Details

Time bar (total: 9.8s)

analyze89.0ms (0.9%)

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 (32.9%)

Results
1.6s2055×body2048valid
571.0ms3387×body256valid
522.0ms1597×body512valid
468.0ms1107×body1024valid
79.0ms110×body4096valid

preprocess48.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
426×fma-def_binary64
293×fma-neg_binary64
85×div-sub_binary64
78×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512512
619212
731812
862312
9114012
10169812
11183012
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)

simplify55.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
426×fma-def_binary64
293×fma-neg_binary64
85×div-sub_binary64
78×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512512
619212
731812
862312
9114012
10169812
11183012
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)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
32.4b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶32.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.6b
(-.f64 1 (cos.f64 x))
✓15.1b
(/.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
@inf
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
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))
0.0ms
x
@0
(-.f64 1 (cos.f64 x))
0.0ms
x
@inf
(-.f64 1 (cos.f64 x))

rewrite71.0ms (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
2213518
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 expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(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 +.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 expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(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))))))))

simplify56.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
619×distribute-rgt-out_binary64
564×associate-/r*_binary64
555×distribute-lft-out_binary64
510×fma-def_binary64
427×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037218
191216
2217214
3656212
42571212
55901212
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)
(+.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))
(+.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 1/720 (pow.f64 x 4) (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 (*.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))))
(fma.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2) (*.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)))
(*.f64 x (*.f64 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 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24))))
(*.f64 (*.f64 x x) (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))))

eval23.0ms (0.2%)

Compiler

Compiled 1062 to 636 computations (40.1% saved)

prune50.0ms (0.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New621779
Fresh000
Picked011
Done000
Total621880
Error
0.0b
Counts
80 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
31.8b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
32.2b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
▶31.2b
(fma.f64 -1/24 (*.f64 x x) 1/2)
▶15.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
30.2b
1/2
32.4b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
▶17.0b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
31.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
✓32.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
32.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
15.7b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
32.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
32.4b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
▶31.9b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
32.4b
(/.f64 (pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 x x))
32.4b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)
▶32.5b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
32.4b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
Compiler

Compiled 409 to 294 computations (28.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.4b
(+.f64 1 (cos.f64 x))
✓15.1b
(/.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)

series7.0ms (0.1%)

Counts
4 → 44
Calls

12 calls:

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

rewrite101.0ms (1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122830
2354030
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
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((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(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 -.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)))))) (#(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 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1) (+.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(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 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.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 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (cos.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 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) (#(struct:change 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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 (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 1/8 (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) 2)) (+.f64 1 (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 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 expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))) (#(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 +.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 (cbrt.f64 (pow.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 expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(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))))))

simplify65.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
920×times-frac_binary64
877×distribute-lft-out_binary64
511×associate-/l*_binary64
357×associate-/r*_binary64
346×associate-/l/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068576
1158572
2393520
31256520
42457520
57247520
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))
(+.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 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 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(+.f64 1/2 (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) (*.f64 -1/40320 (pow.f64 x 6)))))
(/.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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 (fma.f64 (*.f64 x x) -1/2 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 x (*.f64 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 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 -1/315 (pow.f64 x 8)))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 (pow.f64 x 6) 2/45 (fma.f64 -1/315 (pow.f64 x 8) (*.f64 x x))))
(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)))
(*.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))))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 (*.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 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 1/720 (pow.f64 x 6)))))
(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)))))
(/.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)))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 13 to 7 computations (46.2% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite59.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11228
213088
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(fma.f64 -1/24 (*.f64 x x) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1/24 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/24 (*.f64 x x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/24 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) 2) (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) (sqrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -1/24 (*.f64 x x)) 3) 1/8) (+.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) (-.f64 1/4 (*.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/24 (*.f64 x x) 1/2)))))))

simplify162.0ms (1.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
08105
11587
22787
35187
411487
533787
6128287
7217987
8234387
9252787
10273587
11303487
12342587
13390487
14447287
15516287
16599787
17638987
18667987
19695787
20702987
21706387
Stop Event
1×node limit
Counts
33 → 26
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)
(+.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 -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 -1/24 (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)
(+.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 -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 -1/24 (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)
(+.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 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
✓0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
✓0.3b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.6b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series6.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
1.0ms
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)

