2tan (problem 3.3.2)

Time bar (total: 12.4s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze61.0ms (0.5%)

Memory
-14.3MiB live, 82.3MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.9s (55.9%)

Memory
-92.8MiB live, 7 216.5MiB allocated
Samples
3.3s26 171×0invalid
808.0ms5 454×0valid
483.0ms2 802×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.2s
const: 757.0ms (23.4% of total)
ival-tan: 694.0ms (21.4% of total)
ival-mult: 324.0ms (10% of total)
ival-fabs: 276.0ms (8.5% of total)
ival-add: 273.0ms (8.4% of total)
ival-<: 260.0ms (8% of total)
ival-<=: 237.0ms (7.3% of total)
ival-sub: 174.0ms (5.4% of total)
ival-and: 99.0ms (3.1% of total)
adjust: 81.0ms (2.5% of total)
exact: 47.0ms (1.5% of total)
ival-assert: 14.0ms (0.4% of total)
Bogosity

explain86.0ms (0.7%)

Memory
11.4MiB live, 155.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2250-7(2.856233422121792e-26 2.893370470922743e-28)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
00-0-eps
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-(tan.f64 (+.f64 x eps))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))cancellation21815
Confusion
Predicted +Predicted -
+2187
-031
Precision
1.0
Recall
0.9688888888888889
Confusion?
Predicted +Predicted MaybePredicted -
+21870
-0823
Precision?
0.9656652360515021
Recall?
1.0
Freqs
test
numberfreq
038
1218
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
19.0ms336×0valid
18.0ms174×1valid
1.0ms2valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-tan: 9.0ms (47% of total)
adjust: 4.0ms (20.9% of total)
ival-add: 3.0ms (15.7% of total)
ival-sub: 3.0ms (15.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess265.0ms (2.1%)

Memory
17.6MiB live, 251.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01843
13543
26243
310943
418443
532843
665443
7149243
8343943
9434043
10666543
11741643
12787243
067
0107
1167
2257
3417
4667
51177
62117
74747
813117
922747
1033037
1135887
1237717
1338507
1438687
1538747
1638807
1738867
1838927
1938987
2039047
2139107
2239167
2339227
2439287
2577797
080417
Stop Event
iter limit
node limit
iter limit
node limit
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
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify213.0ms (1.7%)

Memory
-20.7MiB live, 167.5MiB 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
11618
22518
34118
46618
511718
621118
747418
8131118
9227418
10330318
11358818
12377118
13385018
14386818
15387418
16388018
17388618
18389218
19389818
20390418
21391018
22391618
23392218
24392818
25777918
0804118
Stop Event
iter limit
node limit
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)

localize35.0ms (0.3%)

Memory
37.1MiB live, 80.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(tan.f64 x)
accuracy0.01953125
(tan.f64 (+.f64 x eps))
accuracy23.418471955282186
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Samples
16.0ms87×1valid
13.0ms168×0valid
0.0ms2valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-tan: 7.0ms (45.3% of total)
adjust: 3.0ms (19.4% of total)
ival-add: 3.0ms (19.4% of total)
ival-sub: 2.0ms (12.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series52.0ms (0.4%)

Memory
-14.6MiB live, 81.7MiB 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
43.0ms
x
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms
eps
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms
eps
@inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms
eps
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms
x
@inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify158.0ms (1.3%)

Memory
17.7MiB live, 153.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157970
1488910
21845849
08454797
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)))
(/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (cos.f64 eps)) (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 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) 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 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.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 binary64) #s(literal -1/2 binary64)) x) x (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 x (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (cos.f64 eps)) (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 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (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 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.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 binary64) #s(literal -1/6 binary64)) x) x (+.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (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)))
(fma.f64 (/.f64 eps x) x 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 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* 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)))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (neg.f64 eps) (/.f64 (fma.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)) #s(literal -1/3 binary64) (fma.f64 (*.f64 (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (sin.f64 x) (*.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)) #s(literal -1/3 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 -1/2 binary64) (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps 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)))
(+.f64 (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps 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 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (+.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps 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)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite200.0ms (1.6%)

Memory
13.2MiB live, 333.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15316
244016
3660816
0858816
Stop Event
iter limit
node limit
iter limit
Counts
4 → 158
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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps 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 (/.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 x)) (tan.f64 eps) #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 x)) (tan.f64 eps) #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 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 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 (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 (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 (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #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 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
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(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (*.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 eps (/.f64 (*.f64 eps eps) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(-.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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (tan.f64 x))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))) (cos.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(neg.f64 (neg.f64 (tan.f64 x)))
(tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) x))
(tan.f64 x)
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))

eval27.0ms (0.2%)

