Details

Time bar (total: 18.4s)

analyze666.0ms (3.6%)

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

Compiled 11 to 7 computations (36.4% saved)

sample11.5s (62.3%)

Results
6.2s2107×body2048valid
4.0s3109×body1024valid
794.0ms1523×body512valid
301.0ms1415×body256valid
169.0ms102×body4096valid

preprocess200.0ms (1.1%)

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)

simplify114.0ms (0.6%)

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
34.1b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶34.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Compiler

Compiled 10 to 6 computations (40% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sin.f64 x)
✓0.0b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓1.8b
(-.f64 (sin.f64 x) x)
✓1.8b
(-.f64 (tan.f64 x) x)
Compiler

Compiled 23 to 6 computations (73.9% saved)

series7.0ms (0%)

Counts
4 → 40
Calls

12 calls:

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

rewrite254.0ms (1.4%)

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
0729
116929
2274529
Stop Event
1×node limit
Counts
4 → 440
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))
(sin.f64 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))))))) 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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))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sin.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sin.f64 (exp.f64 (log1p.f64 x))) (cos.f64 1)) (*.f64 (cos.f64 (exp.f64 (log1p.f64 x))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sin.f64 x)) 1))))))

simplify141.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
597×div-sub_binary64
542×fma-def_binary64
510×times-frac_binary64
286×associate-/l*_binary64
217×distribute-neg-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0105744
1315656
21009622
34962594
Stop Event
1×node limit
Counts
480 → 485
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)))))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) 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 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (*.f64 17/315 (pow.f64 x 7))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 17/315 (pow.f64 x 7) (*.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)))))
(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 17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.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)))
(fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) -1/5040 (*.f64 (pow.f64 x 3) -1/6)))
(+.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 9) 1/362880 (*.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 (pow.f64 (sin.f64 x) 2) (/.f64 (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2)) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 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 (/.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 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (+.f64 1 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 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 (sin.f64 x) (*.f64 (pow.f64 x 3) (cos.f64 x))))))
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 (pow.f64 (sin.f64 x) 2) (/.f64 (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2)) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 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 (/.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 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (+.f64 1 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 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 (sin.f64 x) (*.f64 (pow.f64 x 3) (cos.f64 x))))))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/6 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 1/120 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 -1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 7) -1/5040 (fma.f64 (pow.f64 x 5) 1/120 x)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) -1/5040 x)))

eval198.0ms (1.1%)

Compiler

Compiled 16764 to 5096 computations (69.6% saved)

prune62.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4796485
Fresh000
Picked011
Done000
Total4797486
Error
0b
Counts
486 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
✓34.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
29.3b
-1/2
▶33.9b
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
▶34.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
34.4b
1
▶34.1b
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
▶28.9b
(fma.f64 x (*.f64 x 9/40) -1/2)
Compiler

Compiled 53 to 36 computations (32.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
✓0.0b
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
1.8b
(-.f64 (sin.f64 x) x)
1.8b
(-.f64 (tan.f64 x) x)
Compiler

Compiled 44 to 8 computations (81.8% saved)

series6.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
2.0ms
x
@inf
(exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
0.0ms
x
@0
(exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
0.0ms
x
@inf
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
0.0ms
x
@-inf
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))

rewrite148.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
990×prod-diff_binary64
510×log-prod_binary64
358×fma-def_binary64
271×pow2_binary64
249×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0930
119230
2293030
Stop Event
1×node limit
Counts
2 → 273
Calls
Call 1
Inputs
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
(exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))) (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 2) (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (/.f64 (sin.f64 x) (-.f64 (tan.f64 x) x))) (exp.f64 (/.f64 x (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (sin.f64 x) x)) (/.f64 1 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 2)) (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) (sqrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))))))