rewrite90.0ms (0.9%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0936
119833
2274133
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
((#(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 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))) (log.f64 (sqrt.f64 (exp.f64 (/.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 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) 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 (-.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)))) 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x)) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.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)) (*.f64 x x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (/.f64 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 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 2)) (cbrt.f64 (log.f64 (*.f64 x (/.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 x (-.f64 1 (cos.f64 x))))))) (sqrt.f64 (log.f64 (*.f64 x (/.f64 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 x (/.f64 x (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (/.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 (-.f64 1 (cos.f64 x)) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (/.f64 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 (*.f64 3 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (/.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 x (-.f64 1 (cos.f64 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (/.f64 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))))))

simplify64.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
768×fma-def_binary64
570×associate-*l*_binary64
506×unswap-sqr_binary64
471×distribute-rgt-out_binary64
446×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054352
1137348
2328344
3954342
43807342
56663342
Stop Event
1×node limit
Counts
227 → 223
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)
(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 (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 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)))
(/.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))
(*.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2))
(*.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 1/2 x (fma.f64 1/720 (pow.f64 x 5) (*.f64 -1/24 (pow.f64 x 3))))
(fma.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2) (*.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)))))
(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 1/2 x (*.f64 -1/40320 (pow.f64 x 7)))))
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 (*.f64 x x) 1/6 2) (fma.f64 (pow.f64 x 4) 1/120 (*.f64 (pow.f64 x 6) 1/3024)))
(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 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) 1/3024 (fma.f64 (*.f64 x x) 1/6 2)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(cbrt.f64 (-.f64 1 (cos.f64 x)))
✓0.4b
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
1.6b
(-.f64 1 (cos.f64 x))
✓15.1b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
Compiler

Compiled 36 to 21 computations (41.7% saved)

series12.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
2.0ms
x
@inf
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
2.0ms
x
@-inf
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
2.0ms
x
@0
(cbrt.f64 (-.f64 1 (cos.f64 x)))
1.0ms
x
@0
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)

rewrite80.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
438×log-prod_binary64
341×prod-exp_binary64
331×exp-prod_binary64
259×pow-prod-down_binary64
237×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
121726
2255126
Stop Event
1×node limit
Counts
3 → 162
Calls
Call 1
Inputs
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(cbrt.f64 (-.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 (pow.f64 x -2)) (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))))) (#(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> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 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egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3/2) (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (cos.f64 x))) 2) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/6) (pow.f64 (-.f64 1 (cos.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))) 2)) (cbrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))) (sqrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1) 1))))))

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
727×fma-def_binary64
400×div-sub_binary64
355×times-frac_binary64
325×distribute-lft-out_binary64
297×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
029284
172258
2156256
3411254
41495254
54943254
66870254
Stop Event
1×node limit
Counts
190 → 173
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 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
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))
(+.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 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 x (*.f64 -1/24 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 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1/3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
0.4b
(+.f64 1 (cos.f64 x))
✓0.6b
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
✓15.1b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
Compiler

Compiled 57 to 22 computations (61.4% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite80.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
645×log-prod_binary64
471×prod-diff_binary64
252×log-div_binary64
231×fma-def_binary64
214×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01140
125618
2393418
Stop Event
1×node limit
Counts
2 → 93
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.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 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 (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 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(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 (-.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 (/.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 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 (/.f64 1 (+.f64 1 (cos.f64 x))) x) (/.f64 (pow.f64 (sin.f64 x) 2) x))))) 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(2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(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 +.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 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 (-.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 -1 (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(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) 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x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (sin.f64 x) (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 *.f64 (/.f64 1 (+.f64 -1 (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (tan.f64 (/.f64 x 2)))) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (sin.f64 x)) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (pow.f64 (cbrt.f64 (sin.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 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 (neg.f64 (/.f64 -1 (-.f64 1 (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 expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(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 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))))

simplify134.0ms (1.4%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
045394
1101392
2241342
3754340
43326340
Stop Event
1×node limit
Counts
117 → 114
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))
(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)))))
(+.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 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 (*.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 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 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 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 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)))
(/.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 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)))

eval523.0ms (5.3%)

Compiler

Compiled 16298 to 9194 computations (43.6% saved)

prune233.0ms (2.4%)

Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New91216928
Fresh11112
Picked101
Done325
Total92719946
Error
0b
Counts
946 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
▶15.7b
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
▶16.1b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
31.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
32.4b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/3) 3) (*.f64 x x))
32.4b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
▶31.7b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
31.9b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
30.2b
1/2
▶15.5b
(*.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)))
✓31.9b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
17.0b
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
32.2b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
32.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
▶31.2b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
32.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
15.8b
(pow.f64 (/.f64 x (/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) x)) -1)
15.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
✓32.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
31.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
Compiler

Compiled 412 to 296 computations (28.2% saved)

localize47.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (+.f64 1 (cos.f64 x)))
✓0.3b
(pow.f64 (sin.f64 x) 2)
0.4b
(+.f64 1 (cos.f64 x))
✓14.9b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
Compiler

