Details

Time bar (total: 13.0s)

analyze89.0ms (0.7%)

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

Compiled 10 to 7 computations (30% saved)

sample3.6s (28%)

Results
1.8s2115×body2048valid
736.0ms3372×body256valid
617.0ms1137×body1024valid
379.0ms1534×body512valid
77.0ms98×body4096valid
Bogosity

preprocess44.0ms (0.3%)

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)

simplify68.0ms (0.5%)

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))

eval1.0ms (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
33.5b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(cos.f64 x)
✓2.1b
(-.f64 1 (cos.f64 x))
✓15.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 20 to 9 computations (55% saved)

series4.0ms (0%)

Counts
3 → 20
Calls

9 calls:

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

rewrite68.0ms (0.5%)

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
0721
115221
2213521
Stop Event
1×node limit
Counts
3 → 78
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(-.f64 1 (cos.f64 x))
(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))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 x)))))))

simplify61.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
745×distribute-rgt-out_binary64
724×fma-def_binary64
691×distribute-lft-out_binary64
546×associate-*l*_binary64
465×associate-/l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
049270
1118266
2288262
3889258
43464258
56859258
Stop Event
1×node limit
Counts
98 → 102
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)))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
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)))))
(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 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 x (*.f64 x (fma.f64 -1/24 (*.f64 x 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 (*.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 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 1/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (*.f64 (pow.f64 x 6) -1/720))))
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 (fma.f64 (pow.f64 x 4) 1/24 (*.f64 (pow.f64 x 6) -1/720))))
(+.f64 1 (fma.f64 (pow.f64 x 6) -1/720 (fma.f64 x (*.f64 x -1/2) (*.f64 (pow.f64 x 4) 1/24))))
(fma.f64 (pow.f64 x 6) -1/720 (fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 1)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (pow.f64 x 6) -1/720 1)))

eval29.0ms (0.2%)

Compiler

Compiled 1358 to 795 computations (41.5% saved)

prune65.0ms (0.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New8319102
Fresh000
Picked011
Done000
Total8320103
Error
0.0b
Counts
103 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.5b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
17.2b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
32.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
29.7b
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
✓33.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
33.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
▶33.5b
(/.f64 (-.f64 1 (log.f64 (exp.f64 (cos.f64 x)))) (*.f64 x x))
29.8b
(fma.f64 -1/24 (*.f64 x x) 1/2)
33.6b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
33.0b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶49.4b
(/.f64 (-.f64 1 1) (*.f64 x x))
32.8b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
29.0b
1/2
▶16.6b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
33.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
33.7b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
33.5b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
▶45.8b
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
41.6b
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))
33.0b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
Compiler

Compiled 437 to 308 computations (29.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.5b
(+.f64 1 (cos.f64 x))
✓15.8b
(/.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%)

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)))

rewrite133.0ms (1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122830
2354030
Stop Event
1×node limit
Counts
4 → 182
Calls
Call 1
Inputs
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(+.f64 1 (cos.f64 x))
(*.f64 (sin.f64 x) (sin.f64 x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
Outputs
((#(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 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (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 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 x x)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 1 (cos.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 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (pow.f64 x 4))) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (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 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)) (pow.f64 (sin.f64 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (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 (-.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 (/.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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simplify149.0ms (1.1%)

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)))

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓15.3b
(/.f64 (-.f64 1 1) (*.f64 x x))
Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite104.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
071
11161
29641
Stop Event
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 (-.f64 1 1) (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 0)))))

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112
Stop Event
1×saturated
Counts
13 → 1
Calls
Call 1
Inputs
0
0
0
0
0
0
0
0
0
0
0
0
Outputs
0
0
0
0
0
0
0
0
0
0
0
0

localize28.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
✓0.3b
(fma.f64 -1/24 (*.f64 x x) 1/2)
✓36.8b
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
Compiler

Compiled 37 to 16 computations (56.8% saved)

series7.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite175.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
479×log-prod_binary64
395×prod-exp_binary64
359×exp-prod_binary64
290×pow-prod-down_binary64
223×div-exp_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0854
117742
2247530
Stop Event
1×node limit
Counts
3 → 218
Calls
Call 1
Inputs
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 (*.f64 x x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) -1/24) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (*.f64 -1/24 x) x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (*.f64 -1/24 x) x 1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (*.f64 -1/24 x) x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (*.f64 -1/24 x) x 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (*.f64 -1/24 x) x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (*.f64 -1/24 x) x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 (fma.f64 (*.f64 -1/24 x) x 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 (*.f64 x (fma.f64 (*.f64 -1/24 x) x 1/2)) 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simplify258.0ms (2%)

Algorithm
1×egg-herbie
Rules
802×fma-def_binary64
787×sqr-pow_binary64
511×pow-sqr_binary64
491×associate-*l*_binary64
446×cube-prod_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013357
126321
252321
3122321
4416321
51607321
63005321
73653321
83843321
94054321
104335321
114700321
125198321
135727321
146351321
157102321
167408321
177630321
187828321
197886321
207910321
Stop Event
1×node limit
Counts
254 → 155
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)))
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)))
(*.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 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (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)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/24 x) 1/2)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 1/2 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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(*.f64 -1/24 (pow.f64 x 4))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(*.f64 -1/24 (pow.f64 x 4))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))
(+.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 (*.f64 1/2 x) x))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 x (fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 -1/24 x) 1/2))

