Details

Time bar (total: 8.2s)

analyze102.0ms (1.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
Compiler

Compiled 10 to 7 computations (30% saved)

sample3.2s (38.3%)

Results
1.5s2064×body2048valid
510.0ms3364×body256valid
492.0ms1179×body1024valid
488.0ms1556×body512valid
64.0ms93×body4096valid

preprocess26.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
424×fma-def_binary64
293×fma-neg_binary64
86×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512712
619212
731712
862112
9114012
10170012
11182912
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 10 to 7 computations (30% saved)

simplify18.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
424×fma-def_binary64
293×fma-neg_binary64
86×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512712
619212
731712
862112
9114012
10170012
11182912
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
28.5b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶28.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
14.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.1b
(-.f64 1 (cos.f64 x))
✓2.1b
(-.f64 1 (cos.f64 x))
✓14.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite54.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
873×pow1_binary64
819×add-log-exp_binary64
818×log1p-expm1-u_binary64
818×expm1-log1p-u_binary64
801×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
115218
2213018
Stop Event
1×node limit
Counts
2 → 62
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(-.f64 1 (cos.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (neg.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))))

simplify43.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
621×distribute-rgt-out_binary64
555×distribute-lft-out_binary64
544×associate-/r*_binary64
510×fma-def_binary64
425×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037218
191216
2217214
3652212
42438212
55715212
Stop Event
1×node limit
Counts
78 → 79
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))

eval22.0ms (0.3%)

Compiler

Compiled 1062 to 635 computations (40.2% saved)

prune56.0ms (0.7%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New611879
Fresh000
Picked011
Done000
Total611980
Error
0.0b
Counts
80 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
28.6b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
▶28.1b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶27.9b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
▶35.4b
(fma.f64 x (*.f64 -1/24 x) 1/2)
34.2b
1/2
▶14.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
✓28.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
40.5b
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))
15.2b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
27.4b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
28.5b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
27.9b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
▶14.7b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
28.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
27.5b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
28.7b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
28.5b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
38.8b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
35.2b
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
Compiler

Compiled 447 to 328 computations (26.6% saved)

localize22.0ms (0.3%)

Local error

Found 8 expressions with local error:

NewErrorProgram
14.0b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.4b
(+.f64 1 (cos.f64 x))
0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.4b
(+.f64 1 (cos.f64 x))
✓14.0b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 43 to 15 computations (65.1% saved)

series28.0ms (0.3%)

Counts
4 → 44
Calls

12 calls:

TimeVariablePointExpression
21.0ms
x
@-inf
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
2.0ms
x
@-inf
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
1.0ms
x
@inf
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
1.0ms
x
@0
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.0ms
x
@inf
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))

rewrite74.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
582×log-prod_binary64
456×prod-diff_binary64
292×pow2_binary64
250×fma-def_binary64
244×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122830
2352130
Stop Event
1×node limit
Counts
4 → 182
Calls
Call 1
Inputs
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(+.f64 1 (cos.f64 x))
(*.f64 (sin.f64 x) (sin.f64 x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) 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(cos.f64 x))) (sin.f64 x)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1/2 (cos.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 (cos.f64 (+.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 (+.f64 x x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 3)) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 2) (*.f64 1/2 (*.f64 (cos.f64 (+.f64 x x)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (cos.f64 x) 2) 3)) (+.f64 1 (+.f64 (pow.f64 (pow.f64 (cos.f64 x) 2) 2) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 2)) (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (cos.f64 x) 2) 2)) (+.f64 1 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (/.f64 1 (/.f64 1 (tan.f64 (/.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 (neg.f64 (cos.f64 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) 1) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) 1) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (neg.f64 (cos.f64 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))))

simplify56.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
920×times-frac_binary64
873×distribute-lft-out_binary64
517×associate-/l*_binary64
357×associate-/r*_binary64
344×associate-/l/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068576
1158572
2393520
31258520
42444520
57295520
Stop Event
1×node limit
Counts
226 → 220
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4))))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (+.f64 (*.f64 -1/315 (pow.f64 x 8)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2))))
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 1/2 (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 -1/24 (*.f64 x x)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 2)
(fma.f64 x (*.f64 x -1/2) 2)
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/24)))
(+.f64 2 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 1/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 2))
(fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (*.f64 x x) -1/2 2))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 2 (fma.f64 -1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (*.f64 (pow.f64 x 6) -1/720))))
(+.f64 (fma.f64 (*.f64 x x) -1/2 2) (fma.f64 (pow.f64 x 4) 1/24 (*.f64 (pow.f64 x 6) -1/720)))
(+.f64 2 (fma.f64 (pow.f64 x 6) -1/720 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 1/24))))
(+.f64 (fma.f64 (*.f64 x x) -1/2 2) (fma.f64 (pow.f64 x 6) -1/720 (*.f64 (pow.f64 x 4) 1/24)))
(+.f64 (fma.f64 x (*.f64 x -1/2) 2) (fma.f64 (pow.f64 x 4) 1/24 (*.f64 (pow.f64 x 6) -1/720)))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 -1/3 (pow.f64 x 4) (*.f64 x x))
(fma.f64 (pow.f64 x 4) -1/3 (*.f64 x x))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 -1/3 (pow.f64 x 4) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 6) 2/45)))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 (pow.f64 x 6) 2/45 (*.f64 x x)))
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (+.f64 (*.f64 -1/315 (pow.f64 x 8)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 -1/3 (pow.f64 x 4) (fma.f64 -1/315 (pow.f64 x 8) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 -1/315 (pow.f64 x 8) (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 -1/315 (pow.f64 x 8)))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 -1/315 (pow.f64 x 8) (*.f64 (pow.f64 x 6) 2/45))))
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 x (*.f64 1/2 x)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 x (*.f64 1/2 x))))
(*.f64 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 -1/24 x)
0.1b
(fma.f64 x (*.f64 -1/24 x) 1/2)
✓0.1b
(fma.f64 x (*.f64 -1/24 x) 1/2)
✓0.4b
(*.f64 -1/24 x)
Compiler

