Details

Time bar (total: 17.9s)

analyze1.4s (7.6%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
0%0%100%0%0%0%0%4
0%0%100%0%0%0%0%5
0%0%100%0%0%0%0%6
0%0%100%0%0%0%0%7
0%0%100%0%0%0%0%8
0%0%100%0%0%0%0%9
0%0%100%0%0%0%0%10
0%0%100%0%0%0%0%11
0%0%100%0%0%0%0%12
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.4s (52.6%)

Results
6.0s2026×body2048valid
2.0s3127×body1024valid
854.0ms1527×body512valid
424.0ms1456×body256valid
168.0ms120×body4096valid
Bogosity

preprocess129.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
583×fma-neg_binary64
430×fma-def_binary64
418×div-sub_binary64
334×times-frac_binary64
156×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11414
22414
34114
47514
513014
626014
754614
8142014
9256614
10339214
11375714
12388614
13391314
14392314
15392714
16392714
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Outputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify132.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
583×fma-neg_binary64
430×fma-def_binary64
418×div-sub_binary64
334×times-frac_binary64
156×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11414
22414
34114
47514
513014
626014
754614
8142014
9256614
10339214
11375714
12388614
13391314
14392314
15392714
16392714
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Outputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))

eval1.0ms (0%)

Compiler

Compiled 19 to 9 computations (52.6% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
33.1b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Compiler

Compiled 10 to 6 computations (40% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

NewErrorProgram
1.6b
(-.f64 (tan.f64 x) x)
1.6b
(-.f64 (sin.f64 x) x)
0.0b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓0.0b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓1.6b
(-.f64 (sin.f64 x) x)
✓1.6b
(-.f64 (tan.f64 x) x)
Compiler

Compiled 23 to 6 computations (73.9% saved)

series7.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(-.f64 (tan.f64 x) x)
1.0ms
x
@inf
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
1.0ms
x
@-inf
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
1.0ms
x
@0
(-.f64 (tan.f64 x) x)
1.0ms
x
@-inf
(-.f64 (tan.f64 x) x)

rewrite170.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
990×prod-diff_binary64
472×log-prod_binary64
339×fma-def_binary64
251×pow2_binary64
227×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0726
116926
2274526
Stop Event
1×node limit
Counts
3 → 417
Calls
Call 1
Inputs
(-.f64 (tan.f64 x) x)
(-.f64 (sin.f64 x) x)
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (tan.f64 x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (tan.f64 x) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tan.f64 x) x) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tan.f64 x) x) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tan.f64 x) x) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tan.f64 x) x) (fma.f64 -1 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tan.f64 x) x) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (tan.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (tan.f64 x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (tan.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (tan.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (tan.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2) (cbrt.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (tan.f64 x) x)) (sqrt.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)) (/.f64 1 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2)) (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3)) (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)) (+.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3))) (neg.f64 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (neg.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 (tan.f64 x) 2) (-.f64 (pow.f64 (neg.f64 x) 2) (*.f64 (tan.f64 x) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (neg.f64 x) 2)) (-.f64 (tan.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (tan.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (tan.f64 x) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (tan.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (tan.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2)) (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (tan.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (tan.f64 x))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (tan.f64 x)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (tan.f64 x))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (tan.f64 x))) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (tan.f64 x)) (/.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (tan.f64 x))) (/.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 x)) (exp.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 1 (expm1.f64 (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 x)) (+.f64 1 (expm1.f64 (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (tan.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 x) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (tan.f64 x) 1 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (tan.f64 x) 1 (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (tan.f64 x) x) 1 (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (tan.f64 x) x) 1 (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (tan.f64 x) x) 1 (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sin.f64 x) (/.f64 1 (cos.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sin.f64 x) (/.f64 1 (cos.f64 x)) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (tan.f64 x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (tan.f64 x) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (tan.f64 x) x) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (tan.f64 x) x) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (tan.f64 x) x) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 x) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (tan.f64 x)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (tan.f64 x)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (tan.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (tan.f64 x)) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (neg.f64 (cbrt.f64 x)) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x 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x)) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (tan.f64 x) x)) (sqrt.f64 (-.f64 (tan.f64 x) x)) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (tan.f64 x) x)) (sqrt.f64 (-.f64 (tan.f64 x) x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (tan.f64 x) x)) (sqrt.f64 (-.f64 (tan.f64 x) x)) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2))) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2))) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 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(cbrt.f64 (/.f64 (sin.f64 x) (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sin.f64 x) (-.f64 (tan.f64 x) x))) (sqrt.f64 (/.f64 (sin.f64 x) (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 x)) (-.f64 (tan.f64 x) x)) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sin.f64 x)) 1) (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 (tan.f64 x) x)) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2)) (/.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) 2)) (/.f64 (sqrt.f64 (sin.f64 x)) (cbrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (-.f64 (tan.f64 x) x))) (/.f64 (sin.f64 x) (sqrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 (-.f64 (tan.f64 x) x))) (/.f64 (cbrt.f64 (sin.f64 x)) (sqrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (-.f64 (tan.f64 x) x))) (/.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (-.f64 (tan.f64 x) x))) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sin.f64 x) (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3))) (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2)) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sin.f64 x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (+.f64 x (tan.f64 x)) (neg.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))))

simplify78.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
597×div-sub_binary64
510×times-frac_binary64
489×fma-def_binary64
284×associate-/l*_binary64
218×distribute-neg-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0100698
1295610
2964576
34842548
Stop Event
1×node limit
Counts
453 → 455
Calls
Call 1
Inputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (*.f64 62/2835 (pow.f64 x 9)) (*.f64 2/15 (pow.f64 x 5)))))
(*.f64 -1 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(*.f64 -1/6 (pow.f64 x 3))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 1/120 (pow.f64 x 5)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 -1/5040 (pow.f64 x 7))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/362880 (pow.f64 x 9)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 -1/5040 (pow.f64 x 7)))))
(*.f64 -1 x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (sin.f64 x) (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (sin.f64 x) (*.f64 -1 x))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))) 1/2)
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) (pow.f64 x 2)))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
1
(+.f64 1 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 x 2)))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 (*.f64 -1 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 x 2)))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
Outputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5)))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 2/15 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (*.f64 17/315 (pow.f64 x 7))))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (*.f64 62/2835 (pow.f64 x 9)) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 62/2835 (pow.f64 x 9) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (*.f64 62/2835 (pow.f64 x 9)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) (*.f64 62/2835 (pow.f64 x 9)))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(*.f64 -1/6 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/6)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 1/120 (pow.f64 x 5)))
(fma.f64 -1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 1/120))
(fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 5) 1/120))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 -1/5040 (pow.f64 x 7))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) (*.f64 (pow.f64 x 7) -1/5040)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 1/120 (*.f64 (pow.f64 x 7) -1/5040)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/362880 (pow.f64 x 9)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 -1/5040 (pow.f64 x 7)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/362880 (pow.f64 x 9) (fma.f64 1/120 (pow.f64 x 5) (*.f64 (pow.f64 x 7) -1/5040))))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 9) 1/362880 (fma.f64 (pow.f64 x 5) 1/120 (*.f64 (pow.f64 x 7) -1/5040))))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) -1/5040 (*.f64 (pow.f64 x 9) 1/362880))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) (*.f64 -1 x))
(+.f64 (neg.f64 x) (sin.f64 x))
(-.f64 (sin.f64 x) x)
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 x 9/40) -1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 x (*.f64 x 9/40) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 27/112000 (pow.f64 x 6)))) -1/2)
(fma.f64 x (*.f64 x 9/40) (fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 27/112000 (pow.f64 x 6) -1/2)))
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(+.f64 1 (-.f64 (/.f64 (neg.f64 (sin.f64 x)) x) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(-.f64 1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))
(-.f64 (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(+.f64 1 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(fma.f64 -1 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)) 1)
(+.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (*.f64 x x)) (/.f64 -1 x))))
(+.f64 1 (*.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) (pow.f64 x 2)))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 x 3))) (+.f64 1 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 x 3)) (fma.f64 -1 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)) 1))
(+.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 x x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(+.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 -1 (*.f64 x x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 x 3)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 1 (-.f64 (/.f64 (neg.f64 (sin.f64 x)) x) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(-.f64 1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))
(+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 x 2)))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 1 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(fma.f64 -1 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)) 1)
(+.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (*.f64 x x)) (/.f64 -1 x))))
(+.f64 1 (*.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(+.f64 (*.f64 -1 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 x 2)))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
(+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 x 3))) (+.f64 1 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 x 3)) (fma.f64 -1 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)) 1))
(+.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 x x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(+.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 -1 (*.f64 x x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 x 3)))))

eval193.0ms (1.1%)

Compiler

Compiled 16335 to 4913 computations (69.9% saved)

prune65.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4487455
Fresh000
Picked011
Done000
Total4488456
Error
0b
Counts
456 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
30.3b
-1/2
✓33.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
▶45.8b
(*.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (+.f64 x (tan.f64 x)))
▶30.3b
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
▶29.6b
(fma.f64 x (*.f64 x 9/40) -1/2)
▶33.8b
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
34.3b
1
▶33.2b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
Compiler