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.3b
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
✓1.9b
(log1p.f64 (neg.f64 (cos.f64 x)))
✓15.7b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 28 to 7 computations (75% saved)

series122.0ms (0.9%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
49.0ms
x
@inf
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
43.0ms
x
@-inf
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
25.0ms
x
@0
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
2.0ms
x
@0
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
1.0ms
x
@0
(log1p.f64 (neg.f64 (cos.f64 x)))

rewrite94.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
746×pow1_binary64
691×add-log-exp_binary64
690×expm1-log1p-u_binary64
689×log1p-expm1-u_binary64
673×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0831
116323
2215223
Stop Event
1×node limit
Counts
3 → 73
Calls
Call 1
Inputs
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(log1p.f64 (neg.f64 (cos.f64 x)))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2) (*.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) x) (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 (cos.f64 x) 1)) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (+.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (cos.f64 x) 1) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2) 1) (/.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) 1) (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (+.f64 (cos.f64 x) 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2) x) (/.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (+.f64 (cos.f64 x) 1) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 (cos.f64 x) 1) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (+.f64 (cos.f64 x) 1) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 (cos.f64 x) 1)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 (cos.f64 x) 1) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 (cos.f64 x)) (log.f64 (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2)) (log.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1))) (log.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (cos.f64 x))) (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 x))) 2) (cbrt.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (cos.f64 x))) (sqrt.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (cos.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.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 (cos.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (cos.f64 x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 2) (cbrt.f64 (+.f64 (cos.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) (sqrt.f64 (+.f64 (cos.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 2)) (+.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (cos.f64 x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (cos.f64 x) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (cos.f64 x) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 x))) 2)) (cbrt.f64 (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (cos.f64 x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (cos.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (cos.f64 x) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (cos.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (cos.f64 x) 1)))))))