simplify80.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
738×div-sub_binary64
679×times-frac_binary64
596×fma-def_binary64
431×associate-/l*_binary64
364×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01301101
1395992
21362913
37664913
Stop Event
1×node limit
Counts
297 → 309
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 (*.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)))))
(exp.f64 -1/2)
(+.f64 (exp.f64 -1/2) (*.f64 9/40 (*.f64 (exp.f64 -1/2) (pow.f64 x 2))))
(+.f64 (*.f64 351/22400 (*.f64 (exp.f64 -1/2) (pow.f64 x 4))) (+.f64 (exp.f64 -1/2) (*.f64 9/40 (*.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (*.f64 351/22400 (*.f64 (exp.f64 -1/2) (pow.f64 x 4))) (+.f64 (exp.f64 -1/2) (+.f64 (*.f64 -27/896000 (*.f64 (exp.f64 -1/2) (pow.f64 x 6))) (*.f64 9/40 (*.f64 (exp.f64 -1/2) (pow.f64 x 2))))))
(exp.f64 1)
(+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) (exp.f64 1)) x) (exp.f64 1))
(+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (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))) (exp.f64 1)) (pow.f64 x 2)) (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) (exp.f64 1)) x) (exp.f64 1)))
(+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (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))) (exp.f64 1)) (pow.f64 x 2)) (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) (exp.f64 1)) x) (+.f64 (/.f64 (*.f64 (+.f64 (/.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 (/.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)) (*.f64 1/6 (pow.f64 (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))) 3)))) (exp.f64 1)) (pow.f64 x 3)) (exp.f64 1))))
(exp.f64 1)
(+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (exp.f64 1)) x)) (exp.f64 1))
(+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (exp.f64 1)) x)) (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (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)))) (exp.f64 1)) (pow.f64 x 2)) (exp.f64 1)))
(+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (exp.f64 1)) x)) (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (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)))) (exp.f64 1)) (pow.f64 x 2)) (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (cos.f64 x))) (+.f64 (/.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 1/6 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (exp.f64 1)) (pow.f64 x 3))) (exp.f64 1))))
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 (*.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 27/112000 (pow.f64 x 6) (fma.f64 -27/2800 (pow.f64 x 4) -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 (+.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))))
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1
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(exp.f64 -1/2)
(+.f64 (exp.f64 -1/2) (*.f64 9/40 (*.f64 (exp.f64 -1/2) (pow.f64 x 2))))
(+.f64 (exp.f64 -1/2) (*.f64 9/40 (*.f64 (*.f64 x x) (exp.f64 -1/2))))
(fma.f64 9/40 (*.f64 x (*.f64 x (exp.f64 -1/2))) (exp.f64 -1/2))
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(fma.f64 351/22400 (*.f64 (pow.f64 x 4) (exp.f64 -1/2)) (+.f64 (exp.f64 -1/2) (*.f64 9/40 (*.f64 (*.f64 x x) (exp.f64 -1/2)))))
(fma.f64 351/22400 (*.f64 (pow.f64 x 4) (exp.f64 -1/2)) (fma.f64 9/40 (*.f64 x (*.f64 x (exp.f64 -1/2))) (exp.f64 -1/2)))
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(+.f64 (*.f64 351/22400 (*.f64 (exp.f64 -1/2) (pow.f64 x 4))) (+.f64 (exp.f64 -1/2) (+.f64 (*.f64 -27/896000 (*.f64 (exp.f64 -1/2) (pow.f64 x 6))) (*.f64 9/40 (*.f64 (exp.f64 -1/2) (pow.f64 x 2))))))
(fma.f64 351/22400 (*.f64 (pow.f64 x 4) (exp.f64 -1/2)) (+.f64 (exp.f64 -1/2) (fma.f64 -27/896000 (*.f64 (pow.f64 x 6) (exp.f64 -1/2)) (*.f64 9/40 (*.f64 (*.f64 x x) (exp.f64 -1/2))))))
(+.f64 (fma.f64 9/40 (*.f64 x (*.f64 x (exp.f64 -1/2))) (*.f64 (pow.f64 x 6) (*.f64 (exp.f64 -1/2) -27/896000))) (fma.f64 351/22400 (*.f64 (pow.f64 x 4) (exp.f64 -1/2)) (exp.f64 -1/2)))
(+.f64 (*.f64 (+.f64 (*.f64 (pow.f64 x 6) -27/896000) 1) (exp.f64 -1/2)) (*.f64 (exp.f64 -1/2) (+.f64 (*.f64 (pow.f64 x 4) 351/22400) (*.f64 9/40 (*.f64 x x)))))
(exp.f64 1)
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(fma.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (E.f64) (E.f64))
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(exp.f64 1)
(E.f64)
(+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (exp.f64 1)) x)) (exp.f64 1))
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(-.f64 (E.f64) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 x (E.f64))))
(fma.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (E.f64) (E.f64))
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(fma.f64 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (*.f64 -1/2 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)) (E.f64) (fma.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (E.f64) (E.f64)))
(+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (exp.f64 1)) x)) (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (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)))) (exp.f64 1)) (pow.f64 x 2)) (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)) (cos.f64 x))) (+.f64 (/.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 1/6 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (exp.f64 1)) (pow.f64 x 3))) (exp.f64 1))))
(fma.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 x (E.f64))) (+.f64 (/.f64 (fma.f64 1/2 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2) (neg.f64 (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))) (/.f64 (*.f64 x x) (E.f64))) (fma.f64 -1 (/.f64 (fma.f64 -1 (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2))) (+.f64 (/.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 1/6 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3)))) (/.f64 (pow.f64 x 3) (E.f64))) (E.f64))))
(+.f64 (-.f64 (*.f64 (/.f64 (E.f64) x) (/.f64 (fma.f64 1/2 (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))))) x)) (/.f64 (E.f64) (/.f64 (pow.f64 x 3) (-.f64 (fma.f64 1/6 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 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 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 2)))))) (-.f64 (E.f64) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 x (E.f64)))))
(+.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (E.f64) (E.f64)) (*.f64 (E.f64) (-.f64 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (*.f64 -1/2 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 x x)) (/.f64 (-.f64 (fma.f64 1/6 (pow.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) 3) (*.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)))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) 2))) (pow.f64 x 3)))))

