Details

Time bar (total: 9.6s)

analyze84.0ms (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)

sample3.5s (36.3%)

Results
1.8s2114×body2048valid
633.0ms1138×body1024valid
522.0ms1594×body512valid
453.0ms3301×body256valid
94.0ms109×body4096valid

preprocess51.0ms (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)

simplify33.0ms (0.3%)

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
33.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.0b
(/.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
✓1.8b
(-.f64 1 (cos.f64 x))
✓16.7b
(/.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))

rewrite66.0ms (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))))))))

simplify55.0ms (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)

prune39.0ms (0.4%)

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
32.2b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
33.1b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
42.2b
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))
32.8b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
30.0b
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
▶33.1b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
33.1b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
▶30.1b
(fma.f64 -1/24 (*.f64 x x) 1/2)
▶17.4b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
33.2b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
▶18.3b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
32.3b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
33.1b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
32.4b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
29.3b
1/2
▶32.6b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
32.3b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
✓33.0b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 407 to 300 computations (26.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.3b
(+.f64 1 (cos.f64 x))
✓16.8b
(/.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)

series6.0ms (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)))

rewrite83.0ms (0.9%)

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
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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((x 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)

series1.0ms (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)

rewrite41.0ms (0.4%)

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)))))))

simplify155.0ms (1.6%)

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)
✓0.4b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.8b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series5.0ms (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)
0.0ms
x
@inf
(/.f64 (-.f64 1 (cos.f64 x)) x)

rewrite85.0ms (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))))))

simplify59.0ms (0.6%)

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))

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(exp.f64 (-.f64 1 (cos.f64 x)))
1.8b
(-.f64 1 (cos.f64 x))
✓1.9b
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
✓16.7b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series4.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite65.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
909×pow1_binary64
848×add-log-exp_binary64
848×log1p-expm1-u_binary64
848×expm1-log1p-u_binary64
829×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
117326
2226226
Stop Event
1×node limit
Counts
3 → 90
Calls
Call 1
Inputs
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (-.f64 1 (cos.f64 x)))
Outputs
((#(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 (+.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 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (cos.f64 x)) 1)))) (#(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 (+.f64 1 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))) (/.f64 (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 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 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 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))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (E.f64) (exp.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (exp.f64 (cos.f64 x)) (E.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (E.f64) (exp.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (E.f64)) (neg.f64 (exp.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.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 sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))

simplify57.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
772×distribute-rgt-out_binary64
692×fma-def_binary64
691×distribute-lft-out_binary64
472×associate-*l*_binary64
450×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045318
1113314
2275310
3805306
43067306
56851306
Stop Event
1×node limit
Counts
118 → 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 (-.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)))))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4)))))
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 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 1/2 (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 -1/40320 (pow.f64 x 8) (*.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 1/2 (*.f64 x x)))
(fma.f64 1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/12)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 (pow.f64 x 4) 1/12 1))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/12))))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) 1/12 1)))

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))
0.3b
(+.f64 1 (cos.f64 x))
✓0.6b
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
✓16.8b
(/.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)

series4.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite74.0ms (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
01154
125627
2393427
Stop Event
1×node limit
Counts
3 → 132
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))))
(/.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 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(/.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))))) (#(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 *.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x 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) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (/.f64 1 (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 (/.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 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 (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 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (pow.f64 (cbrt.f64 (sin.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 (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))))))
((#(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 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))) (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))))) (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 (cos.f64 x)) (pow.f64 (sin.f64 x) -2))))) (#(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)))) (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1 (cbrt.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 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 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 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (neg.f64 (cos.f64 x))) (/.f64 1 (neg.f64 (pow.f64 (sin.f64 x) 2))))))) (#(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 (tan.f64 (/.f64 x 2))) (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)))))) (#(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))) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 (/.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (sin.f64 x)) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (cos.f64 x)) (-.f64 1 (cos.f64 (+.f64 x 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 (-.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 (/.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1 (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (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 (-.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 (sin.f64 x) 2) 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 (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))))))

simplify48.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
648×fma-def_binary64
619×associate-/r*_binary64
590×distribute-lft-out_binary64
565×distribute-rgt-out_binary64
555×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060564
1133562
2319512
3937510
43864510
Stop Event
1×node limit
Counts
168 → 163
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))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 x (*.f64 -1/24 x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(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 -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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.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 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
(*.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)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(*.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)))))
(*.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))))
(/.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)))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (fma.f64 1/3024 (pow.f64 x 4) (/.f64 2 (*.f64 x x)))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x)))))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))

eval311.0ms (3.2%)