Compiled 58 to 33 computations (43.1% saved)

series6.0ms (0.1%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 1 (+.f64 1 (cos.f64 x)))
1.0ms
x
@-inf
(/.f64 1 (+.f64 1 (cos.f64 x)))
1.0ms
x
@0
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
1.0ms
x
@0
(/.f64 1 (+.f64 1 (cos.f64 x)))
1.0ms
x
@inf
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))

rewrite104.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
495×log-prod_binary64
386×exp-prod_binary64
292×pow-prod-down_binary64
276×pow2_binary64
190×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01127
123724
2299724
Stop Event
1×node limit
Counts
3 → 122
Calls
Call 1
Inputs
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(pow.f64 (sin.f64 x) 2)
(/.f64 1 (+.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 (sin.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (sin.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 (sin.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 4)) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) 1) (/.f64 (sin.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) 1) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (pow.f64 (sin.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) x) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (*.f64 (cbrt.f64 x) x)) (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (cbrt.f64 x) x)) (/.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 (sin.f64 x)) 4) (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 x) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 x) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 x) x) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) x) -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x)))) 2)) (cbrt.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x))))) (sqrt.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 (sin.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sin.f64 x) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sin.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sin.f64 x) x) -2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (/.f64 (sin.f64 x) x))) 1) 1))))))
((#(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 (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 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(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 (sin.f64 x) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 3/2) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 5) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 (-.f64 x x)) (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 4)) (+.f64 1 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 6)) (+.f64 1 (+.f64 (pow.f64 (cos.f64 x) 4) (pow.f64 (cos.f64 x) 2))))))) (#(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 (sin.f64 x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))) (#(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 (*.f64 2 (log.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 x)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 x))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (pow.f64 (+.f64 1 (cos.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (cos.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 (/.f64 1 (+.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 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.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 (/.f64 1 (+.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log1p.f64 (cos.f64 x))))))) (#(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 (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 (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))) 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 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) 2)))) (#(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 (exp.f64 -1) (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (+.f64 -1 (neg.f64 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (cos.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (cos.f64 x))))) (sqrt.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))))) (#(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 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.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 expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (cos.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (neg.f64 (log1p.f64 (cos.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (neg.f64 (log1p.f64 (cos.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (cos.f64 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (cos.f64 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (cos.f64 x))) 1) 1))))))

simplify57.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
680×fma-def_binary64
669×distribute-rgt-out_binary64
662×distribute-lft-out_binary64
654×times-frac_binary64
550×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
050290
1120286
2282282
3834282
43446282
Stop Event
1×node limit
Counts
146 → 148
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) 1)
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) (+.f64 1 (*.f64 2/45 (pow.f64 x 4))))
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 2/45 (pow.f64 x 4)) (*.f64 -1/315 (pow.f64 x 6)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(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))))
1/2
(+.f64 (*.f64 1/8 (pow.f64 x 2)) 1/2)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (*.f64 1/48 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (+.f64 (*.f64 17/5760 (pow.f64 x 6)) (*.f64 1/48 (pow.f64 x 4)))))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 (cos.f64 x) 1))
Outputs
1
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) 1)
(fma.f64 -1/3 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/3 x) 1)
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) (+.f64 1 (*.f64 2/45 (pow.f64 x 4))))
(fma.f64 -1/3 (*.f64 x x) (+.f64 1 (*.f64 2/45 (pow.f64 x 4))))
(fma.f64 -1/3 (*.f64 x x) (fma.f64 2/45 (pow.f64 x 4) 1))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 2/45) -1/3) 1)
(+.f64 (*.f64 -1/3 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 2/45 (pow.f64 x 4)) (*.f64 -1/315 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/3 (*.f64 x x) 1) (fma.f64 2/45 (pow.f64 x 4) (*.f64 -1/315 (pow.f64 x 6))))
(fma.f64 -1/3 (*.f64 x x) (fma.f64 2/45 (pow.f64 x 4) (fma.f64 -1/315 (pow.f64 x 6) 1)))
(fma.f64 -1/315 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 2/45) -1/3) 1))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 2/45) -1/3) (fma.f64 -1/315 (pow.f64 x 6) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x))
(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x 2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x 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 x x (*.f64 -1/3 (pow.f64 x 4)))
(+.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 -1/3 (pow.f64 x 4) (fma.f64 x x (*.f64 2/45 (pow.f64 x 6))))
(+.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 -1/3 (pow.f64 x 4) (fma.f64 -1/315 (pow.f64 x 8) (fma.f64 x x (*.f64 2/45 (pow.f64 x 6)))))
1/2
(+.f64 (*.f64 1/8 (pow.f64 x 2)) 1/2)
(fma.f64 1/8 (*.f64 x x) 1/2)
(fma.f64 (*.f64 x x) 1/8 1/2)
(fma.f64 x (*.f64 x 1/8) 1/2)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (*.f64 1/48 (pow.f64 x 4))))
(+.f64 (fma.f64 1/8 (*.f64 x x) 1/2) (*.f64 (pow.f64 x 4) 1/48))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 4) 1/48 1/2))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) 1/48 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/48) 1/8) 1/2)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (+.f64 (*.f64 17/5760 (pow.f64 x 6)) (*.f64 1/48 (pow.f64 x 4)))))
(+.f64 (fma.f64 1/8 (*.f64 x x) 1/2) (fma.f64 17/5760 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/48)))
(+.f64 (fma.f64 (*.f64 x x) 1/8 1/2) (fma.f64 (pow.f64 x 4) 1/48 (*.f64 (pow.f64 x 6) 17/5760)))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 6) 17/5760 (fma.f64 (pow.f64 x 4) 1/48 1/2)))
(fma.f64 (pow.f64 x 6) 17/5760 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/48) 1/8) 1/2))
(fma.f64 (pow.f64 x 4) 1/48 (fma.f64 (pow.f64 x 6) 17/5760 (fma.f64 x (*.f64 x 1/8) 1/2)))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 1 (cos.f64 x)))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 1 (cos.f64 x)))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 1 (cos.f64 x)))
(/.f64 1 (+.f64 (cos.f64 x) 1))
(/.f64 1 (+.f64 1 (cos.f64 x)))