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.0b
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
1.8b
(-.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
@inf
(/.f64 (-.f64 (sin.f64 x) x) (neg.f64 x))
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))

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)))))))

simplify65.0ms (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))

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x))
✓0.0b
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
1.8b
(-.f64 (sin.f64 x) x)
1.8b
(-.f64 (tan.f64 x) x)
Compiler

Compiled 35 to 9 computations (74.3% saved)

series7.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
2.0ms
x
@inf
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
1.0ms
x
@0
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
1.0ms
x
@inf
(/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x))
0.0ms
x
@-inf
(/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x))

rewrite235.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
990×prod-diff_binary64
538×log-prod_binary64
344×fma-def_binary64
225×egg-rr
195×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0931
121128
2320128
Stop Event
1×node limit
Counts
2 → 274
Calls
Call 1
Inputs
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
(/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sin.f64 x) (-.f64 (tan.f64 x) x)) (/.f64 x (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sin.f64 x) x) (/.f64 1 (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) 2) (cbrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))) (sqrt.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sin.f64 x) x)) 1) (/.f64 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simplify81.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
804×fma-def_binary64
681×times-frac_binary64
439×associate-/l*_binary64
306×associate-+l+_binary64
271×associate-+r+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01191051
1392872
21698760
Stop Event
1×node limit
Counts
298 → 308
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 -1 (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(-.f64 (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (sin.f64 x) x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.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 (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))) (pow.f64 x 2))) (+.f64 1 (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))))
(+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 3)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))) (pow.f64 x 2))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))))
-2
(-.f64 (*.f64 -9/10 (pow.f64 x 2)) 2)
(-.f64 (+.f64 (*.f64 -513/1400 (pow.f64 x 4)) (*.f64 -9/10 (pow.f64 x 2))) 2)
(-.f64 (+.f64 (*.f64 -297/2000 (pow.f64 x 6)) (+.f64 (*.f64 -513/1400 (pow.f64 x 4)) (*.f64 -9/10 (pow.f64 x 2)))) 2)
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 1 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (pow.f64 x 2)) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (pow.f64 (sin.f64 x) 2)) (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (pow.f64 x 2)) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
1
(+.f64 1 (*.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 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))))
(+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.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)
(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))
(-.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 1 (-.f64 (/.f64 (neg.f64 (sin.f64 x)) x) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 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 -1 (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x))) (pow.f64 x 2))))) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))
(+.f64 1 (-.f64 (*.f64 -1 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (+.f64 (sin.f64 x) (*.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)))))
(-.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (/.f64 (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) x)))
(+.f64 1 (+.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (*.f64 x x) (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.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 -1 (/.f64 (+.f64 (*.f64 -1 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (*.f64 (sin.f64 x) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (-.f64 (*.f64 -1 (sin.f64 x)) (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.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) (fma.f64 -1 (/.f64 (fma.f64 -1 (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (+.f64 (sin.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))))) (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (+.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (sin.f64 x) (*.f64 -1 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))))))) (pow.f64 x 3)) (neg.f64 (/.f64 (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (+.f64 (sin.f64 x) (*.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)))))
(+.f64 1 (+.f64 (-.f64 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 x x)) (/.f64 (fma.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (pow.f64 x 3))) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(+.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (-.f64 1 (fma.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (/.f64 (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x))) x) (/.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 (sin.f64 x) (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (*.f64 (sin.f64 x) 0) (/.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 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))) (pow.f64 x 2))) (+.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) x) (/.f64 (*.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (+.f64 (sin.f64 x) (*.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)))))