Compiled 13 to 9 computations (30.8% saved)

series3.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(fma.f64 x (*.f64 -1/24 x) 1/2)
1.0ms
x
@inf
(fma.f64 x (*.f64 -1/24 x) 1/2)
1.0ms
x
@0
(*.f64 -1/24 x)
0.0ms
x
@-inf
(*.f64 -1/24 x)
0.0ms
x
@inf
(*.f64 -1/24 x)

rewrite41.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0612
112212
2132812
Stop Event
1×node limit
Counts
2 → 32
Calls
Call 1
Inputs
(*.f64 -1/24 x)
(fma.f64 x (*.f64 -1/24 x) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/24 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 -1/24 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/24) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 -1/24 x)) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 -1/24 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) (sqrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 -1/24 x)) 3) 1/8) (+.f64 (*.f64 (*.f64 x (*.f64 -1/24 x)) (*.f64 x (*.f64 -1/24 x))) (-.f64 1/4 (*.f64 (*.f64 x (*.f64 -1/24 x)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 -1/24 x)) (*.f64 x (*.f64 -1/24 x))) 1/4) (-.f64 (*.f64 x (*.f64 -1/24 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 -1/24 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 -1/24 x) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 -1/24 x) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 -1/24 x) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 -1/24 x) 1/2)))))))

simplify136.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1106×sqr-pow_binary64
618×cube-prod_binary64
554×fabs-mul_binary64
536×pow-sqr_binary64
446×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
08105
11587
22787
35187
411487
534587
6125487
7215387
8231787
9250187
10270987
11300487
12339787
13387787
14443887
15512087
16595387
17634787
18663587
19691387
20698787
21702387
22796487
Stop Event
1×node limit
Counts
44 → 37
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
2.1b
(-.f64 1 (cos.f64 x))
0.7b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
0.1b
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
✓0.1b
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
✓0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
✓0.7b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series7.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.0ms
x
@inf
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.0ms
x
@-inf
(/.f64 (-.f64 1 (cos.f64 x)) x)
1.0ms
x
@0
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.0ms
x
@0
(/.f64 (-.f64 1 (cos.f64 x)) x)

rewrite81.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
490×log-prod_binary64
382×exp-prod_binary64
266×pow-prod-down_binary64
252×pow2_binary64
244×prod-diff_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0936
119833
2273333
Stop Event
1×node limit
Counts
3 → 199
Calls
Call 1
Inputs
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 (-.f64 1 (cos.f64 x)) x)
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
Outputs
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*.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1/2) (/.f64 x (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))) 2)) (cbrt.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))) (sqrt.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))))

simplify51.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
768×fma-def_binary64
561×associate-*l*_binary64
505×unswap-sqr_binary64
471×distribute-rgt-out_binary64
430×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054352
1137348
2328344
3945342
43539342
56368342
Stop Event
1×node limit
Counts
227 → 222
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 1/720 (pow.f64 x 5))))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/40320 (pow.f64 x 7)) (*.f64 1/720 (pow.f64 x 5)))))
2
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (+.f64 (*.f64 1/3024 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 1/720 (pow.f64 x 5))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/720 (pow.f64 x 5))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (*.f64 1/2 x)))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/40320 (pow.f64 x 7)) (*.f64 1/720 (pow.f64 x 5)))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 -1/40320 (pow.f64 x 7) (*.f64 1/720 (pow.f64 x 5)))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 1/720 (pow.f64 x 5) (*.f64 -1/40320 (pow.f64 x 7)))))
(fma.f64 1/2 x (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (*.f64 -1/40320 (pow.f64 x 7)))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (fma.f64 -1/40320 (pow.f64 x 7) (*.f64 1/2 x))))
(fma.f64 -1/40320 (pow.f64 x 7) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/720 (pow.f64 x 5)))))
2
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(+.f64 (fma.f64 1/6 (*.f64 x x) 2) (*.f64 (pow.f64 x 4) 1/120))
(fma.f64 (*.f64 x x) 1/6 (fma.f64 (pow.f64 x 4) 1/120 2))
(fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 4) 1/120 2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/120 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (+.f64 (*.f64 1/3024 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 (fma.f64 1/6 (*.f64 x x) 2) (fma.f64 1/3024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/120)))
(+.f64 (fma.f64 (pow.f64 x 4) 1/120 (*.f64 (pow.f64 x 6) 1/3024)) (fma.f64 (*.f64 x x) 1/6 2))
(fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 6) 1/3024 (fma.f64 (pow.f64 x 4) 1/120 2)))
(fma.f64 (pow.f64 x 4) 1/120 (fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 6) 1/3024 2)))
(fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) 1/3024 2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/120 1/6) (fma.f64 (pow.f64 x 6) 1/3024 2))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
16.1b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
0.1b
(*.f64 (cos.f64 x) (pow.f64 x -2))
✓0.1b
(*.f64 (cos.f64 x) (pow.f64 x -2))
✓16.1b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
Compiler