Compiler

Compiled 15370 to 8668 computations (43.6% saved)

prune129.0ms (1.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New86017877
Fresh12012
Picked101
Done415
Total87718895
Error
0b
Counts
895 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
▶17.3b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
32.2b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
33.1b
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
32.2b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
30.2b
(/.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))
32.6b
(pow.f64 (/.f64 x (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x))) -1)
29.6b
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x x))
▶17.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
▶32.2b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓33.0b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
47.6b
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
32.5b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
29.3b
1/2
32.5b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
▶30.1b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
▶33.0b
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
30.9b
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
41.4b
(cbrt.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -3))
Compiler

Compiled 417 to 286 computations (31.4% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
✓16.8b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series4.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite66.0ms (0.7%)

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 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))) 1) 1))))))
((#(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))))))

simplify61.0ms (0.6%)

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))))

localize7.0ms (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)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite40.0ms (0.4%)

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))))))))

simplify171.0ms (1.8%)

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))

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiled 23 to 12 computations (47.8% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite53.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
115512
2227512
Stop Event
1×node limit
Counts
1 → 40
Calls
Call 1
Inputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 2) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (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 (-.f64 1 (cos.f64 x)) 1) (/.f64 (/.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))

simplify51.0ms (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
52 → 49
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.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))

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (-.f64 1 (cos.f64 x)))
✓0.2b
(/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x)))))
1.8b
(-.f64 1 (cos.f64 x))
✓16.7b
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
Compiler

Compiled 51 to 34 computations (33.3% saved)

series3.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite70.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
439×log-prod_binary64
287×pow-prod-down_binary64
237×pow2_binary64
215×prod-diff_binary64
210×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01139
125127
2340427
Stop Event
1×node limit
Counts
3 → 168
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (-.f64 1 (cos.f64 x)))
Outputs
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x))))))) (#(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 *.f64 (/.f64 1 (-.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 1 (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)))))) (#(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 (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 (pow.f64 (-.f64 1 (cos.f64 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 -1 (-.f64 1 (cos.f64 x))) (neg.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (pow.f64 (-.f64 1 (cos.f64 x)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (/.f64 1 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (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 (-.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 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) -1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -3) (pow.f64 (-.f64 1 (cos.f64 x)) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 -1 (-.f64 1 (cos.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (neg.f64 (-.f64 1 (cos.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) -2) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)) 0)))))

simplify57.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
651×distribute-rgt-out_binary64
636×fma-def_binary64
577×associate-/l/_binary64
577×distribute-lft-out_binary64
493×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050324
1120322
2289320
3829318
43058318
56687318
Stop Event
1×node limit
Counts
196 → 193
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)))))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 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))))
(+.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))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 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 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 x (*.f64 1/2 x))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.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 -1/40320 (pow.f64 x 8) (*.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2))))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (fma.f64 1/3024 (pow.f64 x 4) (/.f64 2 (*.f64 x x)))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 x (*.f64 x 1/120) 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x)))))

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓16.4b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
Compiler

Compiled 34 to 18 computations (47.1% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite67.0ms (0.7%)

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 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 4)) (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (tan.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (tan.f64 (*.f64 x 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) x) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (cbrt.f64 x) x)) (/.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 x) x)) (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 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x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))))

simplify68.0ms (0.7%)

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)))

eval213.0ms (2.2%)

Compiler

Compiled 10906 to 6607 computations (39.4% saved)

prune105.0ms (1.1%)

Pruning

17 alts after pruning (12 fresh and 5 done)

PrunedKeptTotal
New6376643
Fresh6612
Picked011
Done145
Total64417661
Error
0b
Counts
661 → 17
Alt Table
Click to see full alt table
StatusErrorProgram
32.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
30.1b
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
33.1b
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
▶32.2b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
29.6b
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x x))
✓17.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓32.2b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
▶16.8b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
✓33.0b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
▶47.6b
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
▶32.5b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
29.3b
1/2
▶46.5b
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
✓30.1b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
✓33.0b
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
30.9b
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
32.5b
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 327 to 222 computations (32.1% saved)

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
✓0.2b
(*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))
✓16.1b
(/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x)
Compiler