(-.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (/.f64 (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) x)))
(+.f64 1 (+.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (*.f64 x x) (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 3)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))) (pow.f64 x 2))) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 -1 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (/.f64 (pow.f64 x 3) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (fma.f64 -1 (/.f64 (fma.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 x x)) (+.f64 1 (fma.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))) (fma.f64 -1 (/.f64 (*.f64 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 x 3)) (neg.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x)))))))
(+.f64 (+.f64 1 (+.f64 (/.f64 (*.f64 (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (pow.f64 x 3)) (-.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (*.f64 (/.f64 (sin.f64 x) (pow.f64 x 3)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))))) (+.f64 (/.f64 (*.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (+.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))) (*.f64 x x)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 3)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))
(+.f64 (fma.f64 -1 (fma.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (pow.f64 x 3)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x)))) (*.f64 (+.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) 1) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))) 1) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 3)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) (/.f64 (*.f64 x x) (+.f64 (*.f64 (sin.f64 x) 0) (/.f64 (sin.f64 x) (cos.f64 x)))))))
-2
(-.f64 (*.f64 -9/10 (pow.f64 x 2)) 2)
(fma.f64 -9/10 (*.f64 x x) -2)
(fma.f64 (*.f64 x x) -9/10 -2)
(fma.f64 (*.f64 -9/10 x) x -2)
(-.f64 (+.f64 (*.f64 -513/1400 (pow.f64 x 4)) (*.f64 -9/10 (pow.f64 x 2))) 2)
(+.f64 (*.f64 (pow.f64 x 4) -513/1400) (fma.f64 -9/10 (*.f64 x x) -2))
(fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2))
(fma.f64 x (*.f64 x -9/10) (fma.f64 (pow.f64 x 4) -513/1400 -2))
(-.f64 (+.f64 (*.f64 -297/2000 (pow.f64 x 6)) (+.f64 (*.f64 -513/1400 (pow.f64 x 4)) (*.f64 -9/10 (pow.f64 x 2)))) 2)
(+.f64 (fma.f64 -297/2000 (pow.f64 x 6) (fma.f64 -513/1400 (pow.f64 x 4) (*.f64 (*.f64 x x) -9/10))) -2)
(fma.f64 (pow.f64 x 6) -297/2000 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
(fma.f64 (pow.f64 x 6) -297/2000 (fma.f64 x (*.f64 x -9/10) (fma.f64 (pow.f64 x 4) -513/1400 -2)))
1
(-.f64 (+.f64 1 (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (-.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (neg.f64 (sin.f64 x)) 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 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (pow.f64 x 2)) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (-.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (*.f64 x x) (sin.f64 x)))) (/.f64 (neg.f64 (sin.f64 x)) x)))
(+.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (-.f64 1 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))
(+.f64 1 (*.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (-.f64 -1 (/.f64 (sin.f64 x) x))))
(-.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (pow.f64 (sin.f64 x) 2)) (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 -1 (sin.f64 x))) (sin.f64 x)) (pow.f64 x 2)) (*.f64 -1 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)))))) (*.f64 -1 (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (+.f64 (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 2))) 1) (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (*.f64 x x) (sin.f64 x))))) (/.f64 (neg.f64 (sin.f64 x)) x))
(+.f64 1 (+.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (-.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))))
(+.f64 (-.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (sin.f64 x))))
1
(+.f64 1 (*.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))
(+.f64 1 (-.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (neg.f64 (sin.f64 x)) 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 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x))))
(+.f64 1 (-.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (*.f64 x x) (sin.f64 x)))) (/.f64 (neg.f64 (sin.f64 x)) x)))
(+.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (-.f64 1 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)))))
(+.f64 1 (*.f64 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x) (-.f64 -1 (/.f64 (sin.f64 x) x))))
(+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 3))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (sin.f64 x) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)))))
(-.f64 (+.f64 (+.f64 (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 2))) 1) (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 x (cos.f64 x))) (/.f64 (*.f64 -1 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (*.f64 x x) (sin.f64 x))))) (/.f64 (neg.f64 (sin.f64 x)) x))
(+.f64 1 (+.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x) (-.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))))))
(+.f64 (-.f64 1 (/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)) (*.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 x x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (sin.f64 x))))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 x (*.f64 x 9/40) -1/2)
✓0.2b
(*.f64 x 9/40)
Compiler

Compiled 13 to 9 computations (30.8% saved)

series5.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite92.0ms (0.5%)

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)))))))

simplify233.0ms (1.3%)

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)

eval810.0ms (4.4%)