Memory
-40.6MiB live, 64.9MiB allocated
Compiler

Compiled 5 935 to 840 computations (85.8% saved)

prune8.0ms (0.1%)

Memory
21.0MiB live, 21.0MiB allocated
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1767183
Fresh000
Picked011
Done000
Total1768184
Accuracy
100.0%
Counts
184 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
20.9%
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
63.4%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
99.5%
#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))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
Compiler

Compiled 457 to 230 computations (49.7% saved)

simplify239.0ms (1.9%)

Memory
-13.3MiB live, 239.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
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 (+.f64 eps x) x))
cost-diff0
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff4
(-.f64 (+.f64 eps x) x)
cost-diff0
(/.f64 (sin.f64 x) (cos.f64 x))
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.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
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
cost-diff2
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
cost-diff6
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
cost-diff10
(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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049702
092694
1163660
2413632
31867559
08432558
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)))
(*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
(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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 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)
x
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(literal -1 binary64)
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
#s(literal -1/6 binary64)
eps
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
#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 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 x)
#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
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/3 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (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)) eps (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal 1 binary64)) eps)))
(fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/3 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (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)) eps (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)))
(fma.f64 (*.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/3 binary64)) eps) (neg.f64 eps) (*.f64 (/.f64 (sin.f64 x) (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)) eps (/.f64 (sin.f64 x) (cos.f64 x)))))
(*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
(*.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/3 binary64)) (neg.f64 eps))
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
(neg.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/3 binary64)))
(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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
(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)
x
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -5/6 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(-.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -5/6 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
(-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(literal -1 binary64)
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
#s(literal 1/6 binary64)
#s(literal -1/6 binary64)
eps
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))
(*.f64 (/.f64 (sin.f64 x) (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)) eps (/.f64 (sin.f64 x) (cos.f64 x))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(*.f64 (sin.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)) eps (/.f64 (sin.f64 x) (cos.f64 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 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)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
#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 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(tan.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(sin.f64 eps)
(-.f64 (+.f64 eps x) x)
eps
(+.f64 eps x)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 x)
#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

localize185.0ms (1.5%)

Memory
2.1MiB live, 336.7MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(cos.f64 x)
accuracy0.015625
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy0.01953125
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy0.3299018916517782
#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))
accuracy0.0
(cos.f64 x)
accuracy0.0078125
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy0.0078125
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy23.426843462287888
(-.f64 (+.f64 eps x) x)
accuracy0.0
(cos.f64 x)
accuracy0.015625
(/.f64 (sin.f64 x) (cos.f64 x))
accuracy0.01953125
(tan.f64 (+.f64 x eps))
accuracy23.418471955282186
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy0.0
(sin.f64 eps)
accuracy0.0
(cos.f64 eps)
accuracy0.0078125
(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy0.7350565505067123
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy0.14826272569165694
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
accuracy0.18359375
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
accuracy0.28125
(*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
accuracy0.99609375
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
Samples
70.0ms90×1valid
64.0ms165×0valid
1.0ms2valid
Compiler

Compiled 651 to 55 computations (91.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 102.0ms
ival-mult: 24.0ms (23.4% of total)
ival-div: 16.0ms (15.6% of total)
ival-add: 15.0ms (14.7% of total)
adjust: 10.0ms (9.8% of total)
const: 9.0ms (8.8% of total)
ival-cos: 6.0ms (5.9% of total)
ival-sin: 6.0ms (5.9% of total)
ival-pow2: 6.0ms (5.9% of total)
ival-tan: 5.0ms (4.9% of total)
ival-sub: 4.0ms (3.9% of total)
exact: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series49.0ms (0.4%)

Memory
-14.4MiB live, 75.7MiB allocated
Counts
25 → 110
Calls
Call 1
Inputs
(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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(/.f64 (sin.f64 x) (cos.f64 x))
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
#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))
(*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(cos.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
Outputs
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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))))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ eps (* 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))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ 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)))
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(- (/ (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) (* (cos x) (cos (+ eps x))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(cos x)
(* (cos x) (cos (+ eps x)))
(pow (cos x) 2)
(- (/ (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)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (* eps (- 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 (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (/ 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)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* (cos x) (cos (- x (* -1 eps))))
Calls

6 calls:

TimeVariablePointExpression
14.0ms
x
@inf
((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) 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) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (- (tan (+ x eps)) (tan x)) (cos x) (* (cos (+ eps x)) (cos x)) (pow (cos x) 2))
7.0ms
eps
@-inf
((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) 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) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (- (tan (+ x eps)) (tan x)) (cos x) (* (cos (+ eps x)) (cos x)) (pow (cos x) 2))
7.0ms
eps
@0
((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) 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) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (- (tan (+ x eps)) (tan x)) (cos x) (* (cos (+ eps x)) (cos x)) (pow (cos x) 2))
7.0ms
x
@-inf
((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) 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) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (- (tan (+ x eps)) (tan x)) (cos x) (* (cos (+ eps x)) (cos x)) (pow (cos x) 2))
6.0ms
x
@0
((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) 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) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (- (tan (+ x eps)) (tan x)) (cos x) (* (cos (+ eps x)) (cos x)) (pow (cos x) 2))

simplify175.0ms (1.4%)

Memory
42.3MiB live, 220.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04902271
115642155
258122066
081761945
Stop Event
iter limit
node limit
Counts
110 → 108
Calls
Call 1
Inputs
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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))))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ eps (* 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))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ 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)))
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(- (/ (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) (* (cos x) (cos (+ eps x))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(cos x)
(* (cos x) (cos (+ eps x)))
(pow (cos x) 2)
(- (/ (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)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (* eps (- 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 (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (/ 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)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* (cos x) (cos (- x (* -1 eps))))
Outputs
-1/2
#s(literal -1/2 binary64)
(- (* -4/3 (pow x 2)) 1/2)
(-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -17/9 binary64) (*.f64 x x)) #s(literal 4/3 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(-.f64 (*.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -248/135 binary64) (*.f64 x x)) #s(literal 17/9 binary64)) x) x) #s(literal 4/3 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))
(* -5/6 (pow x 2))
(*.f64 #s(literal -5/6 binary64) (*.f64 x x))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(*.f64 (*.f64 (-.f64 (*.f64 #s(literal -13/18 binary64) (*.f64 x x)) #s(literal 5/6 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(*.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -10/27 binary64) (*.f64 x x)) #s(literal 13/18 binary64)) x) x) #s(literal 5/6 binary64)) (*.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
(*.f64 (-.f64 (*.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -373/1890 binary64) (*.f64 x x)) #s(literal 10/27 binary64)) x) x) #s(literal 13/18 binary64)) (*.f64 x x)) #s(literal 5/6 binary64)) (*.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(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))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(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
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -2/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(-.f64 (*.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 #s(literal -17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64)) x) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (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 (/.f64 (fma.f64 (*.f64 (sin.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)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (*.f64 (neg.f64 x) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (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)))) #s(literal 1/2 binary64)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -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 (+.f64 (/.f64 (fma.f64 (*.f64 (sin.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)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (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 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (*.f64 (neg.f64 x) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (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)))) #s(literal 1/6 binary64)))) 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)))
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)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.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))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 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 #s(literal 2/3 binary64) eps) (*.f64 x x) 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 -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.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))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (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))
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 x x) #s(literal 2/45 binary64)) x) x) #s(literal 1/3 binary64)) (*.f64 x x))
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (*.f64 #s(literal 1/3 binary64) eps))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/9 binary64) (*.f64 #s(literal 4/3 binary64) eps)) x) x (*.f64 #s(literal 1/3 binary64) eps))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 248/135 binary64) (*.f64 #s(literal 17/9 binary64) eps)) x) x (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(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 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(-.f64 (neg.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64))
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))
(- (/ (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)))
(fma.f64 (/.f64 eps x) x x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(*.f64 (-.f64 (neg.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) eps)
(cos x)
(cos.f64 x)
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(- (/ (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 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (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 (fma.f64 (/.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)) (sin.f64 x) (*.f64 (neg.f64 eps) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* 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 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/3 binary64)))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)))) eps (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (* 1/3 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (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 (fma.f64 (/.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)) (sin.f64 x) (*.f64 (neg.f64 eps) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(*.f64 (/.f64 (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 x) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/2 binary64))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 x) (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps 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)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

rewrite232.0ms (1.9%)