Compiled 138 to 96 computations (30.4% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x 9/40)
0.0b
(fma.f64 x (*.f64 x 9/40) -1/2)
✓0.0b
(fma.f64 x (*.f64 x 9/40) -1/2)
✓0.1b
(*.f64 x 9/40)
Compiler

Compiled 13 to 9 computations (30.8% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 x 9/40)
1.0ms
x
@-inf
(fma.f64 x (*.f64 x 9/40) -1/2)
1.0ms
x
@0
(*.f64 x 9/40)
0.0ms
x
@inf
(fma.f64 x (*.f64 x 9/40) -1/2)
0.0ms
x
@-inf
(*.f64 x 9/40)

rewrite62.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
534×pow1_binary64
522×add-sqr-sqrt_binary64
497×add-log-exp_binary64
497×log1p-expm1-u_binary64
497×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0612
112212
2132712
Stop Event
1×node limit
Counts
2 → 32
Calls
Call 1
Inputs
(*.f64 x 9/40)
(fma.f64 x (*.f64 x 9/40) -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 9/40)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 9/40) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 9/40) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 9/40)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 9/40)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x 9/40) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 9/40))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 9/40) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 9/40)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (*.f64 x (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 9/40)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 3) -1/8) (+.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) (-.f64 1/4 (*.f64 (*.f64 x (*.f64 x 9/40)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))))

simplify159.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
559×fabs-mul_binary64
523×pow-sqr_binary64
450×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010135
120135
230135
351135
4116135
5349135
61281135
72180135
82344135
92528135
102736135
113034135
123427135
133908135
144476135
155168135
166007135
176401135
186689135
196967135
207039135
217073135
Stop Event
1×node limit
Counts
56 → 38
Calls
Call 1
Inputs
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
Outputs
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.6b
(-.f64 (sin.f64 x) x)
0.0b
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
✓0.0b
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
1.6b
(-.f64 (sin.f64 x) x)
Compiler

Compiled 17 to 5 computations (70.6% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
1.0ms
x
@inf
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
0.0ms
x
@-inf
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))

rewrite47.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
771×pow1_binary64
723×add-log-exp_binary64
722×log1p-expm1-u_binary64
722×expm1-log1p-u_binary64
706×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0611
11419
224139
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sin.f64 x) x) (neg.f64 (/.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sin.f64 x) x) (/.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sin.f64 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (*.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (+.f64 x (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 x (sin.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 x (sin.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) -1) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) -1) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 x (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 x (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))))

simplify68.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
628×associate-/l/_binary64
478×distribute-lft-out_binary64
469×distribute-rgt-out_binary64
413×unswap-sqr_binary64
360×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
029138
167126
2150126
3460126
42076126
54597126
65386126
77923126
Stop Event
1×node limit
Counts
48 → 47
Calls
Call 1
Inputs
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6))))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 -1/362880 (pow.f64 x 8)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
Outputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 -1/120 (pow.f64 x 4) (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 -1/120 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/120 1/6))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/6 (*.f64 x x) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 -1/120 (pow.f64 x 4) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/120 1/6) (*.f64 1/5040 (pow.f64 x 6)))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 -1/362880 (pow.f64 x 8)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6)))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 -1/362880 (pow.f64 x 8) (fma.f64 1/6 (*.f64 x x) (*.f64 1/5040 (pow.f64 x 6)))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 -1/362880 (pow.f64 x 8)))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/362880 -1/120) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 -1/362880 (pow.f64 x 8)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
13.0b
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
0.2b
(*.f64 9/40 (pow.f64 x 2))
0.1b
(*.f64 -27/2800 (pow.f64 x 4))
0.0b
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓0.0b
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓0.1b
(*.f64 -27/2800 (pow.f64 x 4))
✓0.2b
(*.f64 9/40 (pow.f64 x 2))
✓13.0b
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
Compiler

Compiled 47 to 38 computations (19.1% saved)

series5.0ms (0%)

Counts
4 → 12
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
1.0ms
x
@0
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
0.0ms
x
@inf
(*.f64 -27/2800 (pow.f64 x 4))
0.0ms
x
@0
(*.f64 -27/2800 (pow.f64 x 4))
0.0ms
x
@inf
(*.f64 9/40 (pow.f64 x 2))

rewrite84.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
539×log-prod_binary64
503×fma-def_binary64
344×pow-prod-down_binary64
334×pow2_binary64
274×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01345
129443
2350643
Stop Event
1×node limit
Counts
4 → 180
Calls
Call 1
Inputs
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 -27/2800 (pow.f64 x 4))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 81/1600) (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))) (/.f64 (*.f64 (pow.f64 x 8) 729/7840000) (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 81/1600 (*.f64 (pow.f64 x 8) 729/7840000)) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (pow.f64 x 8) 729/7840000)) (/.f64 1 (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 81/1600 (*.f64 (pow.f64 x 8) 729/7840000)) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4))) (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (pow.f64 x 8) 729/7840000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000)) (-.f64 (fma.f64 (pow.f64 x 4) 81/1600 (*.f64 (pow.f64 x 8) 729/7840000)) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000)) (fma.f64 (pow.f64 x 8) 729/7840000 (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (pow.f64 x 8) 729/7840000)) (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000))) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 4) 81/1600 (*.f64 (pow.f64 x 8) 729/7840000)) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (pow.f64 x 8) 729/7840000))) (neg.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 8) 729/7840000) (*.f64 (pow.f64 x 4) 81/1600)) (fma.f64 -27/2800 (pow.f64 x 4) (neg.f64 (*.f64 9/40 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2)))) (#(struct:change 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x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 9/40 (*.f64 x x) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 9/40) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 9/40) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 9/40 (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 9/40 (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) -27/2800) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 (*.f64 x x)) 1 (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 (*.f64 x x)) 1 (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) -27/2800 (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -27/2800 (pow.f64 x 4)) 1 (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) 1 -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 9/40 (*.f64 x x)) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 9/40 (*.f64 x x)) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -27/2800 (pow.f64 x 4)) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) (*.f64 9/40 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) 9/40) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) 9/40) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (*.f64 (*.f64 (cbrt.f64 x) x) -27/2800) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 9/40 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 81/1600)) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 9/40 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 81/1600)) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81/1600)) (cbrt.f64 (*.f64 9/40 (*.f64 x x))) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81/1600)) (cbrt.f64 (*.f64 9/40 (*.f64 x x))) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 -27/2800 (pow.f64 x 4))) (cbrt.f64 (*.f64 (pow.f64 x 8) 729/7840000)) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 729/7840000)) (cbrt.f64 (*.f64 -27/2800 (pow.f64 x 4))) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 9/40)) (*.f64 x (sqrt.f64 9/40)) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 9/40)) (*.f64 x (sqrt.f64 9/40)) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 -27/2800)) (*.f64 (*.f64 x x) (sqrt.f64 -27/2800)) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 6) 729/64000 (*.f64 (pow.f64 x 12) -19683/21952000000)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 81/1600 (*.f64 (pow.f64 x 8) 729/7840000)) (*.f64 (*.f64 (*.f64 9/40 (*.f64 x x)) -27/2800) (pow.f64 x 4)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 x 4) 81/1600) (*.f64 (pow.f64 x 8) 729/7840000)) (/.f64 1 (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2)) 2) (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2)) (*.f64 9/40 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2)) (sqrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2)) (*.f64 9/40 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 x) x (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 x) x (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 (fma.f64 -27/2800 (pow.f64 x 4) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -27/2800 (*.f64 x x)) (*.f64 x x) (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -27/2800 (pow.f64 (cbrt.f64 x) 8)) (*.f64 (cbrt.f64 x) x) (fma.f64 9/40 (*.f64 x x) -1/2))))))

simplify183.0ms (1%)

Algorithm
1×egg-herbie
Rules
1057×sqr-pow_binary64
538×fma-def_binary64
506×pow-sqr_binary64
443×cube-prod_binary64
410×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015114
129114
252114
3120114
4384114
51425114
62666114
73128114
83297114
93496114
103767114
114124114
124573114
135102114
145726114
156479114
166787114
177013114
187211114
197267114
207289114
Stop Event
1×node limit
Counts
192 → 189
Calls
Call 1
Inputs
(*.f64 9/40 (pow.f64 x 2))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
Outputs
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -27/2800 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -27/2800 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -27/2800 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -27/2800 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -27/2800 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))

localize34.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
0.0b
(exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
0.0b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
0.0b
(log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
✓0.0b
(exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
✓0.0b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
1.6b
(-.f64 (sin.f64 x) x)
1.6b
(-.f64 (tan.f64 x) x)
Compiler