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 -1/24 (*.f64 x x))
Compiler

Compiled 19 to 10 computations (47.4% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite187.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
432×pow1_binary64
422×add-sqr-sqrt_binary64
411×*-un-lft-identity_binary64
403×add-log-exp_binary64
403×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11027
211507
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 -1/24 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/24 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/576 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/24) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 (*.f64 x x))))))))

simplify192.0ms (2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533184
6125084
7212384
8228784
9247184
10267984
11297684
12337184
13385284
14441884
15510284
16593584
17632784
18661984
19689584
20696984
21700384
22794484
Stop Event
1×node limit
Counts
26 → 16
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 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(*.f64 x (*.f64 -1/24 x))

localize28.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiled 28 to 16 computations (42.9% saved)

series5.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite177.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
484×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
2270821
Stop Event
1×node limit
Counts
2 → 131
Calls
Call 1
Inputs
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Outputs
((#(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 x (/.f64 1 (-.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 (/.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 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 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 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 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 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 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 expm1.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(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 (*.f64 3 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 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 +.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> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(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 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(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 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (cbrt.f64 (*.f64 (pow.f64 x -4) (pow.f64 (-.f64 1 (cos.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x -4) (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (*.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (/.f64 (-.f64 1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.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 (pow.f64 x -3/2) (/.f64 (pow.f64 x -1/2) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) x) (/.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) 1) (/.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.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) (/.f64 (/.f64 1 x) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2))) (/.f64 (pow.f64 x -1/2) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) -1/2) (/.f64 (/.f64 1 x) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) (/.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -2) 1) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) 1) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.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 (pow.f64 x -2) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(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 (E.f64) (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -4) (pow.f64 (-.f64 1 (cos.f64 x)) 2)) 1/2)))) (#(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 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 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 pow.f64 (/.f64 (pow.f64 x -3) (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 1 x) (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x -4) (pow.f64 (-.f64 1 (cos.f64 x)) 2)))))) (#(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)) (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 x -3) (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3)))))) (#(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 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 exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) -1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (neg.f64 (log.f64 x)) (*.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) -1) (*.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (*.f64 (log.f64 (/.f64 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)) x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 1 x) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -2) 1 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -3/2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -3/2) (pow.f64 x -1/2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (cbrt.f64 (pow.f64 x -2)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (/.f64 1 x) (cbrt.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) 1) (/.f64 (/.f64 1 (cbrt.f64 x)) x) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 x -1/2) 1) (pow.f64 x -3/2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 x) 2)) (pow.f64 x -5/6) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 5) (/.f64 1 (cbrt.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))))

simplify76.0ms (0.8%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
043199
1104195
2241193
3682191
42502191
54938191
67594191
Stop Event
1×node limit
Counts
147 → 147
Calls
Call 1
Inputs
(/.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)))))
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
(/.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)))
(+.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))))
(fma.f64 x (fma.f64 1/120 (*.f64 x x) 1/6) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 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))))
(fma.f64 x (*.f64 x -1/24) (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 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 x (*.f64 x -1/24) 1/2)))
(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 (*.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))

localize67.0ms (0.7%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓15.1b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
Compiler

