.5366878961861644
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
accuracy0.9785646236900496
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy0.015625
(*.f64 (sin.f64 x) (tan.f64 x))
accuracy0.01953125
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
accuracy0.0234375
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy0.15300751953688402
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
Samples
178.0ms101×1valid
101.0ms151×0valid
9.0ms5exit
4.0ms3valid
Compiler

Compiled 2 728 to 195 computations (92.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 225.0ms
ival-mult: 59.0ms (26.2% of total)
ival-div: 33.0ms (14.7% of total)
ival-add: 32.0ms (14.2% of total)
adjust: 23.0ms (10.2% of total)
const: 18.0ms (8% of total)
ival-pow2: 15.0ms (6.7% of total)
ival-pow: 13.0ms (5.8% of total)
ival-neg: 10.0ms (4.4% of total)
ival-tan: 8.0ms (3.6% of total)
ival-cos: 5.0ms (2.2% of total)
ival-sin: 5.0ms (2.2% of total)
ival-sub: 2.0ms (0.9% of total)
exact: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series85.0ms (0.5%)

Memory
-7.3MiB live, 106.4MiB allocated
Counts
29 → 189
Calls
Call 1
Inputs
(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))))
(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)))))
(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)))
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))
(neg.f64 (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (tan.f64 x))
(cos.f64 (+.f64 eps x))
(neg.f64 (cos.f64 (+.f64 eps x)))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) 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)
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))))
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (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
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 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 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))))))))
(/ -1 (cos eps))
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps)))
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(* -1 (sin eps))
(- (* -1 (* x (cos eps))) (sin eps))
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps))
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))))))))))
(pow x 4)
(* (pow x 4) (+ 1 (* 1/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2))))))))
(* (pow x 2) (+ 1 (* 1/6 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2))))))))
(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 (cos eps))
(- (* x (sin eps)) (cos eps))
(- (* x (+ (sin eps) (* 1/2 (* x (cos eps))))) (cos eps))
(- (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) (* -1/2 (cos eps)))))) (cos eps))
(* 4/3 x)
(* 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)))))))
(* 2/3 eps)
(+ (* 2/3 eps) (* 4/3 x))
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) 1/3)
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)
(+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ -1 (cos (+ eps x)))
(* -1 (sin (+ eps x)))
(sin (+ eps x))
(+ 1 (/ (* eps (sin x)) (cos x)))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/ (pow (sin x) 2) (cos x))
(cos (+ eps x))
(* -1 (cos (+ eps 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 (+ (* -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))))))))))
(* x (+ 4/3 (* 2/3 (/ eps 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)))
(/ -1 (cos (- eps (* -1 x))))
(* -1 (sin (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(* -1 (cos (- eps (* -1 x))))
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3)))
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (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 (/ (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)))
(/ -1 (cos x))
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x)))
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(* -1 (sin x))
(- (* -1 (* eps (cos x))) (sin x))
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x))
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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 (cos x))
(- (* eps (sin x)) (cos x))
(- (* eps (+ (sin x) (* 1/2 (* eps (cos x))))) (cos x))
(- (* eps (+ (sin x) (* eps (- (* -1/6 (* eps (sin x))) (* -1/2 (cos x)))))) (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))))))
(- (* -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))))))
(* -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))))))))
(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))
(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps))))
(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(* eps (+ 1 (/ x eps)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* -1 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (* (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 3) (+ (* -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))))
(* (pow eps 3) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 3) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (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)))))))
(* 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)))))))
(* -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))))
(* eps (+ 2/3 (* 4/3 (/ x eps))))
(* -1 (* eps (+ (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) (* -1 (/ (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) eps)))))
(* -1 (* eps (- (* -1 (/ (- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ -1 (cos (- x (* -1 eps))))
(* -1 (sin (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (* (pow eps 3) (+ (* -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 (* (pow eps 3) (+ (* -1 (/ (+ (* -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)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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))))))))
(cos (- x (* -1 eps)))
(* -1 (cos (- x (* -1 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 (- (* -4/3 (/ x eps)) 2/3)))
Calls