Compiler

Compiled 40399 to 12776 computations (68.4% saved)

prune174.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New125261258
Fresh202
Picked101
Done224
Total125781265
Error
0b
Counts
1265 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓34.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
29.3b
-1/2
▶34.5b
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
▶28.9b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
34.4b
1
▶34.4b
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
✓34.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
▶33.9b
(-.f64 1 (/.f64 (sin.f64 x) x))
Compiler

Compiled 61 to 43 computations (29.5% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.0b
(+.f64 x (sin.f64 x))
✓0.1b
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
1.0ms
x
@0
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
0.0ms
x
@inf
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 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
866×pow1_binary64
810×add-log-exp_binary64
810×log1p-expm1-u_binary64
810×expm1-log1p-u_binary64
790×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
115515
2227215
Stop Event
1×node limit
Counts
2 → 76
Calls
Call 1
Inputs
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
(+.f64 x (sin.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (/.f64 (sin.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (/.f64 (sin.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (/.f64 (sin.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (+.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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 x (cbrt.f64 (+.f64 x (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (/.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 x (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 x (-.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (sin.f64 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))) (*.f64 (neg.f64 x) (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))) (*.f64 (neg.f64 x) (-.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) 1) (*.f64 (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) 1) (*.f64 (-.f64 x (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) -1) (*.f64 (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) -1) (*.f64 (-.f64 x (sin.f64 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (sin.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 3)) (+.f64 1 (-.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) x))) (-.f64 1 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (sin.f64 x)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (sin.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 x (sin.f64 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (/.f64 1 x)) (fma.f64 x x (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 x)) (-.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (+.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 (/.f64 1 x) (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))) (-.f64 x (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x (sin.f64 x)) -1) (neg.f64 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 cbrt.f64 (/.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 x) 3) (pow.f64 (+.f64 x (sin.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x (sin.f64 x)) 3) (pow.f64 (/.f64 1 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 (log.f64 (+.f64 1 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (/.f64 1 x) (/.f64 (sin.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) x (/.f64 (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 1 (+.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 (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 x) 2) (cbrt.f64 x) (sin.f64 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 (sqrt.f64 x) (sqrt.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)))))

simplify101.0ms (0.6%)

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
100 → 94
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))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (*.f64 x 9/40))
0.2b
(*.f64 x 9/40)
Compiler

Compiled 19 to 13 computations (31.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
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))

rewrite46.0ms (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))))))))

simplify170.0ms (0.9%)

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))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.1b
(/.f64 (sin.f64 x) x)
✓1.8b
(-.f64 1 (/.f64 (sin.f64 x) x))
Compiler

Compiled 15 to 6 computations (60% saved)

series3.0ms (0%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 1 (/.f64 (sin.f64 x) x))
0.0ms
x
@-inf
(-.f64 1 (/.f64 (sin.f64 x) x))
0.0ms
x
@-inf
(/.f64 (sin.f64 x) x)
0.0ms
x
@inf
(-.f64 1 (/.f64 (sin.f64 x) x))
0.0ms
x
@inf
(/.f64 (sin.f64 x) x)

rewrite57.0ms (0.3%)

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)))))))

simplify69.0ms (0.4%)

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)))

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (sin.f64 x))
✓0.0b
(+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
✓0.0b
(/.f64 (+.f64 x (sin.f64 x)) x)
✓0.0b
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
Compiler

Compiled 33 to 11 computations (66.7% saved)

series5.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@0
(/.f64 (+.f64 x (sin.f64 x)) x)
0.0ms
x
@0
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
0.0ms
x
@0
(+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
0.0ms
x
@inf
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
0.0ms
x
@-inf
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)

rewrite101.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
923×prod-diff_binary64
522×fma-def_binary64
406×log-prod_binary64
246×fma-neg_binary64
232×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0842
119030
2299030
Stop Event
1×node limit
Counts
3 → 253
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
(/.f64 (+.f64 x (sin.f64 x)) x)
(+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))
Outputs
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(-.f64 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2) 1) (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3)) 1) (fma.f64 (/.f64 (+.f64 x (sin.f64 x)) x) (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) 1) (-.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 (+.f64 x (sin.f64 x)) x) (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) -1) 1) (+.f64 1 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) (-.f64 1 (pow.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sin.f64 x)) (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (*.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) (sqrt.f64 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (+.f64 x (sin.f64 x))) (/.f64 1 (neg.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 2) (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))) (/.f64 1 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) 2) (cbrt.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) (sqrt.f64 (+.f64 (/.f64 (+.f64 x (sin.f64 x)) x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 x (sin.f64 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 x (sin.f64 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 x (sin.f64 x)) (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 x (sin.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (+.f64 x (sin.f64 x)) x)))) 1)))))