Compiled 24 to 14 computations (41.7% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite59.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
837×pow1_binary64
783×add-log-exp_binary64
782×log1p-expm1-u_binary64
782×expm1-log1p-u_binary64
766×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0724
116021
2215521
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
(*.f64 (cos.f64 x) (pow.f64 x -2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 1 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 2) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (sqrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (+.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6))) (/.f64 1 (+.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4))) (/.f64 1 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) (sqrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (-.f64 (/.f64 1 x) (sqrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (cos.f64 x)) 1) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))))) (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))) (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6))) (+.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4))) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))) (neg.f64 (+.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))) (neg.f64 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -6) (pow.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 3)) (+.f64 (pow.f64 x -4) (-.f64 (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))) (*.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))) (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -4)) (cbrt.f64 (pow.f64 x -2)) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 1 x) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x -2) (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))))

simplify38.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
535×associate-/r*_binary64
374×associate-/l/_binary64
345×distribute-lft-out_binary64
342×distribute-rgt-neg-in_binary64
327×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
036278
182276
2191274
3536272
41755272
54048272
Stop Event
1×node limit
Counts
75 → 70
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 x (*.f64 -1/24 x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(+.f64 (/.f64 1 (*.f64 x x)) -1/2)
(+.f64 (/.f64 (/.f64 1 x) x) -1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(+.f64 (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x))) -1/2)
(fma.f64 (*.f64 x x) 1/24 (+.f64 (/.f64 1 (*.f64 x x)) -1/2))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) -1/2))
(+.f64 (/.f64 (/.f64 1 x) x) (fma.f64 x (*.f64 x 1/24) -1/2))
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x)))) -1/2)
(fma.f64 (pow.f64 x 4) -1/720 (fma.f64 (*.f64 x x) 1/24 (+.f64 (/.f64 1 (*.f64 x x)) -1/2)))
(+.f64 (fma.f64 x (*.f64 x 1/24) (/.f64 1 (*.f64 x x))) (fma.f64 (pow.f64 x 4) -1/720 -1/2))
(+.f64 (/.f64 (/.f64 1 x) x) (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 -1/2)))
(+.f64 (fma.f64 x (*.f64 x 1/24) -1/2) (fma.f64 (pow.f64 x 4) -1/720 (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 -1/2)))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))

localize23.0ms (0.3%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.4b
(+.f64 1 (cos.f64 x))
0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
0.2b
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
0.1b
(/.f64 1 (+.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
0.4b
(+.f64 1 (cos.f64 x))
✓14.0b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 53 to 23 computations (56.6% saved)

series6.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
0.0ms
x
@0
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
0.0ms
x
@inf
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
0.0ms
x
@-inf
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
0.0ms
x
@-inf
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))

rewrite64.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
680×log-prod_binary64
482×prod-diff_binary64
236×fma-def_binary64
231×log-div_binary64
212×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01134
125418
2387018
Stop Event
1×node limit
Counts
2 → 96
Calls
Call 1
Inputs
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (tan.f64 (/.f64 x 2)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) 1) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (cbrt.f64 (pow.f64 x 4))) (/.f64 (tan.f64 (/.f64 x 2)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (pow.f64 x 4))) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 x) (/.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (/.f64 (+.f64 1 (cos.f64 x)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 (+.f64 x x))) (*.f64 (+.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 1) (*.f64 2 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 (+.f64 x x))) -1) (*.f64 2 (+.f64 -1 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1 (cos.f64 (+.f64 x x)))) (*.f64 (+.f64 -1 (neg.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 (+.f64 x x))) (/.f64 1 (+.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (pow.f64 (sin.f64 x) 2)) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) -1) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (-.f64 1 (cos.f64 (+.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 3) (pow.f64 (pow.f64 (sin.f64 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))))

simplify34.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
732×associate-/l*_binary64
566×distribute-lft-out_binary64
536×distribute-rgt-out_binary64
522×fma-def_binary64
508×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045394
1101392
2241342
3750340
43163340
Stop Event
1×node limit
Counts
120 → 116
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 1/2 (*.f64 x x)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

eval308.0ms (3.7%)

Compiler

Compiled 14359 to 8220 computations (42.8% saved)

prune123.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New78912801
Fresh12113
Picked101
Done325
Total80515820
Error
0b
Counts
820 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
27.4b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
34.2b
1/2
27.4b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
14.4b
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (/.f64 x 2)) (pow.f64 x -2)))
28.6b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
▶28.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
14.7b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
▶35.4b
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
▶27.5b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓28.1b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
14.7b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓28.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
27.9b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
▶28.0b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 284 to 202 computations (28.9% saved)

localize20.0ms (0.2%)

Local error

Found 6 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b
(/.f64 (sin.f64 x) x)
0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.1b
(/.f64 (sin.f64 x) x)
✓0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
Compiler

Compiled 33 to 18 computations (45.5% saved)