Memory
-23.6MiB live, 312.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049380
092361
1365292
23063292
08140277
Stop Event
iter limit
node limit
iter limit
Counts
25 → 453
Calls
Call 1
Inputs
(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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(/.f64 (sin.f64 x) (cos.f64 x))
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
#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))
(*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(cos.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
Outputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
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(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x)) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 eps x))))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 eps x)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 eps x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (+.f64 eps x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 eps x))))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 eps x)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 (+.f64 eps x))))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 (+.f64 eps x)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal -2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 eps x)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 eps x)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (+.f64 eps x)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 eps x))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) (neg.f64 x))) (cos.f64 (-.f64 (+.f64 eps x) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (+.f64 eps x)))) (cos.f64 (-.f64 x (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 2 binary64))
(+.f64 (/.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (fabs.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (fabs.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (fabs.f64 (cos.f64 x)) (fabs.f64 (cos.f64 x)))
(*.f64 (exp.f64 (log.f64 (cos.f64 x))) (exp.f64 (log.f64 (cos.f64 x))))
(*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) (cos.f64 x))
(pow.f64 (fabs.f64 (cos.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (PI.f64)))) (sin.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (PI.f64) x))) (sin.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (PI.f64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (neg.f64 x) (PI.f64)))) (sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (neg.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (PI.f64) x))) (sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (PI.f64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (cos.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)))) (cos.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)))) (cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (neg.f64 x) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (neg.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (PI.f64) x))) (cos.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 (PI.f64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (PI.f64) x))) (cos.f64 (-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (PI.f64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (PI.f64) x) (+.f64 (neg.f64 x) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (PI.f64) x) (+.f64 (neg.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (PI.f64) x) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 (PI.f64) x) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (PI.f64) x) (+.f64 (PI.f64) x))) (cos.f64 (-.f64 (+.f64 (PI.f64) x) (+.f64 (PI.f64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) x)) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) x)) (cos.f64 (-.f64 (neg.f64 x) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (sin.f64 x)))))
(-.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (neg.f64 x) (PI.f64))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 x))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (PI.f64) x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (cos.f64 x)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

eval333.0ms (2.7%)

Memory
-1.1MiB live, 527.3MiB allocated
Compiler

Compiled 84 341 to 7 657 computations (90.9% saved)

prune23.0ms (0.2%)

Memory
17.3MiB live, 64.6MiB allocated
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1 21271 219
Fresh202
Picked505
Done011
Total1 21981 227
Accuracy
100.0%
Counts
1 227 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
63.3%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
63.2%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
100.0%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
Compiler

Compiled 399 to 256 computations (35.8% saved)

simplify183.0ms (1.5%)

Memory
27.8MiB live, 169.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 eps x)
cost-diff0
(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff0
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
cost-diff4
(-.f64 (+.f64 eps x) x)
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
cost-diff2
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
cost-diff3
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
cost-diff4
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
cost-diff0
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
cost-diff0
(fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)
cost-diff0
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
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-diff0
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff0
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057498
091469
1182439
2488433
31935428
47186428
08363419
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
#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
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
eps
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps)
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
#s(literal 2/45 binary64)
eps
(*.f64 #s(literal -1/3 binary64) eps)
#s(literal -1/3 binary64)
(*.f64 eps #s(literal -2/3 binary64))
#s(literal -2/3 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(sin.f64 (-.f64 (+.f64 eps x) x))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
(cos.f64 x)
#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
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
eps
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps)
(fma.f64 (*.f64 eps (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))) (*.f64 x x) eps)
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
(*.f64 eps (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
(*.f64 #s(literal 17/45 binary64) eps)
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
(*.f64 #s(literal -13/45 binary64) eps)
#s(literal 2/45 binary64)
eps
(*.f64 #s(literal -1/3 binary64) eps)
#s(literal -1/3 binary64)
(*.f64 eps #s(literal -2/3 binary64))
(*.f64 #s(literal -2/3 binary64) eps)
#s(literal -2/3 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(sin.f64 eps)
(-.f64 (+.f64 eps x) x)
eps
(+.f64 eps x)
(+.f64 x eps)
eps
x
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize220.0ms (1.8%)

Memory
-22.7MiB live, 256.7MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy0.12848103160136612
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0.15234375
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
accuracy23.426843462287888
(-.f64 (+.f64 eps x) x)
accuracy0.2734375
(*.f64 eps #s(literal -2/3 binary64))
accuracy0.2734375
(*.f64 #s(literal 2/3 binary64) eps)
accuracy0.3299018916517782
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
accuracy0.4296875
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
accuracy0.0
(*.f64 x x)
accuracy0.1831094138497632
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
accuracy0.2734375
(*.f64 #s(literal 2/3 binary64) eps)
accuracy0.3299018916517782
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
accuracy0.0
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
accuracy0.0
(*.f64 x x)
accuracy0.3299018916517782
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
accuracy0.7252611781214494
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy0.0
(cos.f64 x)
accuracy0.0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy0.0078125
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy0.0078125
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
Samples
90.0ms171×0valid
68.0ms85×1valid
Compiler