simplify137.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
2082×fma-def_binary64
477×sqr-pow_binary64
438×associate-/r*_binary64
395×*-commutative_binary64
326×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
029324
163318
2144312
3402306
41370306
53402306
64025306
74435306
84855306
95613306
105947306
117462306
127930306
Stop Event
1×node limit
Counts
289 → 188
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))
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))
3
(+.f64 3 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 3 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 3 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
2
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
2
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.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))
(+.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 (pow.f64 x 4) -1/5040 (fma.f64 x (*.f64 x 1/120) -1/6)) 2)
(fma.f64 x (*.f64 x (fma.f64 (pow.f64 x 4) -1/5040 (fma.f64 x (*.f64 x 1/120) -1/6))) 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))
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))
(+.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 (pow.f64 x 4) -1/5040 (fma.f64 x (*.f64 x 1/120) -1/6)) 2)
(fma.f64 x (*.f64 x (fma.f64 (pow.f64 x 4) -1/5040 (fma.f64 x (*.f64 x 1/120) -1/6))) 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))
3
(+.f64 3 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 (*.f64 -1/6 (*.f64 x x)) 3)
(fma.f64 -1/6 (*.f64 x x) 3)
(+.f64 3 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/6 (*.f64 x x) (*.f64 1/120 (pow.f64 x 4))) 3)
(+.f64 (*.f64 1/120 (pow.f64 x 4)) (fma.f64 -1/6 (*.f64 x x) 3))
(fma.f64 -1/6 (*.f64 x x) (fma.f64 1/120 (pow.f64 x 4) 3))
(+.f64 3 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/6 (*.f64 x x) (fma.f64 -1/5040 (pow.f64 x 6) (*.f64 1/120 (pow.f64 x 4)))) 3)
(+.f64 (fma.f64 1/120 (pow.f64 x 4) (*.f64 -1/5040 (pow.f64 x 6))) (fma.f64 -1/6 (*.f64 x x) 3))
(+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (fma.f64 -1/6 (*.f64 x x) (fma.f64 1/120 (pow.f64 x 4) 3)))
(fma.f64 -1/6 (*.f64 x x) (fma.f64 -1/5040 (pow.f64 x 6) (fma.f64 1/120 (pow.f64 x 4) 3)))
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x 1/120) -1/6)) (fma.f64 -1/5040 (pow.f64 x 6) 3))
2
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
2
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))
(+.f64 2 (/.f64 (sin.f64 x) x))

eval137.0ms (0.7%)

Compiler

Compiled 7013 to 3396 computations (51.6% saved)

prune68.0ms (0.4%)

Pruning

10 alts after pruning (5 fresh and 5 done)

PrunedKeptTotal
New4814485
Fresh112
Picked011
Done145
Total48310493
Error
0b
Counts
493 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓34.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
29.3b
-1/2
▶34.4b
(/.f64 (+.f64 x (sin.f64 x)) x)
▶34.5b
(*.f64 (/.f64 1 x) x)
✓28.9b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
34.4b
1
▶34.4b
(-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
✓34.4b
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
✓34.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓33.9b
(-.f64 1 (/.f64 (sin.f64 x) x))
Compiler

Compiled 74 to 52 computations (29.7% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 1 x) x)
Compiler

Compiled 11 to 7 computations (36.4% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite53.0ms (0.3%)

Algorithm
1×egg-rewrite-iter-limit
1×batch-egg-rewrite
Rules
325×pow1_binary64
315×add-sqr-sqrt_binary64
307×*-un-lft-identity_binary64
301×add-log-exp_binary64
301×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051
11011
28901
051
Stop Event
1×iter limit
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (/.f64 1 x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112
1412
Stop Event
1×saturated
Counts
13 → 1
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
Outputs
1
1
1
1
1
1
1
1
1
1
1
1