Compiled 58 to 11 computations (81% saved)

series11.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
3.0ms
x
@-inf
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
2.0ms
x
@0
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
1.0ms
x
@-inf
(exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
1.0ms
x
@inf
(exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))

rewrite117.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
576×log-prod_binary64
426×fma-def_binary64
313×pow2_binary64
254×fma-neg_binary64
215×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01132
125031
2353931
Stop Event
1×node limit
Counts
2 → 170
Calls
Call 1
Inputs
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
(exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
Outputs
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(-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) (/.f64 1 (+.f64 (pow.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 2) (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 (tan.f64 x) x)) (-.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) (/.f64 1 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1)) 2) (cbrt.f64 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1)) (sqrt.f64 (+.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (tan.f64 x) x)) -2) (/.f64 (-.f64 (sin.f64 x) x) (cbrt.f64 (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 (tan.f64 x) x) -1/2) (/.f64 (-.f64 (sin.f64 x) x) (sqrt.f64 (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sin.f64 x) x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 (sin.f64 x) x)) (-.f64 (tan.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 (sin.f64 x) x)) 1) (/.f64 (sqrt.f64 (-.f64 (sin.f64 x) x)) (-.f64 (tan.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sin.f64 x) x)) 2) (cbrt.f64 (pow.f64 (-.f64 (tan.f64 x) x) 2))) (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 (sin.f64 x) x)) (cbrt.f64 (pow.f64 (-.f64 (tan.f64 x) x) 2))) (/.f64 (sqrt.f64 (-.f64 (sin.f64 x) x)) (cbrt.f64 (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sin.f64 x) x)) 2) (sqrt.f64 (-.f64 (tan.f64 x) x))) (/.f64 (cbrt.f64 (-.f64 (sin.f64 x) x)) (sqrt.f64 (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1)) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 x 3))) (fma.f64 x (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (+.f64 x (tan.f64 x)) 1)))))

simplify86.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
712×fma-def_binary64
506×associate-*l*_binary64
496×associate-*r*_binary64
364×distribute-rgt-in_binary64
363×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01411786
14471654
215651380
Stop Event
1×node limit
Counts
194 → 206
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))) 1/2)
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/4 (*.f64 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))) (+.f64 (*.f64 1/48 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (*.f64 1/6 (+.f64 (*.f64 1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (+.f64 (*.f64 -3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (cos.f64 x))) (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2)))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
1
(+.f64 1 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 1 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 (*.f64 -2 (/.f64 (+.f64 (*.f64 1/4 (*.f64 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (+.f64 (*.f64 1/6 (+.f64 (*.f64 3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (cos.f64 x))) (+.f64 (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (cos.f64 x) 2))) (*.f64 1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3))))) (*.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (pow.f64 x 3))) (+.f64 1 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
1/2
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))))
2
(-.f64 (+.f64 2 (*.f64 -1 (/.f64 (sin.f64 x) x))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 2 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/4 (*.f64 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))) (+.f64 (*.f64 1/48 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (*.f64 1/6 (+.f64 (*.f64 1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (+.f64 (*.f64 -3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (cos.f64 x))) (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3))) (+.f64 2 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2)))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
2
(+.f64 2 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 2 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 2 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (+.f64 (*.f64 -2 (/.f64 (+.f64 (*.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)) (+.f64 (*.f64 1/4 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (*.f64 1/6 (+.f64 (*.f64 3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (cos.f64 x))) (+.f64 (*.f64 1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)) (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
Outputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 27/112000 (pow.f64 x 6)))) -1/2)
(+.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 9/40 (*.f64 x x) -1/2))
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 27/112000 (pow.f64 x 6) -1/2)))
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))))
(-.f64 1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))
(-.f64 (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
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1
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1/2
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(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
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(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 27/112000 (pow.f64 x 6)))))
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2
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(-.f64 (+.f64 2 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(+.f64 2 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 2 (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))) (*.f64 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) 1/8)) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(+.f64 2 (+.f64 (*.f64 (/.f64 2 x) (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) 1/8)) x)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 2 (fma.f64 2 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2) 0)) (*.f64 x x)) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(-.f64 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/4 (*.f64 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))) (+.f64 (*.f64 1/48 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (*.f64 1/6 (+.f64 (*.f64 1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)) (+.f64 (*.f64 -3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (cos.f64 x))) (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3))) (+.f64 2 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (*.f64 2 (/.f64 (+.f64 (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (cos.f64 x)))) (*.f64 1/8 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (pow.f64 x 2)))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (fma.f64 2 (/.f64 (fma.f64 1/4 (*.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (fma.f64 -1/4 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))))))) (fma.f64 1/48 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 3) (*.f64 1/6 (fma.f64 1/4 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 3) (fma.f64 -3/2 (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2))) (*.f64 3 (/.f64 (pow.f64 (sin.f64 x) 2) (/.f64 (pow.f64 (cos.f64 x) 2) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))))))))))) (pow.f64 x 3)) (+.f64 2 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 2 (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))) (*.f64 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) 1/8)) (*.f64 x x)))))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))))
(fma.f64 2 (/.f64 (fma.f64 1/4 (*.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 -1/4 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))))) (fma.f64 1/6 (fma.f64 1/4 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) (fma.f64 -3/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (/.f64 (*.f64 (*.f64 3 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))) (*.f64 1/48 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 (/.f64 2 x) (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) 1/8)) x)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(fma.f64 2 (/.f64 (fma.f64 1/4 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2)) (*.f64 -1/4 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 3))) (+.f64 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1/4 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2))) (*.f64 1/2 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))) (*.f64 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 3) 1/16))) (pow.f64 x 3)) (+.f64 2 (fma.f64 2 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2) 0)) (*.f64 x x)) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))))
2
(+.f64 2 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(-.f64 (+.f64 2 (neg.f64 (/.f64 (sin.f64 x) x))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))))
(-.f64 2 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(+.f64 2 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))
(+.f64 2 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 2 (-.f64 (fma.f64 -1 (/.f64 (sin.f64 x) x) (*.f64 2 (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))) (*.f64 (pow.f64 (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) 2) 1/8)) (*.f64 x x)))) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x)))))
(+.f64 2 (+.f64 (*.f64 (/.f64 2 x) (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) 1/8)) x)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))
(+.f64 2 (fma.f64 2 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2) 0)) (*.f64 x x)) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(+.f64 2 (+.f64 (*.f64 2 (/.f64 (+.f64 (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (pow.f64 x 2))) (+.f64 (*.f64 -2 (/.f64 (+.f64 (*.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)) (+.f64 (*.f64 1/4 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (*.f64 1/6 (+.f64 (*.f64 3/2 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (cos.f64 x))) (+.f64 (*.f64 1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)) (*.f64 3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
(+.f64 2 (fma.f64 2 (/.f64 (fma.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 1/2 (fma.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x)))))) (*.f64 x x)) (fma.f64 -2 (/.f64 (fma.f64 1/4 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (cos.f64 x))))) (fma.f64 1/6 (fma.f64 3/2 (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2))) (fma.f64 3 (/.f64 (pow.f64 (sin.f64 x) 2) (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (*.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (pow.f64 x 3)) (neg.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))
(+.f64 2 (fma.f64 2 (/.f64 (fma.f64 1/2 (fma.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 1/8 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2))) (*.f64 x x)) (fma.f64 -2 (/.f64 (fma.f64 1/4 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 -1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))))) (fma.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) (*.f64 1/6 (fma.f64 3/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (fma.f64 1/4 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) (/.f64 3 (/.f64 (pow.f64 (cos.f64 x) 2) (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))))))) (pow.f64 x 3)) (/.f64 (fma.f64 -1 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 (fma.f64 -2 (/.f64 (fma.f64 1/4 (-.f64 (*.f64 1/4 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2))) (fma.f64 1/48 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) (fma.f64 1/4 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2)) (+.f64 (*.f64 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) 1/24) (*.f64 1/2 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))) (pow.f64 x 3)) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (fma.f64 2 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2) 0)) (*.f64 x x)) 2))

localize24.0ms (0.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
1.6b
(-.f64 (sin.f64 x) x)
0.2b
(pow.f64 (tan.f64 x) 2)
0.1b
(*.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (+.f64 x (tan.f64 x)))
0.0b
(+.f64 x (tan.f64 x))
✓0.2b
(pow.f64 (tan.f64 x) 2)
1.6b
(-.f64 (sin.f64 x) x)
✓1.6b
(-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))
✓12.2b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)))
Compiler