Compiled 334 to 50 computations (85% saved)

Precisions
Click to see histograms. Total time spent on operations: 131.0ms
ival-mult: 30.0ms (23% of total)
ival-add: 26.0ms (19.9% of total)
ival-sub: 25.0ms (19.2% of total)
const: 17.0ms (13% of total)
adjust: 9.0ms (6.9% of total)
ival-pow2: 6.0ms (4.6% of total)
ival-sin: 5.0ms (3.8% of total)
ival-div: 4.0ms (3.1% of total)
ival-tan: 4.0ms (3.1% of total)
ival-cos: 4.0ms (3.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series39.0ms (0.3%)

Memory
-16.1MiB live, 44.0MiB allocated
Counts
26 → 80
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#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)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
(cos.f64 x)
(*.f64 #s(literal 2/3 binary64) eps)
(*.f64 eps #s(literal -2/3 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (- (/ (* x (* (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))))))
(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 (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* 2/3 (* eps (pow x 2))))
(* 2/3 eps)
(+ (* 2/3 eps) (* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps))))
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/24 (pow x 2))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (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))
(* 2/3 (* eps (pow x 4)))
(* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
x
(* x (+ 1 (/ eps x)))
(cos x)
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -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 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* 17/45 eps)
(* -13/45 eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* -2/3 eps)
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
11.0ms
eps
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (- (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)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (cos x) (* 2/3 eps) (* eps -2/3) (* 1/24 (* x x)) (cos x) (* (cos (+ eps x)) (cos x)))
11.0ms
eps
@0
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (- (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)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (cos x) (* 2/3 eps) (* eps -2/3) (* 1/24 (* x x)) (cos x) (* (cos (+ eps x)) (cos x)))
5.0ms
eps
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (- (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)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (cos x) (* 2/3 eps) (* eps -2/3) (* 1/24 (* x x)) (cos x) (* (cos (+ eps x)) (cos x)))
5.0ms
x
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (- (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)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (cos x) (* 2/3 eps) (* eps -2/3) (* 1/24 (* x x)) (cos x) (* (cos (+ eps x)) (cos x)))
3.0ms
x
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (- (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)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* eps -2/3)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (cos x) (* 2/3 eps) (* eps -2/3) (* 1/24 (* x x)) (cos x) (* (cos (+ eps x)) (cos x)))

simplify147.0ms (1.2%)

Memory
3.1MiB live, 137.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03571496
111731407
243211350
083031278
Stop Event
iter limit
node limit
Counts
80 → 78
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (- (/ (* x (* (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))))))
(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 (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* 2/3 (* eps (pow x 2))))
(* 2/3 eps)
(+ (* 2/3 eps) (* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps))))
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/24 (pow x 2))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (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))
(* 2/3 (* eps (pow x 4)))
(* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
x
(* x (+ 1 (/ eps x)))
(cos x)
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -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 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* 17/45 eps)
(* -13/45 eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* -2/3 eps)
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(* -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)))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 x (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.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))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.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 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (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 (/.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 (sin.f64 eps) x) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) 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 (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 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (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)))) #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))))))
(*.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) #s(literal 1 binary64))) 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 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #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))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (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))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(*.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) #s(literal 1 binary64))) eps)
(+ eps (* 2/3 (* eps (pow x 2))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(+ (* 2/3 eps) (* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps))))
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(+ eps x)
(+.f64 x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* 1/24 (pow x 2))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* 2/3 (* eps (pow x 4)))
(*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 2/3 binary64))
(* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) eps (/.f64 eps (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) eps (+.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (/.f64 eps (*.f64 x x)))) (pow.f64 x #s(literal 4 binary64)))
(* 2/3 (* eps (pow x 2)))
(*.f64 (*.f64 #s(literal 2/3 binary64) (*.f64 x x)) eps)
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) eps (/.f64 eps (*.f64 x x))) x) x)
(* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps)))
(*.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) eps))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 #s(literal -13/45 binary64) eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) x) x)
x
(* x (+ 1 (/ eps x)))
(fma.f64 (/.f64 eps x) x x)
(cos x)
(cos.f64 x)
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(*.f64 (/.f64 (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 x) (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (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 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)) (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* 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 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/3 binary64)))) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(*.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) #s(literal 1 binary64))) eps)
(* eps (+ 1 (* 2/3 (pow x 2))))
(*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* -13/45 eps)
(*.f64 #s(literal -13/45 binary64) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(* -2/3 eps)
(*.f64 #s(literal -2/3 binary64) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (-.f64 (*.f64 #s(literal -2/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 #s(literal -2/3 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 #s(literal -17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite240.0ms (1.9%)