Compiled 39 to 23 computations (41% saved)

series4.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite77.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
554×log-prod_binary64
425×exp-prod_binary64
320×pow-prod-down_binary64
258×pow2_binary64
184×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0942
119442
2269642
Stop Event
1×node limit
Counts
3 → 146
Calls
Call 1
Inputs
(/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x)
(*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sin.f64 x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sin.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 x (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) 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-2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (sqrt.f64 x)) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) (/.f64 x (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) (/.f64 x (sin.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (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 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.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 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) (/.f64 x (sin.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) 1) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x))) 1) (*.f64 (log.f64 x) 1)))))))

simplify49.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
832×fma-def_binary64
821×distribute-rgt-out_binary64
691×unswap-sqr_binary64
685×associate-*r*_binary64
342×associate-/l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
058708
1155706
2380704
31136702
43795702
Stop Event
1×node limit
Counts
182 → 174
Calls
Call 1
Inputs
(*.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)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) 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 (*.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)))
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 (pow.f64 x 3)) (*.f64 1/2 x))
(fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3)))
(*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 1/720 (pow.f64 x 5))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/720 (pow.f64 x 5))))
(fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (*.f64 1/2 x)))
(fma.f64 1/2 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))
(fma.f64 1/2 x (*.f64 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/720) -1/24)))
(+.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 1/720 (pow.f64 x 5) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 -1/40320 (pow.f64 x 7) (*.f64 1/2 x))))
(fma.f64 1/720 (pow.f64 x 5) (fma.f64 -1/40320 (pow.f64 x 7) (fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 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 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x)))
(+.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 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(+.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 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))))
(*.f64 x (fma.f64 1/720 (pow.f64 x 5) (fma.f64 -1/40320 (pow.f64 x 7) (fma.f64 -1/24 (pow.f64 x 3) (*.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) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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 (/.f64 (sin.f64 x) (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))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 x -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.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 1/720 (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 x (*.f64 x -1/24) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/24) (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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.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) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 x) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (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 (cos.f64 (*.f64 1/2 x)) (*.f64 x x))))
(/.f64 (*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (sin.f64 x) x)) (cos.f64 (*.f64 1/2 x)))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/2 (*.f64 x x))
✓31.3b
(/.f64 (*.f64 1/2 (*.f64 x x)) x)
Compiler

Compiled 27 to 12 computations (55.6% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite50.0ms (0.5%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0617
113014
2177114
Stop Event
1×node limit
Counts
2 → 56
Calls
Call 1
Inputs
(/.f64 (*.f64 1/2 (*.f64 x x)) x)
(*.f64 1/2 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/2 (pow.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 1/2 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (*.f64 x x)) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (pow.f64 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))) (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))) 2) (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 x -1))) (sqrt.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 (*.f64 x (sqrt.f64 1/2)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) -1/2) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 x) (*.f64 x (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) 1) (/.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) 1) (/.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 1/2)) 1) (/.f64 (*.f64 x (sqrt.f64 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/2 x) 1) (/.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (*.f64 x x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (/.f64 1/2 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (*.f64 1/2 (*.f64 x x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 1/2)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (*.f64 x (sqrt.f64 1/2)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 x) 2)) (/.f64 x (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 x)) (/.f64 (*.f64 x x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (sqrt.f64 x)) (/.f64 1/2 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (*.f64 1/2 (*.f64 x x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 x)) (/.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (pow.f64 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (pow.f64 x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 x -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 1/2 (pow.f64 x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (pow.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (pow.f64 x -1))))))))
((#(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))))))))

simplify174.0ms (1.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
07132
114132
222132
341132
4104132
5325132
61257132
72139132
82303132
92487132
102695132
112992132
123387132
133866132
144432132
155118132
165953132
176345132
186637132
196917132
206989132
217023132
227964132
Stop Event
1×node limit
Counts
80 → 59
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 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 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 2 (*.f64 x x))
✓0.5b
(/.f64 1 (/.f64 2 (*.f64 x x)))
✓32.3b
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
Compiler

Compiled 30 to 15 computations (50% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite58.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
859×pow1_binary64
804×add-log-exp_binary64
804×log1p-expm1-u_binary64
804×expm1-log1p-u_binary64
786×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
117826
2237526
Stop Event
1×node limit
Counts
3 → 84
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(/.f64 1 (/.f64 2 (*.f64 x x)))
(/.f64 2 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) 1/2) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)) (cbrt.f64 (/.f64 (*.f64 1/4 (pow.f64 x 4)) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 1/4 (pow.f64 x 4)) (pow.f64 x 4))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (*.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) (/.f64 (*.f64 (sqrt.f64 1/2) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 (*.f64 (sqrt.f64 1/2) x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (*.f64 x x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (/.f64 (*.f64 x x) x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) 1) (/.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) 1) (/.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) x) (/.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (*.f64 (*.f64 x x) 1/2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) (cbrt.f64 (pow.f64 x 4))) (/.f64 (*.f64 (sqrt.f64 1/2) x) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (*.f64 x x) 1/2) (neg.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 1/4 (pow.f64 x 4)) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 x x) 1/2) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 1/2) x) x) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (*.f64 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 (sqrt.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 (pow.f64 x -2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) -1) (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) -1) (pow.f64 (/.f64 (sqrt.f64 2) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 2 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 x -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) x) 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 (*.f64 x x) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) 1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (neg.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))))))