6 calls:

TimeVariablePointExpression
26.0ms
eps
@inf
((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps 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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
16.0ms
x
@-inf
((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps 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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
13.0ms
x
@inf
((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps 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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
9.0ms
eps
@0
((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps 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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
8.0ms
x
@0
((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps 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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))

simplify226.0ms (1.4%)

Memory
9.8MiB live, 214.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07265927
123685709
279415650
081175392
Stop Event
iter limit
node limit
Counts
189 → 187
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)
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))))
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (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
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 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 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))))))))
(/ -1 (cos eps))
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps)))
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(* -1 (sin eps))
(- (* -1 (* x (cos eps))) (sin eps))
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps))
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))))))))))
(pow x 4)
(* (pow x 4) (+ 1 (* 1/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2))))))))
(* (pow x 2) (+ 1 (* 1/6 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2))))))))
(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 (cos eps))
(- (* x (sin eps)) (cos eps))
(- (* x (+ (sin eps) (* 1/2 (* x (cos eps))))) (cos eps))
(- (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) (* -1/2 (cos eps)))))) (cos eps))
(* 4/3 x)
(* 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)))))))
(* 2/3 eps)
(+ (* 2/3 eps) (* 4/3 x))
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) 1/3)
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)
(+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ -1 (cos (+ eps x)))
(* -1 (sin (+ eps x)))
(sin (+ eps x))
(+ 1 (/ (* eps (sin x)) (cos x)))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/ (pow (sin x) 2) (cos x))
(cos (+ eps x))
(* -1 (cos (+ eps 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 (+ (* -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))))))))))
(* x (+ 4/3 (* 2/3 (/ eps 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)))
(/ -1 (cos (- eps (* -1 x))))
(* -1 (sin (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(* -1 (cos (- eps (* -1 x))))
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3)))
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (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 (/ (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)))
(/ -1 (cos x))
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x)))
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(* -1 (sin x))
(- (* -1 (* eps (cos x))) (sin x))
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x))
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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 (cos x))
(- (* eps (sin x)) (cos x))
(- (* eps (+ (sin x) (* 1/2 (* eps (cos x))))) (cos x))
(- (* eps (+ (sin x) (* eps (- (* -1/6 (* eps (sin x))) (* -1/2 (cos x)))))) (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))))))
(- (* -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))))))
(* -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))))))))
(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))
(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps))))
(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(* eps (+ 1 (/ x eps)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* -1 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (* (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 3) (+ (* -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))))
(* (pow eps 3) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 3) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (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)))))))
(* 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)))))))
(* -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))))
(* eps (+ 2/3 (* 4/3 (/ x eps))))
(* -1 (* eps (+ (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) (* -1 (/ (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) eps)))))
(* -1 (* eps (- (* -1 (/ (- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (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))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ -1 (cos (- x (* -1 eps))))
(* -1 (sin (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (* (pow eps 3) (+ (* -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 (* (pow eps 3) (+ (* -1 (/ (+ (* -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)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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))))))))
(cos (- x (* -1 eps)))
(* -1 (cos (- x (* -1 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 (- (* -4/3 (/ x eps)) 2/3)))
Outputs
-1/3
#s(literal -1/3 binary64)
(- (* -2/3 (* eps x)) 1/3)
(fma.f64 (*.f64 #s(literal -2/3 binary64) eps) x #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 x eps) #s(literal -4/3 binary64)) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/3 (* eps x)))
(fma.f64 #s(literal 2/3 binary64) (*.f64 x eps) #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 x eps) #s(literal 4/3 binary64)) x)) x #s(literal 1/3 binary64))
(- (* -4/3 (pow x 2)) 1/3)
(fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -17/9 binary64) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal -248/135 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (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)) (sin.f64 eps)) (/.f64 x (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 (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 #s(literal -1/2 binary64) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.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)))
eps
(+ eps (* eps (pow x 2)))
(fma.f64 (*.f64 x x) eps eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) 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)))
(+ (* 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 (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)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (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 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(cos x)
(cos.f64 x)
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(* -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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(- (* -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))))))
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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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(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))
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(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps))))
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(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))
(*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.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)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))))
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(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (* eps (sin x)) (cos x))
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64))
(* -1 (* (pow eps 4) (* (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 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (neg.f64 (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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)))))
(* (pow eps 4) (+ (* -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))))
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(* eps (+ 2/3 (* 4/3 (/ x eps))))
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(*.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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))))
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -1 (* (pow eps 3) (+ (* -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)))))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (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 (* (pow eps 3) (+ (* -1 (/ (+ (* -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)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) eps) (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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))))) (neg.f64 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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))))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (/.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (neg.f64 eps)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (neg.f64 eps)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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))))) (neg.f64 eps))))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(* -1 (cos (- x (* -1 eps))))
(neg.f64 (cos.f64 (+.f64 x 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 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (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)) (neg.f64 eps))
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3)))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 eps))