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiled 24 to 11 computations (54.2% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite66.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
610×unpow-prod-down_binary64
388×log-prod_binary64
298×exp-prod_binary64
228×pow2_binary64
225×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0812
11839
225239
Stop Event
1×node limit
Counts
1 → 88
Calls
Call 1
Inputs
(-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (+.f64 (/.f64 (sin.f64 x) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (*.f64 (+.f64 (/.f64 (sin.f64 x) x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 (sin.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 2 (/.f64 (sin.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (sin.f64 x) x) -1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 (sin.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 2) (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1) (pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1) (/.f64 1 (+.f64 (/.f64 (sin.f64 x) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1) (pow.f64 (/.f64 1 (+.f64 (/.f64 (sin.f64 x) x) 3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1) (-.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 (/.f64 (sin.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1) 1) (pow.f64 (-.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 2) 3) (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3)) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 (sin.f64 x) x) 3) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (-.f64 1 (*.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1) (+.f64 (/.f64 (sin.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1)) (neg.f64 (+.f64 (/.f64 (sin.f64 x) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 8 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) -1) 3)) (+.f64 4 (-.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) -1) 2) (*.f64 2 (+.f64 (/.f64 (sin.f64 x) x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) -1) 2)) (-.f64 2 (+.f64 (/.f64 (sin.f64 x) x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) (+.f64 (/.f64 (sin.f64 x) x) 3)) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 3) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (/.f64 (sin.f64 x) x) 3) (+.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 2)) (cbrt.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))) (sqrt.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 (sin.f64 x) x) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 2 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (/.f64 (sin.f64 x) x) 1)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sin.f64 x) (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sin.f64 x) x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sin.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 2 (/.f64 (sin.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 (sin.f64 x) x) -1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (sin.f64 x)) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (/.f64 x (sin.f64 x)) -2)) (cbrt.f64 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) (cbrt.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2)) (cbrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 2)) (*.f64 (cbrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sin.f64 x) x)) (sqrt.f64 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) (*.f64 (sqrt.f64 (+.f64 2 (/.f64 (sin.f64 x) x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sin.f64 x)) (pow.f64 (neg.f64 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 8 (pow.f64 (/.f64 x (sin.f64 x)) -3)) (/.f64 1 (fma.f64 (/.f64 (sin.f64 x) x) (-.f64 (/.f64 (sin.f64 x) x) 2) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sin.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 4 (pow.f64 (/.f64 x (sin.f64 x)) -2)) (/.f64 1 (-.f64 2 (/.f64 (sin.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) -1)) 2) (cbrt.f64 (+.f64 (/.f64 (sin.f64 x) x) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) -1)) (sqrt.f64 (+.f64 (/.f64 (sin.f64 x) x) -1)) 2)))) (#(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)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sin.f64 x)) 1) (/.f64 (sqrt.f64 (sin.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (sin.f64 x) (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (sin.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (sin.f64 x)) (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (/.f64 (sin.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sin.f64 x)) (sqrt.f64 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)) 1) 2)))))

simplify118.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
1583×fma-def_binary64
599×sqr-pow_binary64
433×associate-/r*_binary64
399×*-commutative_binary64
326×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
024108
153106
2114104
3318102
41160102
52922102
63545102
73955102
84378102
95118102
105452102
116781102
127245102
137803102
Stop Event
1×node limit
Counts
100 → 97
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))
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 (*.f64 x 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)))))
(fma.f64 -1/5040 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/120 -1/6) 2))
(fma.f64 x (fma.f64 1/120 (pow.f64 x 3) (*.f64 -1/6 x)) (fma.f64 -1/5040 (pow.f64 x 6) 2))
(fma.f64 -1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/5040) 1/120) 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))

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

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

Compiled 14 to 4 computations (71.4% saved)

eval69.0ms (0.4%)

Compiler

Compiled 3252 to 1786 computations (45.1% saved)

prune34.0ms (0.2%)

Pruning

10 alts after pruning (2 fresh and 8 done)

PrunedKeptTotal
New2391240
Fresh112
Picked011
Done077
Total24010250
Error
0b
Counts
250 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓34.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
34.4b
1
29.3b
-1/2
✓34.4b
(/.f64 (+.f64 x (sin.f64 x)) x)
✓34.5b
(*.f64 (/.f64 1 x) x)
✓28.9b
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
✓34.4b
(-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
✓34.4b
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
✓34.1b
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
✓33.9b
(-.f64 1 (/.f64 (sin.f64 x) x))
Compiler

Compiled 74 to 52 computations (29.7% saved)

regimes43.0ms (0.2%)

Counts
19 → 3
Calls
Call 1
Inputs
1
1
-1/2
1
-1/2
1
(*.f64 (/.f64 1 x) x)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(/.f64 (+.f64 x (sin.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 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(pow.f64 (/.f64 (-.f64 (tan.f64 x) x) (-.f64 (sin.f64 x) x)) -1)
(log.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))))
Outputs
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
1
Calls

3 calls:

29.0ms
x
5.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms
(/.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 132 to 63 computations (52.3% saved)

bsearch67.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
35.0ms
4.501402963848073e-9
1.638006467822858e+29
32.0ms
-0.7649677704168113
-0.00022617032497058892
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes27.0ms (0.1%)