simplify175.0ms (1.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
07180
113180
225180
351180
4127180
5399180
61504180
72737180
82903180
93087180
103295180
113599180
123994180
134473180
145041180
155727180
166560180
176950180
187240180
197514180
207588180
217624180
Stop Event
1×node limit
Counts
120 → 89
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(*.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))
(*.f64 1/2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
Outputs
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
✓0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
✓0.4b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
1.8b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series3.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite60.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
975×pow1_binary64
907×add-log-exp_binary64
907×log1p-expm1-u_binary64
907×expm1-log1p-u_binary64
90×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0836
117733
2244433
Stop Event
1×node limit
Counts
3 → 91
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(/.f64 x (-.f64 1 (cos.f64 x)))
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)) (cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -2)) (cbrt.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))) (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 (neg.f64 (*.f64 x x)) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) -1) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) -1) (pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x x)) (-.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) x) (-.f64 1 (cos.f64 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 pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (-.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 (/.f64 1 (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 (/.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.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))) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (*.f64 (sin.f64 x) (sin.f64 x))) (+.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 (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 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 -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (-.f64 1 (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 x (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 x x)) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x x)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) x) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) 1) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (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 (*.f64 x x) (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 x x) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (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 (*.f64 x x) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))))

simplify56.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
729×fma-def_binary64
521×associate-*l*_binary64
506×distribute-rgt-out_binary64
492×unswap-sqr_binary64
441×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
053345
1131339
2310335
3889333
43555333
56455333
Stop Event
1×node limit
Counts
119 → 116
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
2
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (+.f64 (*.f64 1/3024 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.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 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 (fma.f64 x (*.f64 x 1/120) 1/6) (/.f64 2 x))
(fma.f64 x (fma.f64 (*.f64 x x) 1/120 1/6) (/.f64 2 x))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
(fma.f64 1/120 (pow.f64 x 3) (+.f64 (fma.f64 1/6 x (/.f64 2 x)) (*.f64 1/3024 (pow.f64 x 5))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x))))
(fma.f64 x (fma.f64 x (*.f64 x 1/120) 1/6) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x)))
(fma.f64 x (fma.f64 (*.f64 x x) 1/120 1/6) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x)))
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 6) 1/3024 (*.f64 (pow.f64 x 4) 1/120)))
(fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) 1/3024 2)))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (-.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))

localize12.0ms (0.1%)

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)))
1.8b
(-.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 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
0.0ms
x
@-inf
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
0.0ms
x
@inf
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))

rewrite174.0ms (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
0815
118312
2270812
Stop Event
1×node limit
Counts
1 → 79
Calls
Call 1
Inputs
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) 1) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(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 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 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 x 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 (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 (/.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 (/.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 (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 (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)) (pow.f64 (cbrt.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) (pow.f64 (cbrt.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 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 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 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)))) (#(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 x 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 (pow.f64 (/.f64 (*.f64 x x) (-.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 (-.f64 1 (cos.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 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 (*.f64 x 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 (/.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 (/.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 (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 (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)) (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)))))))

simplify124.0ms (1.3%)

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
91 → 88
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))

eval207.0ms (2.2%)

Compiler

Compiled 9425 to 6109 computations (35.2% saved)

prune125.0ms (1.3%)

Pruning

26 alts after pruning (18 fresh and 8 done)

PrunedKeptTotal
New62712639
Fresh167
Picked011
Done279
Total63026656
Error
0b
Counts
656 → 26
Alt Table
Click to see full alt table
StatusErrorProgram
33.1b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
29.3b
1/2
46.8b
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
32.6b
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
32.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
30.1b
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
32.5b
(/.f64 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
✓30.1b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
46.5b
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
46.6b
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
✓32.2b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
11.9b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
30.9b
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
29.6b
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x x))
✓17.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
11.9b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
✓32.2b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓16.8b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
46.5b
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
32.5b
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
✓33.0b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
✓47.6b
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
✓32.5b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
47.7b
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
46.6b
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
13.2b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
Compiler

Compiled 307 to 213 computations (30.6% saved)

regimes133.0ms (1.4%)