Compiled 61 to 21 computations (65.6% saved)

series5.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)))
1.0ms
x
@0
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)))
1.0ms
x
@-inf
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)))
0.0ms
x
@-inf
(pow.f64 (tan.f64 x) 2)
0.0ms
x
@inf
(pow.f64 (tan.f64 x) 2)

rewrite110.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
575×log-prod_binary64
415×fma-def_binary64
393×pow-prod-down_binary64
311×pow2_binary64
213×pow1/3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01038
123638
2349138
Stop Event
1×node limit
Counts
3 → 179
Calls
Call 1
Inputs
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)))
(-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))
(pow.f64 (tan.f64 x) 2)
Outputs
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simplify68.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
566×associate-*l/_binary64
415×fma-neg_binary64
404×associate-*r/_binary64
402×associate-/l/_binary64
348×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
074671
1201653
2555651
32428633
47558633
Stop Event
1×node limit
Counts
215 → 213
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(-.f64 (*.f64 37/240 x) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 37/240 x) (*.f64 -349/25200 (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 37/240 x) (+.f64 (*.f64 -953/864000 (pow.f64 x 5)) (*.f64 -349/25200 (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 x)))
(/.f64 1 x)
(+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 1 x))))
(/.f64 1 x)
(+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 1 x))))
(*.f64 2/3 (pow.f64 x 4))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (*.f64 17/45 (pow.f64 x 6)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (*.f64 17/45 (pow.f64 x 6))))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (*.f64 1382/14175 (pow.f64 x 10)))))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (pow.f64 x 2))))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
Outputs
(/.f64 -1/4 x)
(-.f64 (*.f64 37/240 x) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (*.f64 x 37/240) (/.f64 1/4 x))
(fma.f64 x 37/240 (/.f64 -1/4 x))
(-.f64 (+.f64 (*.f64 37/240 x) (*.f64 -349/25200 (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (fma.f64 37/240 x (*.f64 -349/25200 (pow.f64 x 3))) (/.f64 1/4 x))
(fma.f64 x 37/240 (fma.f64 -349/25200 (pow.f64 x 3) (/.f64 -1/4 x)))
(-.f64 (+.f64 (*.f64 37/240 x) (+.f64 (*.f64 -953/864000 (pow.f64 x 5)) (*.f64 -349/25200 (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (fma.f64 37/240 x (fma.f64 -953/864000 (pow.f64 x 5) (*.f64 -349/25200 (pow.f64 x 3)))) (/.f64 1/4 x))
(+.f64 (fma.f64 -349/25200 (pow.f64 x 3) (*.f64 -953/864000 (pow.f64 x 5))) (fma.f64 x 37/240 (/.f64 -1/4 x)))
(fma.f64 x 37/240 (fma.f64 -349/25200 (pow.f64 x 3) (fma.f64 -953/864000 (pow.f64 x 5) (/.f64 -1/4 x))))
(/.f64 1 x)
(+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (sin.f64 x) (*.f64 x x)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x)))
(+.f64 (fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 1 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 (sin.f64 x) (*.f64 x x))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (pow.f64 (cos.f64 x) 2))))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 1 x))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (fma.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4))) (/.f64 1 x))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (-.f64 (-.f64 (/.f64 1 x) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 (sin.f64 x) (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4))))))
(-.f64 (/.f64 1 x) (+.f64 (*.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 4)) (/.f64 (sin.f64 x) (pow.f64 x 3)))) (/.f64 (sin.f64 x) (*.f64 x x))))
(/.f64 1 x)
(+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (sin.f64 x) (*.f64 x x)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (/.f64 1 x)))
(+.f64 (fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 1 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 (sin.f64 x) (*.f64 x x))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (pow.f64 (cos.f64 x) 2))))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 1 x))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (fma.f64 -1 (/.f64 (sin.f64 x) (*.f64 x x)) (fma.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4))) (/.f64 1 x))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (-.f64 (-.f64 (/.f64 1 x) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4)))) (/.f64 (sin.f64 x) (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 4))))))
(-.f64 (/.f64 1 x) (+.f64 (*.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 4)) (/.f64 (sin.f64 x) (pow.f64 x 3)))) (/.f64 (sin.f64 x) (*.f64 x x))))
(*.f64 2/3 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) 2/3)
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (*.f64 17/45 (pow.f64 x 6)))
(fma.f64 2/3 (pow.f64 x 4) (*.f64 17/45 (pow.f64 x 6)))
(fma.f64 (pow.f64 x 4) 2/3 (*.f64 17/45 (pow.f64 x 6)))
(fma.f64 17/45 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 2/3))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (*.f64 17/45 (pow.f64 x 6))))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 62/315 (pow.f64 x 8) (*.f64 17/45 (pow.f64 x 6))))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 17/45 (pow.f64 x 6) (*.f64 62/315 (pow.f64 x 8))))
(fma.f64 17/45 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) 2/3 (*.f64 62/315 (pow.f64 x 8))))
(fma.f64 17/45 (pow.f64 x 6) (fma.f64 62/315 (pow.f64 x 8) (*.f64 (pow.f64 x 4) 2/3)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (*.f64 1382/14175 (pow.f64 x 10)))))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 62/315 (pow.f64 x 8) (fma.f64 17/45 (pow.f64 x 6) (*.f64 1382/14175 (pow.f64 x 10)))))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 62/315 (pow.f64 x 8) (fma.f64 17/45 (pow.f64 x 6) (*.f64 1382/14175 (pow.f64 x 10)))))
(fma.f64 62/315 (pow.f64 x 8) (fma.f64 (pow.f64 x 4) 2/3 (fma.f64 17/45 (pow.f64 x 6) (*.f64 1382/14175 (pow.f64 x 10)))))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 17/45 (pow.f64 x 6) (fma.f64 62/315 (pow.f64 x 8) (*.f64 1382/14175 (pow.f64 x 10)))))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(fma.f64 -1 (*.f64 x x) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 2/3 (pow.f64 x 4) (*.f64 x x))
(fma.f64 (pow.f64 x 4) 2/3 (*.f64 x x))
(fma.f64 x x (*.f64 (pow.f64 x 4) 2/3))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 17/45 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 x x (*.f64 17/45 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 17/45 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 2/3)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 62/315 (pow.f64 x 8)) (+.f64 (*.f64 17/45 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 62/315 (pow.f64 x 8) (fma.f64 17/45 (pow.f64 x 6) (*.f64 x x))))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 62/315 (pow.f64 x 8) (fma.f64 x x (*.f64 17/45 (pow.f64 x 6)))))
(fma.f64 62/315 (pow.f64 x 8) (fma.f64 x x (fma.f64 17/45 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 2/3))))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 62/315 (pow.f64 x 8) (fma.f64 17/45 (pow.f64 x 6) (*.f64 x x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))

eval410.0ms (2.3%)

Compiler

Compiled 24730 to 10766 computations (56.5% saved)

prune207.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1102101112
Fresh112
Picked101
Done325
Total1107131120
Error
0b
Counts
1120 → 13
Alt Table
Click to see full alt table
StatusErrorProgram
▶34.3b
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
▶29.6b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
30.3b
-1/2
✓33.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
34.3b
1
34.4b
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
29.9b
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))
▶29.6b
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
62.9b
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
▶33.8b
(-.f64 1 (/.f64 (sin.f64 x) x))
33.2b
(-.f64 (fma.f64 (/.f64 1 (-.f64 (tan.f64 x) x)) (-.f64 (sin.f64 x) x) 1) 1)
▶30.3b
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓33.2b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
Compiler

Compiled 244 to 178 computations (27% saved)

localize73.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x 9/40)
0.0b
(fma.f64 x (*.f64 x 9/40) -1/2)
0.0b
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
0.0b
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
✓0.0b
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
✓0.0b
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
0.0b
(fma.f64 x (*.f64 x 9/40) -1/2)
0.1b
(*.f64 x 9/40)
Compiler

Compiled 32 to 24 computations (25% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
0.0ms
x
@inf
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
0.0ms
x
@inf
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
0.0ms
x
@-inf
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
0.0ms
x
@-inf
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)

rewrite82.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
913×pow1_binary64
858×add-log-exp_binary64
858×log1p-expm1-u_binary64
858×expm1-log1p-u_binary64
845×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0925
119818
2255318
Stop Event
1×node limit
Counts
2 → 77
Calls
Call 1
Inputs
(+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))) (/.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2) (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) (pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 2) (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 2) (*.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) (*.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) (/.f64 1 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)) (/.f64 1 (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))) (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) (+.f64 1 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) (+.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2) (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)) (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3))) (neg.f64 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))) (neg.f64 (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2) 1) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) 1) (+.f64 1 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)) 1) (-.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (*.f64 x (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 9/40)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) -1) (/.f64 1 (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 1) (-.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) (-.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) -1) (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) -1) (-.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) 2) -1)) (neg.f64 (+.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 3) -1/8) (+.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) (-.f64 1/4 (*.f64 (*.f64 x (*.f64 x 9/40)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2) (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))) (-.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 9/40) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) 2) (cbrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)) -1)))))

simplify271.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
552×fabs-mul_binary64
523×pow-sqr_binary64
451×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
010192
120174
234174
361174
4127174
5366174
61330174
72257174
82421174
92605174
102813174
113113174
123504174
133989174
144557174
155249174
166086174
176476174
186762174
197036174
207106174
217140174
Stop Event
1×node limit
Counts
101 → 85
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(*.f64 9/40 (pow.f64 x 2))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(*.f64 9/40 (pow.f64 x 2))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
Outputs
1/2
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (*.f64 x x)))
(fma.f64 9/40 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 9/40 x) 1/2)
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (*.f64 x 9/40))
0.1b
(*.f64 x 9/40)
0.1b
(*.f64 x 9/40)
✓0.1b
(*.f64 x (*.f64 x 9/40))
Compiler