Compiled 34 to 18 computations (47.1% saved)

series18.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
5.0ms
x
@0
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
2.0ms
x
@inf
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
2.0ms
x
@-inf
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
1.0ms
x
@inf
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))

rewrite153.0ms (1.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
119829
2262129
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
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.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 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 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simplify91.0ms (0.9%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
049465
1119461
2281457
3783455
42898455
56407455
67854455
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))
(fma.f64 x (fma.f64 x (*.f64 x 1/240) 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 x 1/24 (/.f64 1/2 x)) (fma.f64 17/40320 (pow.f64 x 5) (*.f64 1/240 (pow.f64 x 3))))
(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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) 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)
(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 1/2 (fma.f64 1/720 (pow.f64 x 4) (*.f64 (*.f64 x 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)
(+.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))))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2))
(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 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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 (*.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)) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)) (sin.f64 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)))

localize72.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
0.3b
(pow.f64 (sin.f64 x) 2)
✓0.4b
(+.f64 (cos.f64 x) 1)
✓15.1b
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
Compiler

Compiled 41 to 21 computations (48.8% saved)

series5.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite117.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
560×log-prod_binary64
369×pow-prod-down_binary64
287×pow2_binary64
199×pow1/3_binary64
193×log-div_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01140
124034
2329424
Stop Event
1×node limit
Counts
3 → 131
Calls
Call 1
Inputs
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
(+.f64 (cos.f64 x) 1)
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
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 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 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 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 1 (+.f64 (cos.f64 x) 1)) (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 (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))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 (+.f64 (cos.f64 x) -1) (/.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 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 x x)) (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (+.f64 (cos.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 (cos.f64 x) 1)) 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 (cbrt.f64 (pow.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 (cos.f64 x) 1)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) 1) (/.f64 (cbrt.f64 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simplify61.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
736×fma-def_binary64
705×distribute-lft-out_binary64
666×distribute-rgt-out_binary64
639×associate-*l*_binary64
486×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056414
1128410
2312370
3989366
44257366
Stop Event
1×node limit
Counts
159 → 159
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 1 (cos.f64 x))
(+.f64 1 (cos.f64 x))
(+.f64 1 (cos.f64 x))
(+.f64 1 (cos.f64 x))
(*.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)))
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))
(+.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 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)))
(/.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.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 (fma.f64 (*.f64 x x) -1/2 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 (*.f64 x x) (fma.f64 (*.f64 x x) 1/24 -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 x (*.f64 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 (fma.f64 (pow.f64 x 6) -1/720 2)))
(+.f64 1 (cos.f64 x))
(+.f64 1 (cos.f64 x))
(+.f64 1 (cos.f64 x))
(+.f64 1 (cos.f64 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)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x 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))))
(*.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 -1/24 (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)))

eval306.0ms (3.1%)

Compiler

Compiled 12601 to 7934 computations (37% saved)

prune155.0ms (1.6%)

Pruning

19 alts after pruning (14 fresh and 5 done)

PrunedKeptTotal
New7149723
Fresh7512
Picked101
Done156
Total72319742
Error
0b
Counts
742 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
✓16.1b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
31.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓31.7b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
31.9b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
▶31.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
15.4b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
32.5b
(*.f64 (+.f64 (cos.f64 x) -1) (/.f64 1 (*.f64 x (neg.f64 x))))
✓31.9b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶0.2b
(*.f64 (sin.f64 x) (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
16.9b
(*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 (*.f64 x (neg.f64 x)))))
▶46.0b
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
✓31.2b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
▶32.2b
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
13.3b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
31.7b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
▶15.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
✓32.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
30.2b
1/2
32.2b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 373 to 268 computations (28.2% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
✓0.1b
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x))
✓0.1b
(*.f64 (sin.f64 x) (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
Compiler