Memory
12.9MiB live, 157.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057345
091333
1391281
23235281
08252278
Stop Event
iter limit
node limit
iter limit
Counts
26 → 313
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#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)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64)))
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
(-.f64 (+.f64 eps x) x)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(sin.f64 (-.f64 (+.f64 eps x) x))
(+.f64 eps x)
(cos.f64 x)
(*.f64 #s(literal 2/3 binary64) eps)
(*.f64 eps #s(literal -2/3 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
Outputs
(*.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) x)) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal -2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps))))) #s(literal 2 binary64))
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(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 x eps) x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))))))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(fma.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(-.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (cos.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x eps) x)))) (*.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (sin.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x eps) x)))))
(-.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (*.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (-.f64 x eps))) (*.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (+.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 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 x))) (sqrt.f64 (neg.f64 (neg.f64 x))) eps)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) eps)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(+.f64 x eps)
(+.f64 eps x)
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))
(pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (cosh.f64 (log.f64 (cos.f64 x))) (sinh.f64 (log.f64 (cos.f64 x))))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 #s(literal 2/3 binary64) eps)
(*.f64 eps #s(literal 2/3 binary64))
(*.f64 #s(literal -2/3 binary64) eps)
(*.f64 eps #s(literal -2/3 binary64))
(*.f64 (*.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 x (*.f64 #s(literal 1/24 binary64) x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))

eval98.0ms (0.8%)

Memory
12.9MiB live, 113.7MiB allocated
Compiler

Compiled 21 721 to 2 667 computations (87.7% saved)

prune43.0ms (0.3%)

Memory
-14.9MiB live, 30.2MiB allocated
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New5375542
Fresh202
Picked325
Done011
Total5428550
Accuracy
100.0%
Counts
550 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
99.5%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
Compiler

Compiled 354 to 235 computations (33.6% saved)

simplify117.0ms (0.9%)

Memory
22.3MiB live, 164.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff0
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
cost-diff0
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff0
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
cost-diff0
(fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
cost-diff0
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)
cost-diff0
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
cost-diff0
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff0
(+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)))
cost-diff0
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
cost-diff1
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
cost-diff0
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff0
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055500
084492
1158476
2448476
32045476
46483476
08053472
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
(+.f64 #s(literal 1 binary64) #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
eps
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
eps
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) 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))
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
(+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)))
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
eps
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(*.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(sin.f64 eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(cos.f64 (+.f64 x eps))
(+.f64 x eps)

localize177.0ms (1.4%)

Memory
-32.0MiB live, 204.7MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy0.01171875
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
accuracy0.12848103160136612
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0.15234375
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
accuracy0.0
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy0.0078125
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
accuracy0.0078125
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy0.29987662972197304
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy0.00390625
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
accuracy0.1310152312612826
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
accuracy0.27734375
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
accuracy0.3299018916517782
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
accuracy0.0
(*.f64 x x)
accuracy0.01171875
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
accuracy0.3299018916517782
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
accuracy0.7252611781214494
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy0.0078125
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy0.0078125
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy0.12848103160136612
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0.15234375
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
Samples
83.0ms171×0valid
56.0ms85×1valid
Compiler

Compiled 319 to 50 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 108.0ms
ival-add: 36.0ms (33.4% of total)
ival-mult: 18.0ms (16.7% of total)
const: 11.0ms (10.2% of total)
adjust: 9.0ms (8.4% of total)
ival-div: 7.0ms (6.5% of total)
ival-sin: 7.0ms (6.5% of total)
ival-cos: 6.0ms (5.6% of total)
ival-pow2: 6.0ms (5.6% of total)
ival-sub: 4.0ms (3.7% of total)
ival-tan: 4.0ms (3.7% of total)
exact: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series26.0ms (0.2%)