series8.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite64.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
538×log-prod_binary64
403×exp-prod_binary64
356×pow-prod-down_binary64
267×pow2_binary64
200×log-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0932
120432
2286632
Stop Event
1×node limit
Counts
3 → 155
Calls
Call 1
Inputs
(/.f64 (tan.f64 (/.f64 x 2)) x)
(/.f64 (sin.f64 x) x)
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -2)) (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (tan.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (tan.f64 (*.f64 x 1/2)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 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simplify51.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
612×associate-/r/_binary64
606×fma-def_binary64
450×associate-*l*_binary64
450×distribute-rgt-out_binary64
408×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
055492
1128486
2307480
3895474
43214474
56330474
Stop Event
1×node limit
Counts
183 → 179
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 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)))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
Outputs
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 1/24 (*.f64 x x)))
(fma.f64 1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (*.f64 1/240 (pow.f64 x 4))))
(fma.f64 x (*.f64 1/24 x) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(fma.f64 1/24 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (fma.f64 17/40320 (pow.f64 x 6) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 (fma.f64 1/24 (*.f64 x x) 1/2) (fma.f64 1/240 (pow.f64 x 4) (*.f64 17/40320 (pow.f64 x 6))))
(fma.f64 1/24 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) (fma.f64 17/40320 (pow.f64 x 6) 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 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 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 1))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/120) -1/6) 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 1 (fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 (*.f64 (pow.f64 x 6) -1/5040))))
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) -1/5040 1)))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/24))
(fma.f64 (*.f64 x x) -1/24 1/2)
(fma.f64 x (*.f64 x -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/720)))
(+.f64 1/2 (fma.f64 (*.f64 x x) -1/24 (*.f64 (pow.f64 x 4) 1/720)))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/720))))
(+.f64 1/2 (fma.f64 (*.f64 x x) -1/24 (fma.f64 (pow.f64 x 4) 1/720 (*.f64 (pow.f64 x 6) -1/40320))))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 (*.f64 (pow.f64 x 6) -1/40320))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 6) -1/40320 (fma.f64 (pow.f64 x 4) 1/720 1/2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 -1/24 x)
0.1b
(*.f64 x (*.f64 -1/24 x))
✓0.1b
(*.f64 x (*.f64 -1/24 x))
0.4b
(*.f64 -1/24 x)
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 -1/24 x))
0.0ms
x
@inf
(*.f64 x (*.f64 -1/24 x))
0.0ms
x
@-inf
(*.f64 x (*.f64 -1/24 x))

rewrite32.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
446×pow1_binary64
433×add-sqr-sqrt_binary64
423×*-un-lft-identity_binary64
414×add-log-exp_binary64
414×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
211357
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 x (*.f64 -1/24 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x -1/24))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/24))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 x -1/24))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x -1/24))))))))

simplify134.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
1106×sqr-pow_binary64
618×cube-prod_binary64
552×fabs-mul_binary64
536×pow-sqr_binary64
445×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410784
533684
6123784
7211384
8227784
9246184
10266984
11296084
12335384
13383384
14439684
15507884
16591584
17630784
18659384
19686784
20693984
21697584
22791684
Stop Event
1×node limit
Counts
23 → 13
Calls
Call 1
Inputs
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
Outputs
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))

localize13.0ms (0.2%)

Local error

Found 6 expressions with local error:

NewErrorProgram
2.1b
(-.f64 1 (cos.f64 x))
0.1b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
✓0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
✓0.1b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 28 to 16 computations (42.9% saved)

series4.0ms (0%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
1.0ms
x
@-inf
(/.f64 x (-.f64 1 (cos.f64 x)))
0.0ms
x
@inf
(/.f64 x (-.f64 1 (cos.f64 x)))
0.0ms
x
@0
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
0.0ms
x
@0
(/.f64 x (-.f64 1 (cos.f64 x)))

rewrite57.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
485×log-prod_binary64
372×exp-prod_binary64
275×pow-prod-down_binary64
236×pow2_binary64
211×prod-diff_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0824
118321
2269921
Stop Event
1×node limit
Counts
2 → 131
Calls
Call 1
Inputs
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 x (-.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) 1) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x 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x))) -2) (/.f64 x (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2)) (cbrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))) (sqrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) 1) (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) 1) (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))

simplify50.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
602×div-sub_binary64
492×unswap-sqr_binary64
486×distribute-lft-out_binary64
471×fma-def_binary64
449×associate-/l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043199
1104195
2243193
3688191
42325191
54719191
67377191
Stop Event
1×node limit
Counts
147 → 147
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(fma.f64 1/6 x (/.f64 2 x))
(fma.f64 x 1/6 (/.f64 2 x))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 1/6 x (/.f64 2 x)))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))
(fma.f64 x 1/6 (fma.f64 1/120 (pow.f64 x 3) (/.f64 2 x)))
(fma.f64 x (fma.f64 x (*.f64 x 1/120) 1/6) (/.f64 2 x))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
(fma.f64 1/120 (pow.f64 x 3) (+.f64 (fma.f64 1/6 x (/.f64 2 x)) (*.f64 1/3024 (pow.f64 x 5))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x))))
(fma.f64 x 1/6 (fma.f64 1/120 (pow.f64 x 3) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x))))

localize17.0ms (0.2%)

Local error

Found 6 expressions with local error:

NewErrorProgram
14.2b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
2.1b
(-.f64 1 (cos.f64 x))
0.8b
(/.f64 1 (*.f64 x (neg.f64 x)))
✓0.8b
(/.f64 1 (*.f64 x (neg.f64 x)))
2.1b
(-.f64 1 (cos.f64 x))
✓14.2b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
Compiler

Compiled 38 to 18 computations (52.6% saved)

series9.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
7.0ms
x
@inf
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
1.0ms
x
@-inf
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
1.0ms
x
@0
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
0.0ms
x
@inf
(/.f64 1 (*.f64 x (neg.f64 x)))
0.0ms
x
@0
(/.f64 1 (*.f64 x (neg.f64 x)))

rewrite47.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
877×pow1_binary64
816×add-log-exp_binary64
816×log1p-expm1-u_binary64
816×expm1-log1p-u_binary64
108×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01025
121819
2315619
Stop Event
1×node limit
Counts
2 → 56
Calls
Call 1
Inputs
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 1 (*.f64 x (neg.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 (*.f64 x x)) (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) (+.f64 -1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 -1 (cos.f64 x))) 2) (/.f64 (*.f64 x x) (cbrt.f64 (+.f64 -1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 -1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (+.f64 -1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 (*.f64 x x) (+.f64 -1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (*.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) -1) (*.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) -1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 x)) (*.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 x)) (*.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1 (cos.f64 x)) 1) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 2)) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (*.f64 x x))) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (*.f64 x x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (+.f64 -1 (cos.f64 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1 (cos.f64 x)) (/.f64 1 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (+.f64 -1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 -1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 -1 (cos.f64 x)) 3) (pow.f64 (/.f64 1 (*.f64 x x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (*.f64 x x)) 3) (pow.f64 (+.f64 -1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (*.f64 x x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x x) -2)) (/.f64 1 (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 2) -1) (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (*.f64 x x))))))))