Compiled 19 to 13 computations (31.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 x (*.f64 x 9/40))
0.0ms
x
@inf
(*.f64 x (*.f64 x 9/40))
0.0ms
x
@-inf
(*.f64 x (*.f64 x 9/40))

rewrite43.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
448×pow1_binary64
434×add-sqr-sqrt_binary64
425×*-un-lft-identity_binary64
415×add-log-exp_binary64
415×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
211417
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 x (*.f64 x 9/40))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x 9/40))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 9/40)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 9/40))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 9/40)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 9/40))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 9/40))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 9/40))))))))

simplify200.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
554×fabs-mul_binary64
523×pow-sqr_binary64
441×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533184
6125084
7212384
8228784
9247184
10267984
11297684
12337184
13385284
14441884
15510284
16593584
17632784
18661984
19689584
20696984
21700384
22794484
Stop Event
1×node limit
Counts
23 → 13
Calls
Call 1
Inputs
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
Outputs
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.6b
(-.f64 1 (/.f64 (sin.f64 x) x))
0.1b
(/.f64 (sin.f64 x) x)
✓0.1b
(/.f64 (sin.f64 x) x)
✓1.6b
(-.f64 1 (/.f64 (sin.f64 x) x))
Compiler

Compiled 15 to 6 computations (60% saved)

series4.0ms (0%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(-.f64 1 (/.f64 (sin.f64 x) x))
1.0ms
x
@0
(-.f64 1 (/.f64 (sin.f64 x) x))
1.0ms
x
@-inf
(/.f64 (sin.f64 x) x)
1.0ms
x
@inf
(-.f64 1 (/.f64 (sin.f64 x) x))
1.0ms
x
@inf
(/.f64 (sin.f64 x) x)

rewrite70.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
716×pow1_binary64
667×add-log-exp_binary64
667×log1p-expm1-u_binary64
667×expm1-log1p-u_binary64
654×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
112815
2172415
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(-.f64 1 (/.f64 (sin.f64 x) x))
(/.f64 (sin.f64 x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (/.f64 (neg.f64 (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (/.f64 (neg.f64 (sin.f64 x)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (neg.f64 (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) (pow.f64 (cbrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) 2) (cbrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) (sqrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 3)) (/.f64 1 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) x) (pow.f64 (/.f64 (sin.f64 x) x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 2)) (/.f64 1 (+.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) x) (pow.f64 (/.f64 (sin.f64 x) x) 2))) (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (/.f64 (sin.f64 x) x)) (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 3)) (+.f64 1 (+.f64 (/.f64 (sin.f64 x) x) (pow.f64 (/.f64 (sin.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 2)) (+.f64 1 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 3))) (neg.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) x) (pow.f64 (/.f64 (sin.f64 x) x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 2))) (neg.f64 (+.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) x) 3)) (+.f64 1 (-.f64 (*.f64 (/.f64 (neg.f64 (sin.f64 x)) x) (/.f64 (neg.f64 (sin.f64 x)) x)) (/.f64 (neg.f64 (sin.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (/.f64 (neg.f64 (sin.f64 x)) x) (/.f64 (neg.f64 (sin.f64 x)) x))) (-.f64 1 (/.f64 (neg.f64 (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (sin.f64 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (/.f64 (sin.f64 x) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 (neg.f64 (sin.f64 x)) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sin.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2) (cbrt.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sin.f64 x) x)) (sqrt.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sin.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 x)) 1) (/.f64 (sqrt.f64 (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sin.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (sin.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sin.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sin.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sin.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sin.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sin.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sin.f64 x) x)))))))

simplify102.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
614×distribute-lft-out_binary64
596×distribute-rgt-out_binary64
527×fma-def_binary64
484×associate-*l*_binary64
482×distribute-rgt-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041190
195176
2224174
3682172
42923172
55585172
67596172
Stop Event
1×node limit
Counts
74 → 75
Calls
Call 1
Inputs
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6))))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 -1/362880 (pow.f64 x 8)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
1
(+.f64 1 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
Outputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 -1/120 (pow.f64 x 4) (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 -1/120 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -1/120 1/6)))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/120 1/6))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/6 (*.f64 x x) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 1/6 (*.f64 x x))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 -1/120 (pow.f64 x 4) (*.f64 1/5040 (pow.f64 x 6))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 -1/120 (pow.f64 x 4))))
(+.f64 (*.f64 -1/120 (pow.f64 x 4)) (+.f64 (*.f64 -1/362880 (pow.f64 x 8)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/5040 (pow.f64 x 6)))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 -1/362880 (pow.f64 x 8) (fma.f64 1/6 (*.f64 x x) (*.f64 1/5040 (pow.f64 x 6)))))
(fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/5040 (pow.f64 x 6) (fma.f64 -1/362880 (pow.f64 x 8) (*.f64 1/6 (*.f64 x x)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/362880 -1/120) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 1/6 (*.f64 x x))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 -1/120 (pow.f64 x 4) (fma.f64 1/5040 (pow.f64 x 6) (*.f64 -1/362880 (pow.f64 x 8)))))
(fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/362880 -1/120) (*.f64 1/5040 (pow.f64 x 6))))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
1
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (neg.f64 (/.f64 (sin.f64 x) x)))
(-.f64 1 (/.f64 (sin.f64 x) x))
1
(+.f64 1 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -1/6))
(fma.f64 (*.f64 x x) -1/6 1)
(fma.f64 x (*.f64 x -1/6) 1)
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/120)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/6 (*.f64 (pow.f64 x 4) 1/120)))
(fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (*.f64 x x) -1/6 1))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/120 -1/6) 1)
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 1))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/6 (*.f64 x x) (fma.f64 -1/5040 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/120))))
(+.f64 1 (fma.f64 (*.f64 x x) -1/6 (fma.f64 (pow.f64 x 4) 1/120 (*.f64 (pow.f64 x 6) -1/5040))))
(+.f64 (fma.f64 (*.f64 x x) -1/6 1) (fma.f64 (pow.f64 x 6) -1/5040 (*.f64 (pow.f64 x 4) 1/120)))
(fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) -1/5040 (fma.f64 x (*.f64 x -1/6) 1)))
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 6) -1/5040 (fma.f64 (pow.f64 x 4) 1/120 1)))

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 x (sin.f64 x)) x)
0.0b
(+.f64 x (sin.f64 x))
✓0.0b
(+.f64 x (sin.f64 x))
✓0.0b
(/.f64 (+.f64 x (sin.f64 x)) x)
Compiler

Compiled 23 to 7 computations (69.6% saved)

series5.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(/.f64 (+.f64 x (sin.f64 x)) x)
0.0ms
x
@0
(/.f64 (+.f64 x (sin.f64 x)) x)
0.0ms
x
@inf
(/.f64 (+.f64 x (sin.f64 x)) x)
0.0ms
x
@0
(+.f64 x (sin.f64 x))
0.0ms
x
@inf
(+.f64 x (sin.f64 x))

rewrite58.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
730×pow1_binary64
683×add-log-exp_binary64
683×log1p-expm1-u_binary64
683×expm1-log1p-u_binary64
668×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0515
111515
2178215
Stop Event
1×node limit
Counts
2 → 64
Calls
Call 1
Inputs
(/.f64 (+.f64 x (sin.f64 x)) x)
(+.f64 x (sin.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sin.f64 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (*.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x (sin.f64 x))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 x (sin.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 x (sin.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 x (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 x (sin.f64 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (-.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (cbrt.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (sqrt.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (/.f64 1 (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (-.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x))) (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (*.f64 x x) (*.f64 x (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (-.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))) (neg.f64 (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))) (neg.f64 (-.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)) (-.f64 (sin.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sin.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (cbrt.f64 (sin.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sin.f64 x))))))

simplify97.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
506×unswap-sqr_binary64
490×fma-def_binary64
482×distribute-lft-out_binary64
453×associate-/r*_binary64
396×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041204
1104202
2240200
3668198
42454198
54351198
65086198
75712198
86577198
97791198
Stop Event
1×node limit
Counts
88 → 83
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
1
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
1
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(*.f64 2 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (*.f64 1/120 (pow.f64 x 5))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (*.f64 1/120 (pow.f64 x 5)))))
x
(+.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) x)
x
(+.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) x)
(+.f64 (sin.f64 x) x)
Outputs
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/6 (*.f64 x x) (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 -1/6 (*.f64 x x) (fma.f64 1/120 (pow.f64 x 4) 2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/120) -1/6) 2)
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/6 (*.f64 x x) (fma.f64 -1/5040 (pow.f64 x 6) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/6 (*.f64 x x) (fma.f64 1/120 (pow.f64 x 4) (*.f64 -1/5040 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/6 (*.f64 x x) 2) (fma.f64 -1/5040 (pow.f64 x 6) (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 -1/6 (*.f64 x x) (fma.f64 1/120 (pow.f64 x 4) (fma.f64 -1/5040 (pow.f64 x 6) 2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/120) -1/6) (fma.f64 -1/5040 (pow.f64 x 6) 2))
1
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
1
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(+.f64 1 (/.f64 (sin.f64 x) x))
(*.f64 2 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x))
(fma.f64 -1/6 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 -1/6 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/6 (*.f64 x x) 2))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (*.f64 1/120 (pow.f64 x 5))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 2 x (*.f64 1/120 (pow.f64 x 5))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) (*.f64 2 x)))
(fma.f64 2 x (fma.f64 -1/6 (pow.f64 x 3) (*.f64 1/120 (pow.f64 x 5))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (*.f64 1/120 (pow.f64 x 5)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 2 x (fma.f64 -1/5040 (pow.f64 x 7) (*.f64 1/120 (pow.f64 x 5)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 2 x (fma.f64 1/120 (pow.f64 x 5) (*.f64 -1/5040 (pow.f64 x 7)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 -1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) (*.f64 2 x))))
(fma.f64 x (fma.f64 -1/6 (*.f64 x x) 2) (fma.f64 -1/5040 (pow.f64 x 7) (*.f64 1/120 (pow.f64 x 5))))
x
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))
x
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))
(+.f64 (sin.f64 x) x)
(+.f64 x (sin.f64 x))