rewrite210.0ms (1.3%)

Memory
-4.8MiB live, 186.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
090961
0159949
1671654
26324654
09220643
Stop Event
iter limit
node limit
iter limit
Counts
29 → 638
Calls
Call 1
Inputs
(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))))
(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)))))
(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)))
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))
(neg.f64 (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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))))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (tan.f64 x))
(cos.f64 (+.f64 eps x))
(neg.f64 (cos.f64 (+.f64 eps x)))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
Outputs
(*.f64 (-.f64 (pow.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (-.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x))) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))
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(-.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (tan.f64 x)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (tan.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (-.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))))
(exp.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (tan.f64 x) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 x))
(pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 x) (sin.f64 x))) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (+.f64 x eps))))
(*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (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 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(neg.f64 (neg.f64 (cos.f64 (+.f64 x 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) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (+.f64 x eps))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
(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)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
(*.f64 #s(literal -1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal 1 binary64))
(*.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) (+.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)) (*.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))))))
(/.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal 1 binary64))
(/.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(neg.f64 (cos.f64 (+.f64 x eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)))
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (sin.f64 eps) (sin.f64 x)))
(+.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (+.f64 x eps))))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 x #s(literal 4/3 binary64))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(*.f64 eps #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))
(*.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(*.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))))
(/.f64 (-.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps))) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))))
(/.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))
(/.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 16/9 binary64) (*.f64 x x) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) eps) #s(literal 4/3 binary64)) x))))
(/.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))) (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64))))))
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
(fma.f64 x #s(literal 4/3 binary64) (*.f64 #s(literal 2/3 binary64) eps))
(fma.f64 eps #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) x))
(-.f64 (/.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) (/.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(+.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 #s(literal 4/3 binary64) x))
(+.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))

eval205.0ms (1.3%)

Memory
-3.6MiB live, 265.0MiB allocated
Compiler

Compiled 100 471 to 6 524 computations (93.5% saved)

prune44.0ms (0.3%)

Memory
6.0MiB live, 83.8MiB allocated
Pruning

27 alts after pruning (23 fresh and 4 done)

PrunedKeptTotal
New1 045111 056
Fresh61218
Picked415
Done033
Total1 055271 082
Accuracy
100.0%
Counts
1 082 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
60.8%
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
35.0%
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (tan.f64 x)))
60.9%
(-.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))
60.8%
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
60.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps)))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
51.4%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))) (pow.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) #s(literal 2 binary64)))))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 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))
99.9%
#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 #s(approx (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (fma.f64 (*.f64 x x) #s(literal -4/3 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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
24.1%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (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 (-.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)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))))
Compiler

Compiled 4 204 to 1 544 computations (63.3% saved)

simplify178.0ms (1.1%)