Counts
15 → 3
Calls
Call 1
Inputs
1
1
-1/2
1
-1/2
1
(*.f64 (/.f64 1 x) x)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(/.f64 (+.f64 x (sin.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 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
(*.f64 (/.f64 1 x) (+.f64 x (sin.f64 x)))
(-.f64 (+.f64 1 (/.f64 (+.f64 x (sin.f64 x)) x)) 1)
Outputs
(-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
1
Calls

1 calls:

24.0ms
x
Results
ErrorSegmentsBranch
0.6b3x
Compiler

Compiled 72 to 40 computations (44.4% saved)

bsearch67.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
33.0ms
4.501402963848073e-9
1.638006467822858e+29
34.0ms
-13.742055689298413
-0.7649677704168113
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes25.0ms (0.1%)

Counts
12 → 3
Calls
Call 1
Inputs
1
1
-1/2
1
-1/2
1
(*.f64 (/.f64 1 x) x)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
(/.f64 (+.f64 x (sin.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))
Outputs
(/.f64 (+.f64 x (sin.f64 x)) x)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
1
Calls

1 calls:

23.0ms
x
Results
ErrorSegmentsBranch
0.6b3x
Compiler

Compiled 46 to 29 computations (37% saved)

bsearch69.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
35.0ms
4.501402963848073e-9
1.638006467822858e+29
34.0ms
-13.742055689298413
-0.7649677704168113
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes18.0ms (0.1%)

Counts
8 → 3
Calls
Call 1
Inputs
1
1
-1/2
1
-1/2
1
(*.f64 (/.f64 1 x) x)
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
Outputs
1
(+.f64 (*.f64 x (*.f64 x 9/40)) -1/2)
1
Calls

1 calls:

16.0ms
x
Results
ErrorSegmentsBranch
0.6b3x
Compiler

Compiled 21 to 16 computations (23.8% saved)

bsearch67.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
34.0ms
4.501402963848073e-9
1.638006467822858e+29
33.0ms
-13.742055689298413
-0.7649677704168113
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes16.0ms (0.1%)

Counts
7 → 3
Calls
Call 1
Inputs
1
1
-1/2
1
-1/2
1
(*.f64 (/.f64 1 x) x)
Outputs
1
-1/2
1
Calls

1 calls:

14.0ms
x
Results
ErrorSegmentsBranch
0.8b3x
Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch126.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
63.0ms
4.501402963848073e-9
1.638006467822858e+29
61.0ms
-13.742055689298413
-0.7649677704168113
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes8.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
2 → 1
Calls
Call 1
Inputs
1
1
Outputs
1
Calls

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
34.4b1x
Compiler

Compiled 5 to 4 computations (20% saved)

simplify16.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
4×sub-neg_binary64
3×*-commutative_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033144
146144
251144
353144
454144
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -14111164685515122688/18446744073709551616) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) (-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) (/.f64 (+.f64 x (sin.f64 x)) x) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) 1 (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) 1 (if (<=.f64 x 5441862267485753/1208925819614629174706176) -1/2 1))
1
Outputs
(if (<=.f64 x -14111164685515122688/18446744073709551616) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -6890217131599181/9007199254740992) (/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x)) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) (-.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) 1) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) (+.f64 (+.f64 2 (/.f64 (sin.f64 x) x)) -1) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) (/.f64 (+.f64 x (sin.f64 x)) x) (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) 1 (if (<=.f64 x 5441862267485753/1208925819614629174706176) (+.f64 (*.f64 x (*.f64 x 9/40)) -1/2) 1))
(if (<=.f64 x -7736089610203617/562949953421312) 1 (if (<=.f64 x 5441862267485753/1208925819614629174706176) -1/2 1))
1
Compiler

Compiled 106 to 79 computations (25.5% saved)

soundness1.2s (6.3%)

Algorithm
5×egg-herbie
Rules
597×div-sub_binary64
597×div-sub_binary64
583×fma-neg_binary64
583×fma-neg_binary64
583×fma-neg_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
0105744
1315656
21009622
34962594
0714
11414
22414
34114
47514
513014
626014
754614
8142014
9256614
10339214
11375714
12388614
13391314
14392314
15392714
16392714
0105744
1315656
21009622
34962594
Stop Event
1×node limit
1×saturated
1×node limit
1×saturated
1×saturated
Compiler

Compiled 642 to 438 computations (31.8% saved)

end123.0ms (0.7%)

Compiler

Compiled 101 to 72 computations (28.7% saved)

Profiling

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