Compiled 45 to 30 computations (33.3% saved)

series4.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite98.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
584×log-prod_binary64
445×exp-prod_binary64
383×pow-prod-down_binary64
283×pow2_binary64
254×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01138
123138
2297738
Stop Event
1×node limit
Counts
3 → 141
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x))
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
Outputs
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(/.f64 x (tan.f64 (*.f64 x 1/2))) -1)))) (#(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 (*.f64 (pow.f64 x -3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -1/2) (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) 2)))) (#(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 x 1/2)) x)))) (sqrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.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)) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (tan.f64 (*.f64 x 1/2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 1) 1))))))

simplify108.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
736×fma-def_binary64
562×associate-*l*_binary64
492×unswap-sqr_binary64
441×distribute-lft-out_binary64
437×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060653
1148647
2350641
3984637
43983637
57827637
Stop Event
1×node limit
Counts
177 → 167
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 (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)))
(/.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 1/240 (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))
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 (*.f64 x x) (fma.f64 (*.f64 x 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 (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 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 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) (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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 (*.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 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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 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 x (*.f64 x 1/240) 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 x 1/24 (/.f64 1/2 x)) (fma.f64 1/240 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 5))))
(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 x (*.f64 x 1/240) 1/24) (/.f64 1/2 x)))
(fma.f64 x (fma.f64 x (*.f64 x 1/240) 1/24) (fma.f64 17/40320 (pow.f64 x 5) (/.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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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)
(fma.f64 x (*.f64 x 1/24) 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 (pow.f64 x 4) 1/240)))
(+.f64 (fma.f64 (*.f64 x x) 1/24 1/2) (*.f64 (pow.f64 x 4) 1/240))
(fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) 1/240 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 (pow.f64 x 4) 1/240))))
(+.f64 (fma.f64 (*.f64 x x) 1/24 1/2) (fma.f64 (pow.f64 x 4) 1/240 (*.f64 (pow.f64 x 6) 17/40320)))
(+.f64 1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) 1/240 (*.f64 (pow.f64 x 6) 17/40320))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/240) 1/24) (fma.f64 (pow.f64 x 6) 17/40320 1/2))
(fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) 1/240 (fma.f64 (pow.f64 x 6) 17/40320 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 (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 (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 (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 (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 (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 (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 (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)))

localize30.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/2 (*.f64 x x))
✓29.7b
(/.f64 x (*.f64 1/2 (*.f64 x x)))
Compiler

Compiled 33 to 17 computations (48.5% saved)

series6.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/.f64 x (*.f64 1/2 (*.f64 x x)))
1.0ms
x
@0
(/.f64 x (*.f64 1/2 (*.f64 x x)))
1.0ms
x
@inf
(*.f64 1/2 (*.f64 x x))
1.0ms
x
@inf
(/.f64 x (*.f64 1/2 (*.f64 x x)))
1.0ms
x
@0
(*.f64 1/2 (*.f64 x x))

rewrite81.0ms (0.8%)

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
0617
113017
2173917
Stop Event
1×node limit
Counts
2 → 52
Calls
Call 1
Inputs
(/.f64 x (*.f64 1/2 (*.f64 x x)))
(*.f64 1/2 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (/.f64 2 (*.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 x (/.f64 2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (/.f64 2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 2 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 2 (*.f64 x x)))) 2) (cbrt.f64 (*.f64 x (/.f64 2 (*.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 1/2)) x) (/.f64 (sqrt.f64 (/.f64 x 1/2)) 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 1/2) (/.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 1/2))))) (#(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 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4)))) (/.f64 x (cbrt.f64 (*.f64 1/2 (*.f64 x x)))))))) (#(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 x (/.f64 2 (*.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 1/2 (*.f64 x x)))))))) (#(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 x (/.f64 2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 2 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (/.f64 2 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 x 1/2)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (/.f64 x 1/2)) -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 x (/.f64 2 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 (*.f64 x x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (/.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (/.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (/.f64 2 (*.f64 x x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))))))

simplify147.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
759×sqr-pow_binary64
542×associate-/l/_binary64
535×cube-prod_binary64
525×fabs-mul_binary64
451×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07132
113132
223132
346132
4113132
5346132
61319132
72385132
83401132
93585132
103797132
114095132
124509132
134992132
145560132
156246132
167081132
177471132
187757132
Stop Event
1×node limit
Counts
76 → 55
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)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
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)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))

localize23.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 28 to 16 computations (42.9% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite63.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
451×log-prod_binary64
347×exp-prod_binary64
305×prod-diff_binary64
278×pow-prod-down_binary64
226×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
117912
2256712
Stop Event
1×node limit
Counts
1 → 72
Calls
Call 1
Inputs
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 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 (pow.f64 x -2)) (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))) (#(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 x (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(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 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 (-.f64 1 (cos.f64 x)) (/.f64 (*.f64 x x) 1))))) (#(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 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (/.f64 x (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 x (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (neg.f64 x) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) 1) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) -1) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) -1) (pow.f64 (neg.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (neg.f64 (-.f64 1 (cos.f64 x)))) (pow.f64 (neg.f64 x) 2))))) (#(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 (-.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 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 x))))) (#(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 (E.f64) (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6) 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 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x) -1)))) (#(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 pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(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 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))) (#(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 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6))))) (#(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 expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(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 exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) -1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 1 x) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -3/2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -3/2) (pow.f64 x -1/2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 5) (/.f64 1 (cbrt.f64 x)) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))))