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
13.0b
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
0.2b
(*.f64 9/40 (*.f64 x x))
0.1b
(*.f64 -27/2800 (pow.f64 x 4))
0.0b
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓0.0b
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
0.1b
(*.f64 -27/2800 (pow.f64 x 4))
✓0.2b
(*.f64 9/40 (*.f64 x x))
✓13.0b
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
Compiler

Compiled 58 to 39 computations (32.8% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
0.0ms
x
@inf
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
0.0ms
x
@-inf
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
0.0ms
x
@inf
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
0.0ms
x
@-inf
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)

rewrite88.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
717×fma-def_binary64
548×log-prod_binary64
347×fma-neg_binary64
331×pow2_binary64
229×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01442
132636
2391136
Stop Event
1×node limit
Counts
3 → 232
Calls
Call 1
Inputs
(+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 9/40 (*.f64 x x))
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 81/1600) (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))) (/.f64 (*.f64 729/7840000 (pow.f64 x 8)) (fma.f64 9/40 (*.f64 x x) (*.f64 27/2800 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 -27/2800 (pow.f64 x 4) (*.f64 9/40 (*.f64 x x)))))))) 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4) -1/2)))))))

simplify90.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
512×fma-neg_binary64
472×neg-mul-1_binary64
410×associate-*l*_binary64
409×distribute-rgt-neg-in_binary64
368×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
016384
133372
264372
3148372
4472372
51816372
64525372
75677372
87761372
Stop Event
1×node limit
Counts
268 → 242
Calls
Call 1
Inputs
(*.f64 9/40 (pow.f64 x 2))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (pow.f64 x 2))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
Outputs
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 -27/2800 (pow.f64 x 4)) (*.f64 9/40 (pow.f64 x 2)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))
(*.f64 -27/2800 (pow.f64 x 4))
(+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4)))
(fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -27/2800 9/40))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -27/2800) 9/40))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 9/40 x (*.f64 -27/2800 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(+.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 -27/2800 (pow.f64 x 4))) -1/2)
(fma.f64 9/40 (*.f64 x x) (fma.f64 -27/2800 (pow.f64 x 4) -1/2))
(fma.f64 -27/2800 (pow.f64 x 4) (fma.f64 x (*.f64 9/40 x) -1/2))

eval308.0ms (1.7%)

Compiler

Compiled 9186 to 6532 computations (28.9% saved)

prune93.0ms (0.5%)

Pruning

15 alts after pruning (9 fresh and 6 done)

PrunedKeptTotal
New5605565
Fresh246
Picked011
Done156
Total56315578
Error
0b
Counts
578 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
✓33.8b
(-.f64 1 (/.f64 (sin.f64 x) x))
▶63.2b
(*.f64 1 (fma.f64 -1/6 (*.f64 x x) 2))
✓34.3b
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
✓29.6b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
30.3b
-1/2
✓33.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
34.3b
1
▶34.4b
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
▶29.6b
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
33.2b
(-.f64 (fma.f64 (/.f64 1 (-.f64 (tan.f64 x) x)) (-.f64 (sin.f64 x) x) 1) 1)
▶29.6b
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
✓30.3b
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓33.2b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
▶56.7b
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
63.2b
(*.f64 1 (/.f64 (+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x)) x))
Compiler

Compiled 218 to 164 computations (24.8% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (*.f64 x 9/40))
0.1b
(*.f64 x 9/40)
0.0b
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
0.0b
(+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)
✓0.0b
(+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)
✓0.0b
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
0.1b
(*.f64 x 9/40)
0.1b
(*.f64 x (*.f64 x 9/40))
Compiler

Compiled 29 to 21 computations (27.6% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
0.0ms
x
@inf
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
0.0ms
x
@0
(+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)
0.0ms
x
@-inf
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
0.0ms
x
@inf
(+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)

rewrite66.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
671×prod-diff_binary64
609×unpow-prod-down_binary64
410×log-prod_binary64
282×fma-def_binary64
241×pow-prod-down_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0919
119818
2248416
Stop Event
1×node limit
Counts
2 → 134
Calls
Call 1
Inputs
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 9/40 (*.f64 x x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 5/2 (*.f64 9/40 (*.f64 x x)))) (/.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) -3/2) 2) (-.f64 5/2 (*.f64 9/40 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 9/40 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 9/40 (*.f64 x x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) 2) (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) (sqrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 9/40 (*.f64 x x) -3/2) 3)) (/.f64 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x x) 9/40 -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 81/1600)) (*.f64 (cbrt.f64 (*.f64 x 9/40)) x) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) 2) (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 9/40 (*.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 9/40)) 4)) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 9/40)) 4)) (cbrt.f64 (*.f64 9/40 (*.f64 x x))) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 9/40)) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 9/40)) (*.f64 (sqrt.f64 (*.f64 x 9/40)) x) -3/2)))) (#(struct:change 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(*.f64 (*.f64 x 9/40) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 9/40) (sqrt.f64 x)) (sqrt.f64 x) -3/2)))))

simplify172.0ms (1%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
559×fabs-mul_binary64
523×pow-sqr_binary64
453×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012174
124174
238174
365174
4130174
5365174
61306174
72228174
82392174
92576174
102784174
113084174
123479174
133960174
144528174
155220174
166055174
176447174
186735174
197013174
207087174
217123174
Stop Event
1×node limit
Counts
158 → 142
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
-3/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
Outputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
-3/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 3/2)
(fma.f64 9/40 (*.f64 x x) -3/2)
(fma.f64 x (*.f64 9/40 x) -3/2)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 9/40 (*.f64 x x))
0.0b
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
✓0.0b
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
0.2b
(*.f64 9/40 (*.f64 x x))
Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
0.0ms
x
@inf
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
0.0ms
x
@-inf
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)

rewrite49.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
655×pow1_binary64
614×add-log-exp_binary64
612×log1p-expm1-u_binary64
612×expm1-log1p-u_binary64
602×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
11498
217688
Stop Event
1×node limit
Counts
1 → 34
Calls
Call 1
Inputs
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 9/40 (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (*.f64 9/40 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 9/40 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 9/40 (*.f64 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) 2) (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) (sqrt.f64 (fma.f64 9/40 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 729/64000 (pow.f64 (*.f64 x x) 3)) -1) (/.f64 1 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) (fma.f64 9/40 (*.f64 x x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) -1) (/.f64 1 (fma.f64 9/40 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 x (sqrt.f64 9/40)) 1) (-.f64 (*.f64 x (sqrt.f64 9/40)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) (fma.f64 9/40 (*.f64 x x) 1)) (+.f64 (*.f64 729/64000 (pow.f64 (*.f64 x x) 3)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 9/40 (*.f64 x x) 1) (+.f64 (*.f64 81/1600 (pow.f64 x 4)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 729/64000 (pow.f64 (*.f64 x x) 3)) -1) (+.f64 (*.f64 81/1600 (pow.f64 x 4)) (fma.f64 9/40 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 729/64000 (pow.f64 (*.f64 x x) 3)) -1) (+.f64 (*.f64 81/1600 (pow.f64 x 4)) (-.f64 1 (*.f64 (*.f64 9/40 (*.f64 x x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) -1) (fma.f64 9/40 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) -1) (-.f64 (*.f64 9/40 (*.f64 x x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 729/64000 (pow.f64 (*.f64 x x) 3)) -1)) (neg.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) (fma.f64 9/40 (*.f64 x x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 81/1600 (pow.f64 x 4)) -1)) (neg.f64 (fma.f64 9/40 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 9/40 (*.f64 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 9/40 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (*.f64 9/40 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 9/40 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 9/40 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 9/40 (*.f64 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 9/40 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 9/40 (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 81/1600 (pow.f64 x 4))) (cbrt.f64 (*.f64 9/40 (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 9/40)) (*.f64 x (sqrt.f64 9/40)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9/40 x) x -1)))))

simplify167.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
552×fabs-mul_binary64
523×pow-sqr_binary64
452×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0987
11987
23087
35487
412187
535387
6128487
7218287
8234687
9253087
10273887
11303987
12343487
13391787
14448387
15516987
16600887
17640087
18668487
19696287
20703087
21706687
Stop Event
1×node limit
Counts
46 → 39
Calls
Call 1
Inputs
-1
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
Outputs
-1
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1)
(fma.f64 9/40 (*.f64 x x) -1)
(fma.f64 x (*.f64 9/40 x) -1)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (*.f64 x 9/40))
0.1b
(*.f64 x 9/40)
0.0b
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
0.0b
(+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)
✓0.0b
(+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)
✓0.0b
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
0.1b
(*.f64 x 9/40)
0.1b
(*.f64 x (*.f64 x 9/40))
Compiler