simplify48.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
795×div-sub_binary64
733×fma-def_binary64
503×associate-/l*_binary64
428×fma-neg_binary64
330×associate-/r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
028248
165246
2150236
3413226
41412226
54346226
67273226
Stop Event
1×node limit
Counts
80 → 67
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)

localize13.0ms (0.2%)

Local error

Found 6 expressions with local error:

NewErrorProgram
18.1b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
0.1b
(/.f64 (cos.f64 x) x)
0.1b
(/.f64 (/.f64 (cos.f64 x) x) x)
✓0.1b
(/.f64 (/.f64 (cos.f64 x) x) x)
✓0.1b
(/.f64 (cos.f64 x) x)
✓18.1b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 28 to 10 computations (64.3% saved)

series3.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite152.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
690×prod-diff_binary64
481×log-prod_binary64
297×pow-prod-down_binary64
249×pow2_binary64
222×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0830
118830
2276030
Stop Event
1×node limit
Counts
3 → 280
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (cos.f64 x) x)
(/.f64 (/.f64 (cos.f64 x) x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 (neg.f64 (/.f64 1 x)) (/.f64 (cos.f64 x) x) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) 1 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4)) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (+.f64 (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 -1 (*.f64 (cos.f64 x) (pow.f64 x -2)) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4))) (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))) (fma.f64 (/.f64 (neg.f64 (cos.f64 x)) x) (/.f64 1 x) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -2) 1 (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 (pow.f64 x -4)) (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -4)) (pow.f64 (cbrt.f64 x) -2) (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 x) (/.f64 1 x) (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -4) (pow.f64 (cbrt.f64 x) -2) (neg.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -2) 1 (neg.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x)) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2)))) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) (*.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x)) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x)) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2)))) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 x) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) (*.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4)) (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (/.f64 (cos.f64 x) x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) (*.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) (/.f64 (sqrt.f64 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (cos.f64 x)) x) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (/.f64 (cos.f64 x) x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) x) (/.f64 (cbrt.f64 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 x) 1) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) 1) (/.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 x) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (cos.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x (/.f64 x (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 x) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (cos.f64 x) x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))))

simplify72.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
567×fma-def_binary64
492×unswap-sqr_binary64
420×distribute-rgt-neg-in_binary64
419×associate-*l*_binary64
412×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050331
1121325
2293323
3826321
42767321
55909321
Stop Event
1×node limit
Counts
308 → 306
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(fma.f64 -1/2 x (/.f64 1 x))
(fma.f64 x -1/2 (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 -1/2 x (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 x -1/2 (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 -1/720 (pow.f64 x 5) (fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 x -1/2 (/.f64 1 x))))
(fma.f64 x (fma.f64 (*.f64 x x) 1/24 -1/2) (fma.f64 -1/720 (pow.f64 x 5) (/.f64 1 x)))
(fma.f64 x (fma.f64 x (*.f64 x 1/24) -1/2) (fma.f64 -1/720 (pow.f64 x 5) (/.f64 1 x)))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(+.f64 (/.f64 1 (*.f64 x x)) -1/2)
(+.f64 -1/2 (/.f64 1 (*.f64 x x)))
(+.f64 -1/2 (/.f64 (/.f64 1 x) x))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(+.f64 (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x))) -1/2)
(+.f64 -1/2 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) -1/2))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 (*.f64 x x) 1/24 -1/2))
(+.f64 (/.f64 (/.f64 1 x) x) (fma.f64 (*.f64 x x) 1/24 -1/2))
(-.f64 (/.f64 (/.f64 1 x) x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x)))) -1/2)
(fma.f64 (pow.f64 x 4) -1/720 (+.f64 -1/2 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x)))))
(+.f64 -1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 (/.f64 1 (*.f64 x x)))))
(+.f64 -1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 (/.f64 (/.f64 1 x) x))))
(-.f64 (fma.f64 (pow.f64 x 4) -1/720 (/.f64 (/.f64 1 x) x)) (fma.f64 x (*.f64 -1/24 x) 1/2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))

eval333.0ms (4%)

Compiler

Compiled 16217 to 8683 computations (46.5% saved)

prune139.0ms (1.7%)

Pruning

19 alts after pruning (12 fresh and 7 done)

PrunedKeptTotal
New7887795
Fresh358
Picked011
Done066
Total79119810
Error
0b
Counts
810 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.4b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
▶27.9b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
27.4b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
▶14.7b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
▶27.5b
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
28.6b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
✓28.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
19.5b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
✓35.4b
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
27.5b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
✓27.5b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓28.1b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶48.2b
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
✓0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
34.2b
1/2
✓28.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
17.8b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
27.9b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
✓28.0b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 351 to 259 computations (26.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
13.8b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
0.2b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓13.8b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
Compiler