Memory
24.5MiB live, 139.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))))
cost-diff0
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
cost-diff9
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff3
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
cost-diff0
#s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
cost-diff1
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
cost-diff0
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff0
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
cost-diff1
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)
cost-diff2
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x)))
cost-diff2
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
cost-diff5
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
cost-diff11
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01031847
01721822
13321709
28881699
339961596
080971541
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 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))
(*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 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)
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
(*.f64 eps eps)
eps
(neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))
(fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x)))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(tan.f64 x)
x
#s(literal 1 binary64)
(*.f64 eps (tan.f64 x))
#s(literal -1/3 binary64)
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 4/3 binary64)
#s(literal 1 binary64)
x
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)
(pow.f64 eps #s(literal 3 binary64))
#s(literal 3 binary64)
#s(literal 2/3 binary64)
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
#s(literal 1/3 binary64)
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
#s(literal -1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(neg.f64 (sin.f64 (+.f64 x eps)))
(sin.f64 (+.f64 x eps))
(neg.f64 (tan.f64 x))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
#s(literal 2/3 binary64)
eps
(*.f64 #s(literal 4/3 binary64) x)
#s(literal 4/3 binary64)
x
#s(literal 1/3 binary64)
(*.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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.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 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(sin.f64 x)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))
(-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64))
(*.f64 eps (tan.f64 x))
(tan.f64 x)
(fma.f64 eps (tan.f64 x) #s(literal -1 binary64))
#s(literal -1 binary64)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 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 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64) (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) eps) eps)) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 eps eps))) eps))
(*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 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)
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(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
#s(literal 2/3 binary64)
eps
(*.f64 #s(literal 4/3 binary64) x)
#s(literal 4/3 binary64)
x
#s(literal 1/3 binary64)
(*.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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) eps #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 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(sin.f64 x)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 (tan.f64 x) eps #s(literal 1 binary64))
(-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 (pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64))
(*.f64 eps (tan.f64 x))
(*.f64 (tan.f64 x) eps)
(tan.f64 x)
(fma.f64 eps (tan.f64 x) #s(literal -1 binary64))
(fma.f64 (tan.f64 x) eps #s(literal -1 binary64))
#s(literal -1 binary64)

localize725.0ms (4.4%)

Memory
-345.0MiB live, 461.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.23046875
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
accuracy0.3125
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
accuracy0.3203125
(*.f64 #s(literal 4/3 binary64) x)
accuracy0.6014202425464805
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
accuracy0.0
(neg.f64 (sin.f64 (+.f64 x eps)))
accuracy0.021816259768442016
(sin.f64 (+.f64 x eps))
accuracy0.05424472348973429
(cos.f64 (+.f64 x eps))
accuracy24.95173741332391
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
accuracy0.0078125
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
accuracy0.0078125
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
accuracy0.01171875
(*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)
accuracy0.5255790727433751
#s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
accuracy0.0
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)
accuracy0.0
(*.f64 x x)
accuracy0.5366878961861644
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
accuracy0.9785646236900496
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy0.015625
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x)))
accuracy0.01953125
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
accuracy0.0234375
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy0.03191376953688403
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
Samples
475.0ms101×1valid
134.0ms151×0valid
10.0ms5exit
2.0ms3valid
Compiler

Compiled 3 340 to 210 computations (93.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 552.0ms
ival-add: 354.0ms (64.1% of total)
ival-mult: 71.0ms (12.9% of total)
const: 24.0ms (4.3% of total)
adjust: 24.0ms (4.3% of total)
ival-div: 24.0ms (4.3% of total)
ival-pow2: 13.0ms (2.4% of total)
ival-pow: 12.0ms (2.2% of total)
ival-neg: 7.0ms (1.3% of total)
ival-sub: 5.0ms (0.9% of total)
ival-tan: 5.0ms (0.9% of total)
ival-cos: 5.0ms (0.9% of total)
ival-sin: 5.0ms (0.9% of total)
exact: 1.0ms (0.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series83.0ms (0.5%)