simplify53.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
716×fma-def_binary64
649×div-sub_binary64
566×associate-/r*_binary64
374×associate-/l/_binary64
352×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025148
158146
2130144
3356142
41285142
53563142
66488142
Stop Event
1×node limit
Counts
84 → 80
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 -1/24 (*.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 -1/40320 (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)))
(/.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))

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (/.f64 1 x) (neg.f64 x))
1.6b
(-.f64 1 (cos.f64 x))
✓16.4b
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
Compiler

Compiled 37 to 21 computations (43.2% saved)

series8.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@0
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
1.0ms
x
@-inf
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
1.0ms
x
@inf
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
1.0ms
x
@0
(/.f64 (/.f64 1 x) (neg.f64 x))
0.0ms
x
@inf
(/.f64 (/.f64 1 x) (neg.f64 x))

rewrite65.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
913×pow1_binary64
851×add-log-exp_binary64
851×log1p-expm1-u_binary64
851×expm1-log1p-u_binary64
111×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01028
122116
2330916
Stop Event
1×node limit
Counts
2 → 67
Calls
Call 1
Inputs
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(/.f64 (/.f64 1 x) (neg.f64 x))
Outputs
((#(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 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (pow.f64 x -2) (+.f64 -1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (+.f64 -1 (cos.f64 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 x) (/.f64 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 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 x x) (+.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 (*.f64 x x) (+.f64 1 (cos.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 x) (-.f64 1 (pow.f64 (cos.f64 x) 3))) (*.f64 x (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 x (+.f64 1 (cos.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) (cbrt.f64 (*.f64 x x))) (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 (+.f64 -1 (cos.f64 x)) x) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (-.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 (pow.f64 x -2) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 1 (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 (*.f64 (/.f64 1 x) (sqrt.f64 (+.f64 -1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (pow.f64 x -2) (+.f64 -1 (cos.f64 x))))))) (#(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 (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 (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 cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (+.f64 -1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 -1 (cos.f64 x)) 3) (pow.f64 (pow.f64 x -2) 3)))))) (#(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 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 -.f64 (exp.f64 (log1p.f64 (pow.f64 x -2))) 1)))) (#(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 (pow.f64 x -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.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 -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 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 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (pow.f64 x -1/2)) (pow.f64 x -1/2))))) (#(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 x -1/2) 1) (/.f64 (pow.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (cbrt.f64 (*.f64 x x))) (/.f64 (pow.f64 x -1/2) (cbrt.f64 x)))))) (#(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 *.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 x -1/2) -1) (/.f64 (pow.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 x -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (/.f64 (pow.f64 x -2) x) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -2)))))))

simplify65.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
028248
165246
2150236
3414226
41478226
54443226
67371226
Stop Event
1×node limit
Counts
91 → 78
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 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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)))))
(+.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 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 x (*.f64 x (fma.f64 (pow.f64 x 4) -1/40320 -1/24)) (fma.f64 1/720 (pow.f64 x 4) 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)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
✓15.1b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite111.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
545×log-prod_binary64
421×exp-prod_binary64
316×pow-prod-down_binary64
263×pow2_binary64
186×pow1/3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
120128
2280228
Stop Event
1×node limit
Counts
2 → 84
Calls
Call 1
Inputs
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sin.f64 x) (pow.f64 x -2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sin.f64 x) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sin.f64 x) (pow.f64 x -2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sin.f64 x) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 x (/.f64 (sin.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))) (cbrt.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 *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4)) (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 2) 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x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))))))))) (#(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 cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 3) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) 2)) (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))) (sqrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 1) 1))))))

simplify68.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
604×associate-/r/_binary64
596×distribute-rgt-out_binary64
555×distribute-lft-out_binary64
507×fma-def_binary64
449×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041474
1100472
2242470
3741468
42948468
56849468
Stop Event
1×node limit
Counts
108 → 103
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 (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)))
(*.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 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 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))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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)))))
(+.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 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) (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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x 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 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 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 (*.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))))
(fma.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 6)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 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 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24))))
(fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 1/2 (*.f64 x x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))

eval571.0ms (5.8%)

Compiler

Compiled 10987 to 6746 computations (38.6% saved)

prune186.0ms (1.9%)