Compiled 34 to 18 computations (47.1% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite181.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
492×log-prod_binary64
386×prod-exp_binary64
372×exp-prod_binary64
307×pow-prod-down_binary64
255×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
119829
2261929
Stop Event
1×node limit
Counts
2 → 101
Calls
Call 1
Inputs
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) 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/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (*.f64 x 1/2)) x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))) 2)) (cbrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))))) (sqrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1) (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) (sin.f64 x))))))))

simplify91.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
626×associate-/r/_binary64
492×distribute-lft-out_binary64
492×unswap-sqr_binary64
468×fma-def_binary64
413×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
049465
1119461
2281457
3791455
42664455
56110455
67553455
77977455
Stop Event
1×node limit
Counts
125 → 119
Calls
Call 1
Inputs
(/.f64 1/2 x)
(+.f64 (*.f64 1/24 x) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 17/40320 (pow.f64 x 5)) (*.f64 1/240 (pow.f64 x 3)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
Outputs
(/.f64 1/2 x)
(+.f64 (*.f64 1/24 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 1/24 x (/.f64 1/2 x))
(fma.f64 x 1/24 (/.f64 1/2 x))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (fma.f64 1/24 x (/.f64 1/2 x)) (*.f64 1/240 (pow.f64 x 3)))
(fma.f64 x 1/24 (fma.f64 1/240 (pow.f64 x 3) (/.f64 1/2 x)))
(fma.f64 x (fma.f64 1/240 (*.f64 x x) 1/24) (/.f64 1/2 x))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 17/40320 (pow.f64 x 5)) (*.f64 1/240 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/24 x (/.f64 1/2 x)) (fma.f64 17/40320 (pow.f64 x 5) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (fma.f64 17/40320 (pow.f64 x 5) (*.f64 1/240 (pow.f64 x 3))) (fma.f64 x 1/24 (/.f64 1/2 x)))
(fma.f64 x 1/24 (fma.f64 1/240 (pow.f64 x 3) (fma.f64 17/40320 (pow.f64 x 5) (/.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 5) (fma.f64 x (fma.f64 1/240 (*.f64 x x) 1/24) (/.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/24))
(fma.f64 (*.f64 x x) -1/24 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 1/720 (pow.f64 x 4) (*.f64 x (*.f64 x -1/24))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/24 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 (*.f64 x x) -1/24 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
27.4b
(/.f64 x (*.f64 1/2 (*.f64 x x)))
✓27.4b
(/.f64 x (*.f64 1/2 (*.f64 x x)))
Compiler

Compiled 33 to 17 computations (48.5% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite74.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
685×pow1_binary64
642×add-log-exp_binary64
642×log1p-expm1-u_binary64
642×expm1-log1p-u_binary64
629×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
113010
2173510
Stop Event
1×node limit
Counts
1 → 41
Calls
Call 1
Inputs
(/.f64 x (*.f64 1/2 (*.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2 (/.f64 x (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 x (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (/.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))) (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))) 2) (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 x 2)) x) (/.f64 (sqrt.f64 (*.f64 x 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (*.f64 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 x x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 2) (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1/2) (/.f64 (cbrt.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1/2) (/.f64 (sqrt.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) (/.f64 (sqrt.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x x)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x x)) (/.f64 (cbrt.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (*.f64 x (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (*.f64 x (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4)))) (/.f64 x (cbrt.f64 (*.f64 x (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (*.f64 1/4 (pow.f64 x 4)))) (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (*.f64 1/4 (pow.f64 x 4)))) (/.f64 (sqrt.f64 x) (cbrt.f64 (*.f64 x (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (/.f64 x (*.f64 x (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x (sqrt.f64 1/2))) (/.f64 (cbrt.f64 x) (*.f64 x (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x 1/2)) (/.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 1/2)) (/.f64 (cbrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (*.f64 x 1/2)) (/.f64 (sqrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (/.f64 x (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 x (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (/.f64 x (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 x 2)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x 1/2) (/.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (*.f64 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) (*.f64 1/4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (/.f64 x (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 x (*.f64 x 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (/.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (/.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (/.f64 x (*.f64 x x)))))))))

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
Stop Event
1×saturated
Counts
53 → 42
Calls
Call 1
Inputs
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
Outputs
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)
(/.f64 2 x)

localize41.0ms (0.5%)

Local error

Found 6 expressions with local error:

NewErrorProgram
2.1b
(-.f64 1 (cos.f64 x))
0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
0.1b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓0.1b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 23 to 12 computations (47.8% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite44.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
949×pow1_binary64
888×add-log-exp_binary64
888×log1p-expm1-u_binary64
888×expm1-log1p-u_binary64
79×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
115512
2227312
Stop Event
1×node limit
Counts
1 → 40
Calls
Call 1
Inputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 2) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) 1) (/.f64 (/.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))

simplify38.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
716×fma-def_binary64
652×div-sub_binary64
540×associate-/r*_binary64
374×associate-/l/_binary64
355×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025148
158146
2130144
3356142
41216142
53475142
66410142
Stop Event
1×node limit
Counts
52 → 49
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

localize16.0ms (0.2%)

Local error

Found 6 expressions with local error:

NewErrorProgram
14.2b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
2.1b
(-.f64 1 (cos.f64 x))
0.1b
(/.f64 (/.f64 -1 x) x)
✓0.1b
(/.f64 (/.f64 -1 x) x)
2.1b
(-.f64 1 (cos.f64 x))
✓14.2b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
Compiler