Memory
23.6MiB live, 98.1MiB allocated
Counts
31 → 215
Calls
Call 1
Inputs
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x)))
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(*.f64 x x)
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(sin.f64 (+.f64 x eps))
(neg.f64 (sin.f64 (+.f64 x eps)))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
Outputs
-1/3
(- (* -1/3 (* eps x)) 1/3)
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3)
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3)
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps))))))))))))
(* eps x)
(* x (+ eps (* 4/3 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps)))))
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps)))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 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)))
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(+ eps (* 2/3 (pow eps 3)))
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))))))))))
(/ -1 (cos eps))
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps)))
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (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))))
(+ eps x)
(+ 1 (* eps x))
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps))))
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps))))
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps)))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps)))))
(pow x 4)
(* (pow x 4) (+ 1 (* 4/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))
(* (pow x 2) (+ 1 (* 5/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(* -1 (sin eps))
(- (* -1 (* x (cos eps))) (sin eps))
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps))
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps))
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))))
(* 4/3 x)
(* 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)))))))
(* 2/3 eps)
(+ (* 2/3 eps) (* 4/3 x))
(- (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x)))))))
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(* x (+ 1 (* 4/3 (pow eps 2))))
(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ -1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))))
(+ (* -1 (* (pow eps 2) (+ (* -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 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x)))))))
(sin (+ eps x))
(* -1 (sin (+ eps 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 (+ (* -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))))))))))
(* x (+ 4/3 (* 2/3 (/ eps x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ (+ eps (* 2/3 (pow eps 3))) x)))))
(/ -1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2)))))
(sin (- eps (* -1 x)))
(* -1 (sin (- eps (* -1 x))))
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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)))))
(+ x (* eps (+ 1 (* 4/3 (* eps x)))))
(+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x))))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ -1 (cos x))
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x)))
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos 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))))
(+ 1 (/ (* eps (sin x)) (cos x)))
(+ 1 (+ (* eps (- (* -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))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (- (* 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)))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps x) (pow x 2)))
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* -1 (sin x))
(- (* -1 (* eps (cos x))) (sin x))
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x))
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin 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))))))
(- (* -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))))))
(* -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))))))))
(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* 2/3 (pow eps 3))
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))
(* -1 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (* (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 3) (+ (* -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))))
(* (pow eps 3) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 3) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* eps (+ 1 (/ x eps)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
(* -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)))))))
(* -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))))
(* eps (+ 2/3 (* 4/3 (/ x eps))))
(* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* -1 (/ (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) eps)))))
(* (pow eps 3) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (- (* -4/3 (/ x eps)) 2/3)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 4/3 x) (/ 1 eps)) eps)) 2/3)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)) eps)) 2/3)))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (* (pow eps 3) (+ (* -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 (* (pow eps 3) (+ (* -1 (/ (+ (* -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)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x))))
(sin (- x (* -1 eps)))
(* -1 (sin (- x (* -1 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 (- (* -4/3 (/ x eps)) 2/3)))
Calls

6 calls:

TimeVariablePointExpression
22.0ms
x
@-inf
((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
16.0ms
x
@inf
((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
14.0ms
eps
@inf
((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
9.0ms
eps
@0
((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))
9.0ms
eps
@-inf
((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (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)))))) (* 4/3 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) (+ (* 2/3 eps) (* 4/3 x)))

simplify232.0ms (1.4%)