Pruning

20 alts after pruning (14 fresh and 6 done)

PrunedKeptTotal
New6388646
Fresh369
Picked101
Done369
Total64520665
Error
0b
Counts
665 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
✓16.1b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
31.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
46.8b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
0.1b
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
32.2b
(*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x))))
✓31.7b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓31.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
15.4b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
✓0.2b
(*.f64 (sin.f64 x) (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
32.4b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
31.7b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
31.9b
(/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))
✓31.2b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
0.5b
(*.f64 (sin.f64 x) (/.f64 1 (*.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) x)))
13.3b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
30.3b
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
31.7b
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
✓32.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
30.2b
1/2
32.2b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 219 to 156 computations (28.8% saved)

regimes62.0ms (0.6%)

Counts
51 → 1
Calls
Call 1
Inputs
1/2
1/2
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (+.f64 (cos.f64 x) -1) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.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 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1 (*.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) x)))
(*.f64 (sin.f64 x) (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
(*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 (*.f64 x (neg.f64 x)))))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 (pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 x x))
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/3) 3) (*.f64 x x))
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
(*.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)))
(pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)
(pow.f64 (/.f64 x (/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) x)) -1)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
Outputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
Calls

3 calls:

26.0ms
x
12.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b1x
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 577 to 323 computations (44% saved)

regimes89.0ms (0.9%)

Counts
28 → 3
Calls
Call 1
Inputs
1/2
1/2
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (+.f64 (cos.f64 x) -1) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(/.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.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 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
Outputs
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

41.0ms
x
23.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 282 to 168 computations (40.4% saved)

bsearch47.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
22.0ms
9.519044008672343e-19
616.0276296902447
25.0ms
-1.7922668269295663
-7.538911107406542e-5
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes73.0ms (0.7%)

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

3 calls:

34.0ms
x
13.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
11.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 246 to 148 computations (39.8% saved)

bsearch47.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
22.0ms
9.519044008672343e-19
616.0276296902447
24.0ms
-1.7922668269295663
-7.538911107406542e-5
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes50.0ms (0.5%)

Counts
17 → 3
Calls
Call 1
Inputs
1/2
1/2
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
Outputs
(/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.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))
9.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 164 to 100 computations (39% saved)

bsearch47.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
22.0ms
9.519044008672343e-19
616.0276296902447
25.0ms
-1.7922668269295663
-7.538911107406542e-5
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes38.0ms (0.4%)

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

3 calls:

19.0ms
x
8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
7.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 104 to 64 computations (38.5% saved)

bsearch52.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
22.0ms
9.519044008672343e-19
616.0276296902447
30.0ms
-1.7922668269295663
-7.538911107406542e-5
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes20.0ms (0.2%)

Counts
9 → 3
Calls
Call 1
Inputs
1/2
1/2
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

1 calls:

18.0ms
x
Results
ErrorSegmentsBranch
0.3b3x
Compiler

Compiled 68 to 44 computations (35.3% saved)

bsearch52.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
26.0ms
9.519044008672343e-19
616.0276296902447
26.0ms
-1.7922668269295663
-7.538911107406542e-5
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes8.0ms (0.1%)

Counts
8 → 1
Calls
Call 1
Inputs
1/2
1/2
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (*.f64 (/.f64 2 (*.f64 x x)) x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/24 (*.f64 x x) 1/2)
Outputs
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
Calls

1 calls:

6.0ms
x
Results
ErrorSegmentsBranch
13.3b1x
Compiler

Compiled 60 to 39 computations (35% saved)

regimes7.0ms (0.1%)

Accuracy

Total -17.2b remaining (-57%)

Threshold costs -17.2b (-57%)

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

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
30.2b1x
Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify18.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
17×*-commutative_binary64
10×+-commutative_binary64
9×sub-neg_binary64
9×neg-sub0_binary64
9×neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
048275
166275
280273
397273
4115273
5129273
6141273
7145273
8147273
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
1/2
Outputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (/.f64 (/.f64 -1 x) x) (neg.f64 (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (*.f64 (/.f64 (/.f64 -1 x) x) (+.f64 (cos.f64 x) -1)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -504478263369281/281474976710656) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 2471285115124209/2596148429267413814265248164610048) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) 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 (/.f64 1 x) 2)))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/6) (*.f64 -2 (/.f64 -1 x))))
1/2
Compiler

Compiled 192 to 130 computations (32.3% saved)

soundness0.0ms (0%)

end95.0ms (1%)

Compiler

Compiled 185 to 115 computations (37.8% saved)

Profiling

Loading profile data...