Compiled 34 to 21 computations (38.2% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
0.0ms
x
@0
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
0.0ms
x
@-inf
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
0.0ms
x
@-inf
(/.f64 (/.f64 -1 x) x)
0.0ms
x
@0
(/.f64 (/.f64 -1 x) x)

rewrite68.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
479×log-prod_binary64
362×exp-prod_binary64
287×pow-prod-down_binary64
246×pow2_binary64
191×pow-unpow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01024
121319
2295018
Stop Event
1×node limit
Counts
2 → 98
Calls
Call 1
Inputs
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 -1 x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (/.f64 (+.f64 -1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (*.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) 1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) -1) (*.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) -1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 -1 x)) (*.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 -1 x)) (*.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 x)) (*.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 x)) (*.f64 (+.f64 1 (cos.f64 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 -1 (cos.f64 x)) x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (neg.f64 (pow.f64 x -2))) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (neg.f64 (pow.f64 x -2))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (+.f64 -1 (cos.f64 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 -1 (cos.f64 x)) 2) (pow.f64 x -4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (+.f64 -1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))) (sqrt.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 -1 (cos.f64 x)) 2) (pow.f64 x -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 -1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1 (cos.f64 x)) (*.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 x -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 x -2))))) (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (neg.f64 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (neg.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 -1 (cbrt.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (neg.f64 (pow.f64 x -2))) (cbrt.f64 (pow.f64 x -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (neg.f64 (pow.f64 x -2))) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -4)) (cbrt.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (neg.f64 x) -1/2) (*.f64 (pow.f64 (neg.f64 x) -1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1) x) (/.f64 (sqrt.f64 -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) 1) (/.f64 (/.f64 -1 (cbrt.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (neg.f64 x) -1/2) 1) (/.f64 (pow.f64 (neg.f64 x) -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (/.f64 -1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (neg.f64 x) -1/2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (neg.f64 x) -1/2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (/.f64 -1 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 x)) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (sqrt.f64 x)) (/.f64 (/.f64 -1 (cbrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (neg.f64 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (neg.f64 (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (neg.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (neg.f64 x) -3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x (neg.f64 x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (neg.f64 (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (neg.f64 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (neg.f64 (pow.f64 x -2))))) (sqrt.f64 (log.f64 (neg.f64 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (neg.f64 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (neg.f64 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (neg.f64 x) -3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (neg.f64 (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (neg.f64 x)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (neg.f64 (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 -1) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (neg.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (neg.f64 (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (neg.f64 (pow.f64 x -2))))))))

simplify46.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
795×div-sub_binary64
733×fma-def_binary64
503×associate-/l*_binary64
428×fma-neg_binary64
330×associate-/r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
028248
165246
2150236
3413226
41412226
54346226
67273226
Stop Event
1×node limit
Counts
122 → 109
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 -1 (/.f64 (-.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) -1) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 -1 (cos.f64 x))) (*.f64 x x))
(/.f64 (fma.f64 -1 (cos.f64 x) 1) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)
(/.f64 -1 (pow.f64 x 2))
(/.f64 -1 (*.f64 x x))
(/.f64 (/.f64 -1 x) x)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
2.1b
(-.f64 1 (cos.f64 x))
0.1b
(/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x))))
0.1b
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
0.1b
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
✓0.1b
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
✓0.1b
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
✓0.1b
(/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x))))
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 44 to 25 computations (43.2% saved)

series4.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
1.0ms
x
@inf
(/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x))))
0.0ms
x
@0
(/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x))))
0.0ms
x
@-inf
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
0.0ms
x
@0
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))

rewrite68.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
547×log-prod_binary64
358×prod-diff_binary64
309×pow-prod-down_binary64
266×pow2_binary64
248×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01140
124530
2358530
Stop Event
1×node limit
Counts
3 → 182
Calls
Call 1
Inputs
(/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
Outputs
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(/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) -1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) -1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 (-.f64 1 (cos.f64 x))) (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (neg.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2) (neg.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change 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(2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))

simplify54.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
742×fma-def_binary64
505×unswap-sqr_binary64
453×associate-*l*_binary64
449×div-sub_binary64
443×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
064437
1164431
2390427
31076409
43432409
57009409
Stop Event
1×node limit
Counts
218 → 207
Calls
Call 1
Inputs
(*.f64 -1/2 x)
(+.f64 (*.f64 -1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/40320 (pow.f64 x 7)) (+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3)))))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 -2 x)
(-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 -1/6 x) (*.f64 -1/120 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 -1/6 x) (+.f64 (*.f64 -1/3024 (pow.f64 x 5)) (*.f64 -1/120 (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
Outputs
(*.f64 -1/2 x)
(+.f64 (*.f64 -1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 -1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 -1/2 x))
(*.f64 x (fma.f64 x (*.f64 x 1/24) -1/2))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 -1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 -1/720 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (*.f64 x 1/24) -1/2) (*.f64 -1/720 (pow.f64 x 5)))
(+.f64 (*.f64 1/40320 (pow.f64 x 7)) (+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/40320 (pow.f64 x 7) (fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/40320 (pow.f64 x 7) (fma.f64 -1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 -1/720 (pow.f64 x 5)))))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/40320 (pow.f64 x 7)))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/40320 (pow.f64 x 7) (*.f64 -1/2 x))))
(fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/40320 (pow.f64 x 7) (*.f64 -1/2 x))))
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
(*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)
(/.f64 (+.f64 -1 (cos.f64 x)) x)
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 x -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/24) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 -2 x)
(-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))
(-.f64 (*.f64 x -1/6) (/.f64 2 x))
(fma.f64 x -1/6 (/.f64 -2 x))
(-.f64 (+.f64 (*.f64 -1/6 x) (*.f64 -1/120 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))
(-.f64 (fma.f64 -1/6 x (*.f64 (pow.f64 x 3) -1/120)) (/.f64 2 x))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 3) -1/120 (/.f64 -2 x)))
(-.f64 (+.f64 (*.f64 -1/6 x) (+.f64 (*.f64 -1/3024 (pow.f64 x 5)) (*.f64 -1/120 (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (fma.f64 -1/6 x (fma.f64 -1/3024 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/120))) (/.f64 2 x))
(+.f64 (fma.f64 (pow.f64 x 3) -1/120 (*.f64 (pow.f64 x 5) -1/3024)) (fma.f64 x -1/6 (/.f64 -2 x)))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 5) -1/3024 (fma.f64 (pow.f64 x 3) -1/120 (/.f64 -2 x))))
(fma.f64 x (fma.f64 x (*.f64 x -1/120) -1/6) (fma.f64 (pow.f64 x 5) -1/3024 (/.f64 -2 x)))
(fma.f64 (pow.f64 x 3) -1/120 (fma.f64 (pow.f64 x 5) -1/3024 (fma.f64 x -1/6 (/.f64 -2 x))))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))
(*.f64 -1 (/.f64 x (-.f64 1 (cos.f64 x))))
(neg.f64 (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))