Memory
-24.4MiB live, 226.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09227426
130817213
081916814
Stop Event
iter limit
node limit
Counts
215 → 213
Calls
Call 1
Inputs
-1/3
(- (* -1/3 (* eps x)) 1/3)
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3)
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3)
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps))))))))))))
(* eps x)
(* x (+ eps (* 4/3 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps)))))
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps)))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 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)))
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(+ eps (* 2/3 (pow eps 3)))
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))))))))))
(/ -1 (cos eps))
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps)))
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (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))))
(+ eps x)
(+ 1 (* eps x))
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps))))
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps))))
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2)))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps)))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps)))))
(pow x 4)
(* (pow x 4) (+ 1 (* 4/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))
(* (pow x 2) (+ 1 (* 5/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(* -1 (sin eps))
(- (* -1 (* x (cos eps))) (sin eps))
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps))
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps))
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))))
(* 4/3 x)
(* 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)))))))
(* 2/3 eps)
(+ (* 2/3 eps) (* 4/3 x))
(- (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x)))))))
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(* x (+ 1 (* 4/3 (pow eps 2))))
(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ -1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1))
(* eps (+ (* -1 (* (pow eps 2) (+ (* -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 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))))
(+ (* -1 (* (pow eps 2) (+ (* -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 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x)))))))
(sin (+ eps x))
(* -1 (sin (+ eps 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 (+ (* -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))))))))))
(* x (+ 4/3 (* 2/3 (/ eps x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ (+ eps (* 2/3 (pow eps 3))) x)))))
(/ -1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2)))))
(sin (- eps (* -1 x)))
(* -1 (sin (- eps (* -1 x))))
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (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)))))
(+ x (* eps (+ 1 (* 4/3 (* eps x)))))
(+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x))))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (+ (* eps (+ (* -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))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ -1 (cos x))
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x)))
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x)))
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos 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))))
(+ 1 (/ (* eps (sin x)) (cos x)))
(+ 1 (+ (* eps (- (* -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))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (- (* 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)))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps x) (pow x 2)))
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* -1 (sin x))
(- (* -1 (* eps (cos x))) (sin x))
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x))
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin 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))))))
(- (* -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))))))
(* -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))))))))
(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* 2/3 (pow eps 3))
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))
(* -1 (* (pow eps 4) (* (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 4) (+ (* -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))))
(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (* (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 3) (+ (* -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))))
(* (pow eps 3) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
(* (pow eps 3) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* eps (+ 1 (/ x eps)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
(* -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)))))))
(* -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))))
(* eps (+ 2/3 (* 4/3 (/ x eps))))
(* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* -1 (/ (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) eps)))))
(* (pow eps 3) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (- (* -4/3 (/ x eps)) 2/3)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 4/3 x) (/ 1 eps)) eps)) 2/3)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)) eps)) 2/3)))
(* (pow eps 4) (+ (* -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 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))
(* (pow eps 4) (+ (* -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 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) 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 (* (pow eps 3) (+ (* -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 (* (pow eps 3) (+ (* -1 (/ (+ (* -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)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (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))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x))))
(sin (- x (* -1 eps)))
(* -1 (sin (- x (* -1 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 (- (* -4/3 (/ x eps)) 2/3)))
Outputs
-1/3
#s(literal -1/3 binary64)
(- (* -1/3 (* eps x)) 1/3)
(fma.f64 (*.f64 eps x) #s(literal -1/3 binary64) #s(literal -1/3 binary64))
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3)
(fma.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -1/3 binary64) eps)) x #s(literal -1/3 binary64))
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal -13/9 binary64) (*.f64 eps x) #s(literal -4/3 binary64)) x (*.f64 #s(literal -1/3 binary64) eps)) x #s(literal -1/3 binary64))
(- (* -4/3 (pow x 2)) 1/3)
(fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(fma.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal -248/135 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64))
(+ 1 (* 1/3 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3))))))
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps))))))))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(* eps x)
(*.f64 eps x)
(* x (+ eps (* 4/3 (* eps (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 248/315 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 17/15 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) eps) x)
eps
(+ eps (* eps (pow x 2)))
(fma.f64 (*.f64 x x) eps eps)
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)
(/ (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 -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.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))) (/.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)))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(+ eps (* 2/3 (pow eps 3)))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3)))))))
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))))))
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 (fma.f64 #s(literal 5/6 binary64) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)))) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))))))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/6 binary64) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(/ -1 (cos eps))
(/.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps)))
(neg.f64 (fma.f64 x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 eps))))
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(fma.f64 (neg.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))) x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))))) x (/.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps)))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps))
(+ eps x)
(+.f64 eps x)
(+ 1 (* eps x))
(fma.f64 eps x #s(literal 1 binary64))
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps))))
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/3 binary64) eps) x #s(literal 1 binary64))
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 binary64))
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2)))))
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))))))
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2)))))))))
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 (-.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (fma.f64 (fma.f64 (neg.f64 eps) eps #s(literal 1 binary64)) eps (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/3 binary64) eps)) x (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))))) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))))
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps)))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps)))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (fma.f64 (fma.f64 (neg.f64 eps) eps #s(literal 1 binary64)) eps (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/3 binary64) eps)) x (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64)))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (* 4/3 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 6/5 binary64) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 848/945 binary64) (*.f64 x x) #s(literal 6/5 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (* 5/3 (pow x 2))))
(*.f64 (fma.f64 #s(literal 5/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 77/45 binary64) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 88/63 binary64) (*.f64 x x) #s(literal 77/45 binary64)) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x))
(sin eps)
(sin.f64 eps)
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(* 2/3 eps)
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* x (+ 1 (* 4/3 (pow eps 2))))
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(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
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(* eps (+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(+ (* -1 (* (pow eps 2) (+ (* -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))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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x
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(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1))
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(* eps (+ (* -1 (* (pow eps 2) (+ (* -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 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))))
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(/ (pow (sin x) 4) (pow (cos x) 4))
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(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
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(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x)))))))
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(* eps (+ 1 (+ (* eps (+ (* 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -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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(- (* -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))))))
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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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(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))
(/.f64 (*.f64 (*.f64 (sin.f64 x) eps) (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))))) eps)
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.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))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(*.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.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)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
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(* 2/3 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64))
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))
(*.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))
(*.f64 (+.f64 (+.f64 (/.f64 x (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 4) (* (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 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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)))))
(* (pow eps 4) (+ (* -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))))
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(* (pow eps 4) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
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(* (pow eps 4) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
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(* -1 (* (pow eps 3) (* (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)))))))
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(* (pow eps 3) (+ (* -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))))
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(* (pow eps 3) (+ (* -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)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))))))
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(* (pow eps 3) (+ (* -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 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
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(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(* eps (+ (/ 1 eps) (/ (sin x) (cos x))))
(fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64))
(* 2/3 (* (pow eps 3) x))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) x (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (/.f64 #s(literal 1/3 binary64) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
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(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
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(* -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)))))))
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(* 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)))))))
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(* -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)))))))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(* -1 (* (pow eps 3) (+ (* -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)))))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) 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))))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (neg.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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))))) (/.f64 (neg.f64 (fma.f64 (sin.f64 x) (/.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)) (/.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)))) eps))) eps)) (neg.f64 eps))))
(/ -1 (cos (- x (* -1 eps))))
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x)))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps)
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps))))
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x))))
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x))))
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal -1 binary64) #s(literal -1/3 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x))))
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (/.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps) x)) eps) #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (sin (- x (* -1 eps))))
(neg.f64 (sin.f64 (+.f64 eps x)))
(* -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 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) 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)))) (neg.f64 eps))
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3)))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 eps))