Compiled 29 to 21 computations (27.6% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
0.0ms
x
@inf
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
0.0ms
x
@-inf
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
0.0ms
x
@0
(+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)
0.0ms
x
@inf
(+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)

rewrite100.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
597×unpow-prod-down_binary64
420×log-prod_binary64
269×prod-diff_binary64
251×pow-prod-down_binary64
247×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0918
120216
2252816
Stop Event
1×node limit
Counts
2 → 137
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
(+.f64 (*.f64 x (*.f64 x 9/40)) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (*.f64 x 9/40)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 2) (fma.f64 9/40 (*.f64 x x) 3/2)) (/.f64 1 (fma.f64 9/40 (*.f64 x x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)) (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 2) (-.f64 1 (*.f64 (fma.f64 9/40 (*.f64 x x) 1/2) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 3)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 2) (-.f64 1 (*.f64 (fma.f64 9/40 (*.f64 x x) 1/2) -1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 2) -1) (/.f64 1 (fma.f64 9/40 (*.f64 x x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 9/40 (*.f64 x x) 1/2) 2) -1) (pow.f64 (/.f64 1 (fma.f64 9/40 (*.f64 x x) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) 1/2)) 1) (-.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 x (*.f64 x 9/40) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) 1/2)) 1) 1) (pow.f64 (-.f64 (sqrt.f64 (fma.f64 9/40 (*.f64 x x) 1/2)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (fma.f64 x (*.f64 x 9/40) -1/2) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2))) 2) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) -1/2) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2))) 2) 3) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) -1/2))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (*.f64 x 9/40)) 2)) (cbrt.f64 (*.f64 x 9/40)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (*.f64 x 9/40))) (sqrt.f64 (*.f64 x 9/40)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 9/40) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 9/40) (sqrt.f64 x)) (sqrt.f64 x) 1/2)))))

simplify207.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
552×fabs-mul_binary64
523×pow-sqr_binary64
451×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
010192
120174
234174
361174
4127174
5366174
61330174
72257174
82421174
92605174
102813174
113113174
123504174
133989174
144557174
155249174
166086174
176476174
186762174
197036174
207106174
217140174
Stop Event
1×node limit
Counts
161 → 144
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
1/2
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(*.f64 9/40 (pow.f64 x 2))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(*.f64 9/40 (pow.f64 x 2))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
Outputs
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 9/40 x) -1/2)
1/2
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 9/40 (pow.f64 x 2)))
(+.f64 (*.f64 9/40 (*.f64 x x)) 1/2)
(fma.f64 9/40 (*.f64 x x) 1/2)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
0.0b
(+.f64 x (tan.f64 x))
✓0.0b
(+.f64 x (tan.f64 x))
✓0.2b
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
Compiler

Compiled 20 to 9 computations (55% saved)

series5.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
1.0ms
x
@inf
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
1.0ms
x
@0
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
1.0ms
x
@0
(+.f64 x (tan.f64 x))
0.0ms
x
@inf
(+.f64 x (tan.f64 x))

rewrite89.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
897×pow1_binary64
839×add-log-exp_binary64
839×log1p-expm1-u_binary64
839×expm1-log1p-u_binary64
819×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
115815
2234215
Stop Event
1×node limit
Counts
2 → 76
Calls
Call 1
Inputs
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
(+.f64 x (tan.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (/.f64 (tan.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (/.f64 (tan.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (tan.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (/.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (tan.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 x (tan.f64 x))) 2) (/.f64 x (cbrt.f64 (+.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x (tan.f64 x))) (/.f64 x (sqrt.f64 (+.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (*.f64 x (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) (*.f64 x (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (tan.f64 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (*.f64 (neg.f64 x) (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2))) (*.f64 (neg.f64 x) (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) 1) (*.f64 (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) 1) (*.f64 (-.f64 x (tan.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) -1) (*.f64 (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) -1) (*.f64 (-.f64 x (tan.f64 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (tan.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 (tan.f64 x) x) 3)) (+.f64 1 (-.f64 (*.f64 (/.f64 (tan.f64 x) x) (/.f64 (tan.f64 x) x)) (/.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (/.f64 (tan.f64 x) x) (/.f64 (tan.f64 x) x))) (-.f64 1 (/.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (tan.f64 x)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (tan.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 x (tan.f64 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (/.f64 1 x)) (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) (/.f64 1 x)) (-.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2))) (-.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x (tan.f64 x)) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 (tan.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 (tan.f64 x) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (tan.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (/.f64 (tan.f64 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 (tan.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 (tan.f64 x) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x (tan.f64 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 (pow.f64 x -2) x) (pow.f64 (+.f64 x (tan.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x (tan.f64 x)) 3) (/.f64 (pow.f64 x -2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (/.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1 (/.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (/.f64 1 x) (/.f64 (tan.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) x (/.f64 (tan.f64 x) x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (tan.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (tan.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (tan.f64 x))) (pow.f64 (cbrt.f64 (+.f64 x (tan.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (tan.f64 x))) 2) (cbrt.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (tan.f64 x))) (sqrt.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (/.f64 1 (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) (/.f64 1 (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (pow.f64 (tan.f64 x) 2) (-.f64 (*.f64 x x) (*.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2)) (-.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (neg.f64 (fma.f64 x x (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2))) (neg.f64 (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x)) (-.f64 (tan.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (tan.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (tan.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (tan.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (tan.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (tan.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (tan.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (tan.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (tan.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)) x)))))

simplify111.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
512×fma-def_binary64
506×unswap-sqr_binary64
482×distribute-lft-out_binary64
461×associate-/r*_binary64
411×associate-/l/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041264
1100262
2229258
3664258
42493258
54429258
65239258
76274258
87475258
Stop Event
1×node limit
Counts
100 → 96
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4))))
(+.f64 2 (+.f64 (*.f64 17/315 (pow.f64 x 6)) (+.f64 (*.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4)))))
1
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
1
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))))
x
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
x
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
Outputs
2
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (*.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(+.f64 2 (+.f64 (*.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4))))
(+.f64 2 (fma.f64 1/3 (*.f64 x x) (*.f64 2/15 (pow.f64 x 4))))
(fma.f64 1/3 (*.f64 x x) (fma.f64 2/15 (pow.f64 x 4) 2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 2/15) 1/3) 2)
(+.f64 2 (+.f64 (*.f64 17/315 (pow.f64 x 6)) (+.f64 (*.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 17/315 (pow.f64 x 6) (fma.f64 1/3 (*.f64 x x) (*.f64 2/15 (pow.f64 x 4)))))
(fma.f64 17/315 (pow.f64 x 6) (fma.f64 1/3 (*.f64 x x) (fma.f64 2/15 (pow.f64 x 4) 2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 2/15) 1/3) (fma.f64 17/315 (pow.f64 x 6) 2))
1
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
1
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))
(+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(*.f64 x (fma.f64 1/3 (*.f64 x x) 2))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 2/15 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x)))
(+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (*.f64 17/315 (pow.f64 x 7)))))
x
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
x
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))

localize19.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -1/6 (*.f64 x x) 2)
✓0.1b
(fma.f64 -1/6 (*.f64 x x) 2)
Compiler