Memory
43.1MiB live, 43.1MiB allocated
Counts
24 → 91
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
(+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 x x)
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
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))))))
(+ (* 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 (* (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))))))
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(* 1/24 (pow x 2))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 2/3 eps)
(+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))
2/3
(+ 2/3 (* 17/45 (pow x 2)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps 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))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 17/45 (* eps (pow x 6)))
(* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))
(* 17/45 (* eps (pow x 4)))
(* (pow x 4) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(/ (sin eps) (cos x))
(cos x)
(* 17/45 (* eps (pow x 2)))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -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 x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)))
(/ (sin (neg (* -1 eps))) (cos x))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
eps
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (- (tan (+ x eps)) (tan x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* x x)) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ x eps))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (* 1/24 (* x x)) (cos x) (* x x) (* (+ (* 17/45 (* x x)) 2/3) eps) (+ (* 17/45 (* x x)) 2/3) (cos x))
5.0ms
eps
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (- (tan (+ x eps)) (tan x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* x x)) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ x eps))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (* 1/24 (* x x)) (cos x) (* x x) (* (+ (* 17/45 (* x x)) 2/3) eps) (+ (* 17/45 (* x x)) 2/3) (cos x))
5.0ms
eps
@0
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (- (tan (+ x eps)) (tan x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* x x)) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ x eps))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (* 1/24 (* x x)) (cos x) (* x x) (* (+ (* 17/45 (* x x)) 2/3) eps) (+ (* 17/45 (* x x)) 2/3) (cos x))
4.0ms
x
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (- (tan (+ x eps)) (tan x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* x x)) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ x eps))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (* 1/24 (* x x)) (cos x) (* x x) (* (+ (* 17/45 (* x x)) 2/3) eps) (+ (* 17/45 (* x x)) 2/3) (cos x))
4.0ms
x
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (- (tan (+ x eps)) (tan x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* x x)) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ x eps))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (* 1/24 (* x x)) (cos x) (* x x) (* (+ (* 17/45 (* x x)) 2/3) eps) (+ (* 17/45 (* x x)) 2/3) (cos x))

simplify233.0ms (1.9%)

Memory
-72.3MiB live, 155.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03971781
113381692
250831621
084721517
Stop Event
iter limit
node limit
Counts
91 → 90
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
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))))))
(+ (* 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 (* (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))))))
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(* 1/24 (pow x 2))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 2/3 eps)
(+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))
2/3
(+ 2/3 (* 17/45 (pow x 2)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps 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))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 17/45 (* eps (pow x 6)))
(* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))
(* 17/45 (* eps (pow x 4)))
(* (pow x 4) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(/ (sin eps) (cos x))
(cos x)
(* 17/45 (* eps (pow x 2)))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -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 x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)))
(/ (sin (neg (* -1 eps))) (cos x))
Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 x (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
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(* 1/24 (pow x 2))
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#s(literal 2/3 binary64)
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(pow (cos x) 2)
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(*.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (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 (fma.f64 (/.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)) (sin.f64 x) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* 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 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/3 binary64) (*.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))))) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(*.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps)
(* eps (+ 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)) eps)
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) (cos.f64 x))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64)) (cos.f64 x)) (/.f64 eps (cos.f64 x)))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (cos.f64 x)) (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) (cos.f64 x))) (/.f64 eps (cos.f64 x)))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(* -1 (* eps (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal -2/3 binary64) x) x (*.f64 #s(literal -17/45 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)))
(*.f64 (neg.f64 eps) (-.f64 (fma.f64 (*.f64 #s(literal -2/3 binary64) x) x (*.f64 #s(literal -17/45 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)))
(/ (sin (neg (* -1 eps))) (cos x))
(/.f64 (sin.f64 eps) (cos.f64 x))

rewrite227.0ms (1.8%)