rewrite211.0ms (1.3%)

Memory
0.2MiB live, 233.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01011411
01691395
17751097
274171097
084491069
Stop Event
iter limit
node limit
iter limit
Counts
31 → 628
Calls
Call 1
Inputs
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x)))
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)
(fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(*.f64 x x)
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
(sin.f64 (+.f64 x eps))
(neg.f64 (sin.f64 (+.f64 x eps)))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
Outputs
(*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))
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(+.f64 (neg.f64 (*.f64 (cos.f64 eps) (sin.f64 x))) (neg.f64 (*.f64 (sin.f64 eps) (cos.f64 x))))
(+.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal -1 binary64)) (*.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 #s(literal -1 binary64) (*.f64 (sin.f64 eps) (cos.f64 x))))
(+.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 (+.f64 eps x))))
#s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))
(*.f64 #s(literal 4/3 binary64) x)
(*.f64 x #s(literal 4/3 binary64))
(*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps)
(*.f64 eps #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))
(*.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(*.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))))
(/.f64 (-.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps))) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))))
(/.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))
(/.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 16/9 binary64) (*.f64 x x) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) eps) #s(literal 4/3 binary64)) x))))
(/.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))) (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64)))))
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps))
(fma.f64 eps #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) x))
(fma.f64 x #s(literal 4/3 binary64) (*.f64 #s(literal 2/3 binary64) eps))
(-.f64 (/.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) (/.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))))
(+.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 #s(literal 4/3 binary64) x))
(+.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))

eval298.0ms (1.8%)