Counts
53 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) 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 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
(-.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 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) 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)))
(pow.f64 (/.f64 x (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x))) -1)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
(cbrt.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -3))
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.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)) 3) 1/3) (*.f64 x x))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.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))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
Outputs
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
Calls

3 calls:

80.0ms
x
18.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
16.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b3x
0.8b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.8b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 594 to 342 computations (42.4% saved)

bsearch54.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.0017706247697189237
51.23872447435121
30.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes244.0ms (2.5%)

Counts
41 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) 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 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
(-.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 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) 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)))
(pow.f64 (/.f64 x (-.f64 (/.f64 1 x) (/.f64 (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 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
Calls

3 calls:

207.0ms
x
13.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
13.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b3x
0.8b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.8b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 447 to 258 computations (42.3% saved)

bsearch99.0ms (1%)

Algorithm
2×binary-search
Steps
TimeLeftRight
74.0ms
1.704046130785219e-56
3.8860760226339766e-54
25.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes144.0ms (1.5%)

Counts
37 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) 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 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
(-.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 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Calls

3 calls:

88.0ms
x
30.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 402 to 235 computations (41.5% saved)

bsearch93.0ms (1%)

Algorithm
2×binary-search
Steps
TimeLeftRight
62.0ms
0.0017706247697189237
51.23872447435121
31.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes284.0ms (3%)

Counts
35 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) 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 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
Outputs
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Calls

3 calls:

244.0ms
x
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 382 to 226 computations (40.8% saved)

bsearch84.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
58.0ms
0.0017706247697189237
51.23872447435121
26.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes107.0ms (1.1%)

Counts
33 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) 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 1 (/.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 (/.f64 1 (+.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))) (*.f64 x x))
(/.f64 (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))) (*.f64 x x))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
Outputs
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Calls

3 calls:

68.0ms
x
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
14.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 364 to 216 computations (40.7% saved)

bsearch71.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
27.0ms
0.0017706247697189237
51.23872447435121
43.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes124.0ms (1.3%)

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

3 calls:

77.0ms
x
20.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 247 to 143 computations (42.1% saved)

bsearch88.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
42.0ms
0.0017706247697189237
51.23872447435121
46.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes121.0ms (1.3%)

Counts
23 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x)))) (*.f64 x 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))
(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 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (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

3 calls:

68.0ms
x
21.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 237 to 137 computations (42.2% saved)

bsearch52.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
24.0ms
0.0017706247697189237
51.23872447435121
28.0ms
-2354790321086377.5
-1.574530093874914e-6
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes16.0ms (0.2%)

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

11.0ms
x
Results
ErrorSegmentsBranch
11.9b1x
Compiler

Compiled 173 to 101 computations (41.6% saved)

regimes11.0ms (0.1%)

Accuracy

Total -18.9b remaining (-64.4%)

Threshold costs -18.9b (-64.4%)

Counts
13 → 1
Calls
Call 1
Inputs
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (*.f64 (/.f64 1/2 x) (*.f64 x x)) x)
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 (*.f64 (/.f64 1 (/.f64 2 x)) x) (*.f64 x x))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 (/.f64 1 (/.f64 2 (*.f64 x x))) (*.f64 x x))
(*.f64 (*.f64 -1/2 (*.f64 x x)) (/.f64 1 (neg.f64 (*.f64 x x))))
Outputs
1/2
Calls

1 calls:

8.0ms
x
Results
ErrorSegmentsBranch
29.3b1x
Compiler

Compiled 107 to 59 computations (44.9% saved)

simplify22.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
12×*-commutative_binary64
9×+-commutative_binary64
5×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061376
180376
289376
396376
4100376
5101376
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4)))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 1881743065265517/110427941548649020598956093796432407239217743554726184882600387580788736) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.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
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4)))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4)))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 1881743065265517/110427941548649020598956093796432407239217743554726184882600387580788736) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 1881743065265517/110427941548649020598956093796432407239217743554726184882600387580788736) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x)) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x)) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 32662261977575896/18446744073709551616) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -4709580642172755/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 4082782747196987/2305843009213693952) (+.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 2 (/.f64 1 x))))
1/2
Compiler

Compiled 262 to 185 computations (29.4% saved)

soundness83.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
648×fma-def_binary64
619×associate-/r*_binary64
590×distribute-lft-out_binary64
565×distribute-rgt-out_binary64
555×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060564
1133562
2319512
3937510
43864510
Stop Event
1×node limit
Compiler

Compiled 130 to 88 computations (32.3% saved)

end142.0ms (1.5%)

Compiler

Compiled 254 to 165 computations (35% saved)

Profiling

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