Memory
4.5MiB live, 197.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055370
084362
1359320
23035320
011684318
Stop Event
iter limit
node limit
iter limit
Counts
24 → 321
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
(+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 x x)
(*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
Outputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(/.f64 (-.f64 (*.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x eps) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 x eps) (neg.f64 x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (+.f64 (sin.f64 eps) (sin.f64 (+.f64 (+.f64 x eps) x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x eps) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 x eps) (neg.f64 x)))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (+.f64 (sin.f64 eps) (sin.f64 (+.f64 (+.f64 x eps) x))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 x eps) x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) #s(literal 0 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 2 binary64))) (neg.f64 (sin.f64 eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) #s(literal 0 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) #s(literal 0 binary64)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))))))
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps)))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 (cos.f64 eps) #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 x) (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(fma.f64 #s(literal 1 binary64) (sin.f64 eps) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(fma.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(sin.f64 eps)
(-.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (cos.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x eps) x)))) (*.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (sin.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x eps) x)))))
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(fma.f64 eps #s(literal 2/3 binary64) (*.f64 eps (*.f64 #s(literal 17/45 binary64) (*.f64 x x))))
(+.f64 (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))) (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps))
(+.f64 (*.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) eps) (*.f64 #s(literal 2/3 binary64) eps))
(+.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) eps))
(+.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps))
(+.f64 (*.f64 eps (*.f64 #s(literal 17/45 binary64) (*.f64 x x))) (*.f64 eps #s(literal 2/3 binary64)))
(+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 eps (*.f64 #s(literal 17/45 binary64) (*.f64 x x))))
(+.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
(+.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 0 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64)) #s(literal 4/9 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64)) (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))))
(/.f64 (-.f64 #s(literal 4/9 binary64) (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 17/45 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 4/9 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4913/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 8/27 binary64))) (neg.f64 (fma.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 4/9 binary64)) (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64)))
(/.f64 (fma.f64 #s(literal 4913/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 8/27 binary64)) (+.f64 #s(literal 4/9 binary64) (-.f64 (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 34/135 binary64)))))
(/.f64 (fma.f64 #s(literal 4913/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 8/27 binary64)) (fma.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64)))))
(fma.f64 (fabs.f64 (*.f64 #s(literal 17/45 binary64) (neg.f64 x))) x #s(literal 2/3 binary64))
(fma.f64 (fabs.f64 (*.f64 #s(literal 17/45 binary64) x)) x #s(literal 2/3 binary64))
(fma.f64 (*.f64 #s(literal 17/45 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 2/3 binary64))
(fma.f64 (*.f64 #s(literal 17/45 binary64) x) x #s(literal 2/3 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
(fma.f64 x (fabs.f64 (*.f64 (neg.f64 x) #s(literal 17/45 binary64))) #s(literal 2/3 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal 17/45 binary64) x)) #s(literal 2/3 binary64))
(fma.f64 x (*.f64 #s(literal 17/45 binary64) x) #s(literal 2/3 binary64))
(-.f64 (/.f64 (*.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))) (/.f64 #s(literal 4/9 binary64) (-.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))))
(-.f64 #s(literal 2/3 binary64) (*.f64 (neg.f64 (*.f64 #s(literal 17/45 binary64) x)) x))
(-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal -17/45 binary64) (*.f64 x x)))
(-.f64 #s(literal 2/3 binary64) (*.f64 (neg.f64 (*.f64 x x)) #s(literal 17/45 binary64)))
(+.f64 (/.f64 (*.f64 #s(literal 4913/91125 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64))))) (/.f64 #s(literal 8/27 binary64) (fma.f64 #s(literal 289/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64))))))
(+.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))
(+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 17/45 binary64) (*.f64 x x)))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))

eval77.0ms (0.6%)

Memory
-3.3MiB live, 186.5MiB allocated
Compiler

Compiled 23 220 to 2 544 computations (89% saved)

prune83.0ms (0.7%)

Memory
0.1MiB live, 45.7MiB allocated
Pruning

10 alts after pruning (5 fresh and 5 done)

PrunedKeptTotal
New5765581
Fresh000
Picked325
Done033
Total57910589
Accuracy
100.0%
Counts
589 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
99.6%
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
63.4%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
31.0%
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 eps eps)))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x x #s(literal 1 binary64))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
Compiler

Compiled 948 to 344 computations (63.7% saved)

regimes20.0ms (0.2%)

Memory
0.9MiB live, 48.0MiB allocated
Counts
25 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (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(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 eps eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.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))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 (fma.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 -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
Calls

3 calls:

7.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms
x
6.0ms
eps
Results
AccuracySegmentsBranch
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory
14.7MiB live, 14.8MiB allocated
Counts
18 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (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(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 eps eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
Calls

3 calls:

5.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (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(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 eps eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
Outputs
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
Calls

3 calls:

3.0ms
x
3.0ms
eps
3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (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(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 eps eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) eps)))
Calls

3 calls:

3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes35.0ms (0.3%)

Memory
-48.9MiB live, 7.3MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (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(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
Calls

3 calls:

32.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
8.2MiB live, 8.2MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x x #s(literal 1 binary64))) eps))
Calls

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory
7.5MiB live, 7.5MiB 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 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #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
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify44.0ms (0.4%)

Memory
4.9MiB live, 49.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
060170
188162
2181162
3649162
43276162
Stop Event
node limit
Calls
Call 1
Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) 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 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 x x) eps) (*.f64 x x) 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 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) #s(literal 1 binary64)) eps))

soundness1.0s (8.4%)

Memory
5.4MiB live, 624.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157970
1488910
21845849
08454797
0616
01016
15316
244016
3660816
0858816
03971781
113381692
250831621
084721517
03571496
111731407
243211350
083031278
04902271
115642155
258122066
081761945
057345
091333
1391281
23235281
08252278
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 526 to 270 computations (48.7% saved)

preprocess52.0ms (0.4%)

Memory
0.1MiB live, 45.3MiB allocated
Compiler

Compiled 376 to 146 computations (61.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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