eval300.0ms (3.6%)

Compiler

Compiled 12127 to 7577 computations (37.5% saved)

prune109.0ms (1.3%)

Pruning

25 alts after pruning (18 fresh and 7 done)

PrunedKeptTotal
New71114725
Fresh347
Picked101
Done4711
Total71925744
Error
0b
Counts
744 → 25
Alt Table
Click to see full alt table
StatusErrorProgram
34.3b
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
✓27.5b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
27.5b
(*.f64 (/.f64 -1 x) (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))))
27.4b
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
28.6b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
49.0b
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
✓48.2b
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
48.2b
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
✓0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
19.5b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
✓35.4b
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
17.8b
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
27.5b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
28.5b
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
28.1b
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
27.5b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
34.3b
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
27.9b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
28.0b
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
✓27.4b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
34.2b
1/2
✓14.7b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓28.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
17.8b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
48.6b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
Compiler

Compiled 284 to 203 computations (28.5% saved)

regimes37.0ms (0.5%)

Counts
25 → 1
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(*.f64 (/.f64 -1 x) (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Outputs
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Calls

3 calls:

14.0ms
x
7.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
6.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.2b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 280 to 172 computations (38.6% saved)

regimes84.0ms (1%)

Counts
24 → 3
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(*.f64 (/.f64 -1 x) (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
Outputs
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

51.0ms
x
12.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
11.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.9b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 269 to 166 computations (38.3% saved)

bsearch54.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
25.0ms
1.3195296957559512e-8
0.7804904468675326
29.0ms
-916.5785249190432
-0.0013293805683481054
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes71.0ms (0.9%)

Counts
21 → 3
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(*.f64 (/.f64 -1 x) (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))))
Outputs
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

35.0ms
x
14.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
14.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 231 to 140 computations (39.4% saved)

bsearch55.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
25.0ms
1.3195296957559512e-8
0.7804904468675326
29.0ms
-916.5785249190432
-0.0013293805683481054
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes75.0ms (0.9%)

Counts
18 → 3
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
Outputs
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

30.0ms
x
19.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
19.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 194 to 119 computations (38.7% saved)

bsearch60.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
26.0ms
1.3195296957559512e-8
0.7804904468675326
33.0ms
-916.5785249190432
-0.0013293805683481054
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes54.0ms (0.6%)

Counts
16 → 3
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))
(/.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 x)) x)
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

25.0ms
x
11.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
10.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 172 to 108 computations (37.2% saved)

bsearch52.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
25.0ms
1.3195296957559512e-8
0.7804904468675326
27.0ms
-916.5785249190432
-0.0013293805683481054
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes49.0ms (0.6%)

Counts
11 → 3
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Calls

3 calls:

21.0ms
x
10.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
9.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.9b3x
1.0b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
1.0b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 124 to 82 computations (33.9% saved)

bsearch181.0ms (2.2%)

Algorithm
2×binary-search
Steps
TimeLeftRight
143.0ms
1.3195296957559512e-8
0.7804904468675326
38.0ms
-916.5785249190432
-0.0013293805683481054
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes9.0ms (0.1%)

Counts
10 → 1
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (-.f64 (*.f64 -1/6 x) (*.f64 2 (/.f64 1 x)))))
Outputs
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
Calls

1 calls:

6.0ms
x
Results
ErrorSegmentsBranch
17.8b1x
Compiler

Compiled 98 to 66 computations (32.7% saved)

regimes11.0ms (0.1%)

Accuracy

Total -15.7b remaining (-45.8%)

Threshold costs -15.7b (-45.8%)

Counts
8 → 1
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 x (*.f64 -1/24 x)))
(*.f64 (/.f64 -1 x) (*.f64 -1/2 x))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -2 x)))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(*.f64 (neg.f64 (*.f64 1/2 (*.f64 x x))) (/.f64 (/.f64 -1 x) x))
Outputs
1/2
Calls

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
34.2b1x
Compiler

Compiled 70 to 44 computations (37.1% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
8×*-commutative_binary64
5×+-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051300
165300
269300
371300
472300
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
1/2
Outputs
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))) (if (<=.f64 x 1994016898684507/151115727451828646838272) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 x 1/6) (*.f64 2 (/.f64 1 x))))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (*.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 x -1/24))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 x -1/24))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 x -1/24))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 -1/24 x))) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
(if (<=.f64 x -8062309967346097/8796093022208) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 1994016898684507/151115727451828646838272) (+.f64 1/2 (*.f64 x (*.f64 x -1/24))) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/6) (*.f64 2 (/.f64 1 x))))
1/2

end274.0ms (3.3%)

Stop Event
1×fuel
Compiler

Compiled 413 to 279 computations (32.4% saved)

Profiling

Loading profile data...