Memory
0.8MiB live, 242.6MiB allocated
Compiler

Compiled 105 537 to 6 430 computations (93.9% saved)

prune85.0ms (0.5%)

Memory
-4.1MiB live, 116.8MiB allocated
Pruning

30 alts after pruning (26 fresh and 4 done)

PrunedKeptTotal
New1 003141 017
Fresh61218
Picked505
Done044
Total1 014301 044
Accuracy
100.0%
Counts
1 044 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
61.0%
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
60.9%
(-.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))
60.8%
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
60.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
60.8%
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps)))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
Compiler

Compiled 7 913 to 1 517 computations (80.8% saved)

regimes53.0ms (0.3%)

Memory
33.6MiB live, 107.4MiB allocated
Counts
63 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (fma.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)))) (neg.f64 eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps 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)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (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 (-.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)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))))
#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 (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps))
Calls

3 calls:

17.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms
x
15.0ms
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)

regimes190.0ms (1.2%)

Memory
0.4MiB live, 84.1MiB allocated
Counts
53 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps)))
#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 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (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 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.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))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#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))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))) (pow.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) #s(literal 2 binary64)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
Calls

3 calls:

160.0ms
x
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
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)

regimes58.0ms (0.4%)

Memory
-24.5MiB live, 53.0MiB allocated
Counts
51 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#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))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
Calls

3 calls:

25.0ms
x
18.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
eps
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)

regimes42.0ms (0.3%)

Memory
1.6MiB live, 39.9MiB allocated
Counts
50 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
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(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
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(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
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(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
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(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps)))
#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 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (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 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.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))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #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 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#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))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
Calls

3 calls:

15.0ms
x
12.0ms
eps
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes38.0ms (0.2%)

Memory
6.7MiB live, 47.8MiB allocated
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps)))
#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 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (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 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.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))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) #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))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
Calls

3 calls:

14.0ms
eps
10.0ms
x
10.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.2%)

Memory
12.4MiB live, 49.2MiB allocated
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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))
Calls

3 calls:

10.0ms
eps
8.0ms
x
8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.2%)

Memory
-1.0MiB live, 36.8MiB allocated
Counts
32 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.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 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
Calls

3 calls:

11.0ms
eps
8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory
15.7MiB live, 15.7MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
Calls

3 calls:

4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory
-27.6MiB live, 10.7MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
Calls

3 calls:

28.0ms
eps
3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0%)

Memory
9.6MiB live, 9.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
99.1%1x
99.1%1eps
99.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory
7.7MiB live, 7.7MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 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
98.4%1eps
98.4%1x
98.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify58.0ms (0.4%)

Memory
-41.3MiB live, 23.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01741617
13131596
27941584
329551532
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (-.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (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)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #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)) #s(approx (* (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (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) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))

soundness1.6s (9.6%)

Memory
22.9MiB live, 1 002.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057665
0110649
1485546
24365526
08147515
09227426
130817213
081916814
07475061
124184868
080104589
090961
0159949
1671654
26324654
09220643
0157950
1464884
21539873
36077710
08335686
07265927
123685709
279415650
081175392
01011411
01691395
17751097
274171097
084491069
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 2 363 to 515 computations (78.2% saved)

preprocess84.0ms (0.5%)

Memory
-2.1MiB live, 120.4MiB allocated
Compiler

Compiled 3 368 to 392 computations (88.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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