Compiled 22 to 13 computations (40.9% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(fma.f64 -1/6 (*.f64 x x) 2)
1.0ms
x
@inf
(fma.f64 -1/6 (*.f64 x x) 2)
0.0ms
x
@-inf
(fma.f64 -1/6 (*.f64 x x) 2)

rewrite73.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
498×pow1_binary64
488×add-sqr-sqrt_binary64
464×add-log-exp_binary64
464×log1p-expm1-u_binary64
464×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11218
212868
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(fma.f64 -1/6 (*.f64 x x) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (*.f64 -1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/6 (*.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/6 (*.f64 x x)) 1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/6 (*.f64 x x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/6 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/6 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) (pow.f64 (cbrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) 2) (cbrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) (sqrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -1/6 (*.f64 x x)) 3) 8) (+.f64 (*.f64 (*.f64 -1/6 (*.f64 x x)) (*.f64 -1/6 (*.f64 x x))) (-.f64 4 (*.f64 (*.f64 -1/6 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -1/6 (*.f64 x x)) (*.f64 -1/6 (*.f64 x x))) 4) (-.f64 (*.f64 -1/6 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/6 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/6 (*.f64 x x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/6 (*.f64 x x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/6 (*.f64 x x) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/6 (*.f64 x x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/6 (*.f64 x x) 2)))))))

simplify173.0ms (1%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
560×cube-prod_binary64
559×fabs-mul_binary64
523×pow-sqr_binary64
446×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07105
11487
22787
35187
411887
534687
6127187
7217087
8233487
9251887
10272687
11302587
12341887
13389987
14446787
15515587
16599287
17638687
18667687
19695487
20702687
21706287
Stop Event
1×node limit
Counts
33 → 26
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(*.f64 -1/6 (pow.f64 x 2))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(*.f64 -1/6 (pow.f64 x 2))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
Outputs
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(*.f64 -1/6 (pow.f64 x 2))
(*.f64 -1/6 (*.f64 x x))
(*.f64 x (*.f64 -1/6 x))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(*.f64 -1/6 (pow.f64 x 2))
(*.f64 -1/6 (*.f64 x x))
(*.f64 x (*.f64 -1/6 x))
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/6 (*.f64 x x)))
(fma.f64 -1/6 (*.f64 x x) 2)

eval266.0ms (1.5%)

Compiler

Compiled 7386 to 5048 computations (31.7% saved)

prune73.0ms (0.4%)

Pruning

15 alts after pruning (6 fresh and 9 done)

PrunedKeptTotal
New5384542
Fresh224
Picked101
Done1910
Total54215557
Error
0b
Counts
557 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
✓34.3b
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
✓29.6b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
34.3b
(/.f64 (+.f64 x (tan.f64 x)) x)
✓34.4b
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
✓56.7b
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
34.3b
1
63.2b
(*.f64 1 (/.f64 (+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x)) x))
63.2b
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
✓29.6b
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
30.3b
-1/2
33.2b
(-.f64 (fma.f64 (/.f64 1 (-.f64 (tan.f64 x) x)) (-.f64 (sin.f64 x) x) 1) 1)
✓29.6b
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
✓30.3b
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
✓33.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓33.2b
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
Compiler

Compiled 144 to 107 computations (25.7% saved)

regimes60.0ms (0.3%)

Counts
28 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))
(/.f64 (+.f64 x (tan.f64 x)) x)
(-.f64 1 (/.f64 (sin.f64 x) x))
(fma.f64 x (*.f64 x 9/40) -1/2)
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
(*.f64 1 (fma.f64 -1/6 (*.f64 x x) 2))
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
(*.f64 1 (/.f64 (+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x)) x))
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(-.f64 (+.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(-.f64 (fma.f64 (/.f64 1 (-.f64 (tan.f64 x) x)) (-.f64 (sin.f64 x) x) 1) 1)
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)
(*.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (pow.f64 (tan.f64 x) 2) (*.f64 x x))) (+.f64 x (tan.f64 x)))
Outputs
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Calls

3 calls:

38.0ms
x
8.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Results
ErrorSegmentsBranch
0.0b3x
0.1b2(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.1b2(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Compiler

Compiled 263 to 155 computations (41.1% saved)

bsearch65.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
32.0ms
0.0028624513617995866
2.758897867498332
32.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes39.0ms (0.2%)

Counts
22 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))
(/.f64 (+.f64 x (tan.f64 x)) x)
(-.f64 1 (/.f64 (sin.f64 x) x))
(fma.f64 x (*.f64 x 9/40) -1/2)
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
(*.f64 1 (fma.f64 -1/6 (*.f64 x x) 2))
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
(*.f64 1 (/.f64 (+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x)) x))
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
Outputs
(/.f64 (+.f64 x (tan.f64 x)) x)
(-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2)
(/.f64 (+.f64 x (tan.f64 x)) x)
Calls

1 calls:

32.0ms
x
Results
ErrorSegmentsBranch
1.3b3x
Compiler

Compiled 167 to 112 computations (32.9% saved)

bsearch64.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
31.0ms
0.0028624513617995866
2.758897867498332
33.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes37.0ms (0.2%)

Counts
21 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))
(/.f64 (+.f64 x (tan.f64 x)) x)
(-.f64 1 (/.f64 (sin.f64 x) x))
(fma.f64 x (*.f64 x 9/40) -1/2)
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
(*.f64 1 (fma.f64 -1/6 (*.f64 x x) 2))
(*.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
(*.f64 (/.f64 1 x) (+.f64 x (tan.f64 x)))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 x 9/40) -1/2)) 1)
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/120) 1/6))
(*.f64 1 (/.f64 (+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x)) x))
Outputs
(/.f64 (+.f64 x (tan.f64 x)) x)
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(/.f64 (+.f64 x (tan.f64 x)) x)
Calls

1 calls:

31.0ms
x
Results
ErrorSegmentsBranch
1.4b3x
Compiler

Compiled 152 to 101 computations (33.6% saved)

bsearch65.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
32.0ms
0.0028624513617995866
2.758897867498332
33.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes24.0ms (0.1%)

Counts
11 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) 1/4) (-.f64 (*.f64 x (*.f64 x 9/40)) -1/2))
Outputs
1
(+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2))
1
Calls

1 calls:

19.0ms
x
Results
ErrorSegmentsBranch
1.4b3x
Compiler

Compiled 70 to 52 computations (25.7% saved)

bsearch67.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
34.0ms
0.0028624513617995866
2.758897867498332
34.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes20.0ms (0.1%)

Counts
9 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(*.f64 1 (+.f64 (*.f64 -1/6 (*.f64 x x)) 2))
(+.f64 (+.f64 (*.f64 x (*.f64 x 9/40)) 1/2) -1)
Outputs
1
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
1
Calls

1 calls:

17.0ms
x
Results
ErrorSegmentsBranch
1.4b3x
Compiler

Compiled 40 to 30 computations (25% saved)

bsearch65.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
32.0ms
0.0028624513617995866
2.758897867498332
33.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes16.0ms (0.1%)

Accuracy

Total -61.6b remaining (-3798.5%)

Threshold costs -61.6b (-3798.5%)

Counts
6 → 3
Calls
Call 1
Inputs
1
-1/2
1
-1/2
1
(-.f64 (*.f64 9/40 (*.f64 x x)) 1)
Outputs
1
-1/2
1
Calls

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
1.6b3x
Compiler

Compiled 15 to 12 computations (20% saved)

bsearch66.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
32.0ms
0.0028624513617995866
2.758897867498332
34.0ms
-136948893217.82822
-0.0017330070750343736
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify12.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
10×+-commutative_binary64
5×*-commutative_binary64
4×sub-neg_binary64
1×+-lft-identity_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046218
163218
269218
371218
472218
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -4487541332961795/32768) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 6600363461819795/2305843009213693952) (-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (+.f64 x (tan.f64 x)) x) (if (<=.f64 x 6600363461819795/2305843009213693952) (-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2) (/.f64 (+.f64 x (tan.f64 x)) x)))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (+.f64 x (tan.f64 x)) x) (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)) (/.f64 (+.f64 x (tan.f64 x)) x)))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)) 1))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) -1/2 1))
1
Outputs
(if (<=.f64 x -4487541332961795/32768) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 6600363461819795/2305843009213693952) (-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 (+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 -27/2800 (pow.f64 x 4))) -1/2) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (+.f64 x (tan.f64 x)) x) (if (<=.f64 x 6600363461819795/2305843009213693952) (-.f64 (+.f64 (+.f64 0 (*.f64 9/40 (*.f64 x x))) (*.f64 -27/2800 (pow.f64 x 4))) 1/2) (/.f64 (+.f64 x (tan.f64 x)) x)))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (+.f64 x (tan.f64 x)) x) (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 (+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 -27/2800 (pow.f64 x 4))) -1/2) (/.f64 (+.f64 x (tan.f64 x)) x)))
(if (<=.f64 x -4487541332961795/32768) (/.f64 (+.f64 x (tan.f64 x)) x) (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)) (/.f64 (+.f64 x (tan.f64 x)) x)))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 1 (+.f64 (*.f64 x (*.f64 x 9/40)) -3/2)) 1))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -4487541332961795/32768) 1 (if (<=.f64 x 6600363461819795/2305843009213693952) -1/2 1))
1
Compiler

Compiled 156 to 101 computations (35.3% saved)

soundness575.0ms (3.2%)

Algorithm
2×egg-herbie
Rules
583×fma-neg_binary64
583×fma-neg_binary64
430×fma-def_binary64
430×fma-def_binary64
418×div-sub_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11414
22414
34114
47514
513014
626014
754614
8142014
9256614
10339214
11375714
12388614
13391314
14392314
15392714
16392714
0714
11414
22414
34114
47514
513014
626014
754614
8142014
9256614
10339214
11375714
12388614
13391314
14392314
15392714
16392714
Stop Event
1×saturated
1×saturated
Compiler

Compiled 392 to 264 computations (32.7% saved)

end147.0ms (0.8%)

Compiler

Compiled 150 to 90 computations (40% saved)

Profiling

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