simplify98.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
677×distribute-lft-out_binary64
371×*-commutative_binary64
326×unswap-sqr_binary64
295×associate-+l+_binary64
252×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050680
1129489
2384410
31381406
42677406
56757406
Stop Event
1×node limit
Counts
109 → 101
Calls
Call 1
Inputs
(/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))))))
(+.f64 (*.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))))))
(/.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 (log.f64 1/2) (*.f64 2 (log.f64 x)))
(+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))
(+.f64 (*.f64 -1/1440 (pow.f64 x 4)) (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))))
(+.f64 (*.f64 -1/1440 (pow.f64 x 4)) (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 -1/90720 (pow.f64 x 6)) (*.f64 2 (log.f64 x))))))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))
(+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))))
(+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)))))
(+.f64 (*.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 6))) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 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))
Outputs
(/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))
(/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x))
(*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))
1/2
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x)) (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12))
(+.f64 (*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x)) (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))))))
(+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x)) (fma.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x)) (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12)))
(+.f64 (*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x)) (fma.f64 1/360 (*.f64 1/2 (pow.f64 x 4)) (*.f64 -1/24 (*.f64 x x))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 (pow.f64 x 4) 1/720))
(+.f64 (*.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (*.f64 -1/12 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))))))
(fma.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4)) (+.f64 (/.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x)) (fma.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 x x)) (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12))))
(+.f64 (fma.f64 1/360 (*.f64 1/2 (pow.f64 x 4)) (*.f64 -1/24 (*.f64 x x))) (fma.f64 (*.f64 -1/40320 (*.f64 x x)) (pow.f64 x 4) (*.f64 (/.f64 1/2 x) (/.f64 (*.f64 x x) x))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (+.f64 (*.f64 1/720 (pow.f64 x 4)) (*.f64 -1/40320 (pow.f64 x 6))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 (pow.f64 x 4) (+.f64 1/720 (*.f64 (*.f64 x x) -1/40320))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (+.f64 (*.f64 (pow.f64 x 4) 1/720) (*.f64 (pow.f64 x 6) -1/40320)))
(/.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 (log.f64 1/2) (*.f64 2 (log.f64 x)))
(fma.f64 2 (log.f64 x) (log.f64 1/2))
(+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))
(fma.f64 -1/12 (*.f64 x x) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))
(fma.f64 (*.f64 x x) -1/12 (fma.f64 2 (log.f64 x) (log.f64 1/2)))
(fma.f64 2 (log.f64 x) (fma.f64 x (*.f64 x -1/12) (log.f64 1/2)))
(+.f64 (*.f64 -1/1440 (pow.f64 x 4)) (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))))
(fma.f64 -1/1440 (pow.f64 x 4) (fma.f64 -1/12 (*.f64 x x) (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))))
(fma.f64 (pow.f64 x 4) -1/1440 (fma.f64 (*.f64 x x) -1/12 (fma.f64 2 (log.f64 x) (log.f64 1/2))))
(fma.f64 x (*.f64 x -1/12) (fma.f64 (pow.f64 x 4) -1/1440 (fma.f64 2 (log.f64 x) (log.f64 1/2))))
(+.f64 (*.f64 -1/1440 (pow.f64 x 4)) (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 -1/90720 (pow.f64 x 6)) (*.f64 2 (log.f64 x))))))
(fma.f64 -1/1440 (pow.f64 x 4) (fma.f64 -1/12 (*.f64 x x) (+.f64 (log.f64 1/2) (fma.f64 -1/90720 (pow.f64 x 6) (*.f64 2 (log.f64 x))))))
(fma.f64 (pow.f64 x 4) -1/1440 (+.f64 (fma.f64 2 (log.f64 x) (*.f64 -1/90720 (pow.f64 x 6))) (fma.f64 (*.f64 x x) -1/12 (log.f64 1/2))))
(fma.f64 (pow.f64 x 4) -1/1440 (fma.f64 x (*.f64 x -1/12) (fma.f64 2 (log.f64 x) (fma.f64 -1/90720 (pow.f64 x 6) (log.f64 1/2)))))
(fma.f64 x (*.f64 x -1/12) (fma.f64 (pow.f64 x 4) -1/1440 (fma.f64 2 (log.f64 x) (fma.f64 -1/90720 (pow.f64 x 6) (log.f64 1/2)))))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(log.f64 (-.f64 1 (cos.f64 x)))
(log1p.f64 (neg.f64 (cos.f64 x)))
(exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x))))
(*.f64 (*.f64 x x) 1/2)
(*.f64 x (*.f64 x 1/2))
(+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))))
(+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12) (*.f64 x x)))
(fma.f64 -1/12 (*.f64 1/2 (pow.f64 x 4)) (*.f64 (*.f64 x x) 1/2))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2)))))
(fma.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4)) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12) (*.f64 x x))))
(fma.f64 (*.f64 1/720 (*.f64 x x)) (pow.f64 x 4) (fma.f64 -1/12 (*.f64 1/2 (pow.f64 x 4)) (*.f64 (*.f64 x x) 1/2)))
(+.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 (pow.f64 x 6) 1/720))
(+.f64 (*.f64 (pow.f64 x 4) -1/24) (fma.f64 (*.f64 x x) 1/2 (*.f64 (pow.f64 x 6) 1/720)))
(+.f64 (*.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 6))) (+.f64 (*.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 -1/12 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))))))
(fma.f64 -1/20160 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 6)) (fma.f64 1/360 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (pow.f64 x 4)) (+.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) (*.f64 (*.f64 (exp.f64 (+.f64 (log.f64 1/2) (*.f64 2 (log.f64 x)))) -1/12) (*.f64 x x)))))
(fma.f64 (*.f64 -1/40320 (*.f64 x x)) (pow.f64 x 6) (fma.f64 (*.f64 1/720 (*.f64 x x)) (pow.f64 x 4) (fma.f64 -1/12 (*.f64 1/2 (pow.f64 x 4)) (*.f64 (*.f64 x x) 1/2))))
(+.f64 (*.f64 1/720 (pow.f64 x 6)) (fma.f64 (pow.f64 x 6) (*.f64 (*.f64 x x) -1/40320) (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))))
(+.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 (pow.f64 x 6) (+.f64 1/720 (*.f64 (*.f64 x x) -1/40320))))
(+.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (+.f64 (*.f64 (pow.f64 x 6) 1/720) (*.f64 (pow.f64 x 8) -1/40320)))
(-.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))

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(exp.f64 (cos.f64 x))
✓0.3b
(log.f64 (exp.f64 (cos.f64 x)))
✓2.1b
(-.f64 1 (log.f64 (exp.f64 (cos.f64 x))))
✓15.7b
(/.f64 (-.f64 1 (log.f64 (exp.f64 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 31 to 11 computations (64.5% saved)

series4.0ms (0%)

Counts
4 → 40
Calls

12 calls:

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

rewrite77.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
942×pow1_binary64
881×add-log-exp_binary64
880×log1p-expm1-u_binary64
880×expm1-log1p-u_binary64
861×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
117526
2232026
Stop Event
1×node limit
Counts
4 → 100
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (log.f64 (exp.f64 (cos.f64 x)))) (*.f64 x x))
(-.f64 1 (log.f64 (exp.f64 (cos.f64 x))))
(log.f64 (exp.f64 (cos.f64 x)))
(exp.f64 (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 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.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))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (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 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) 2) (cbrt.f64 (exp.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (cos.f64 x))))))))

simplify73.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
722×div-sub_binary64
545×distribute-lft-out_binary64
432×associate-/r/_binary64
429×*-commutative_binary64
419×associate-/l/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
063416
1161412
2409405
31298401
42027399
53461399
65855399
Stop Event
1×node limit
Counts
140 → 133
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 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(exp.f64 1)
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (exp.f64 1))
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 4))) (exp.f64 1)))
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (*.f64 -31/720 (*.f64 (exp.f64 1) (pow.f64 x 6))) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 4))) (exp.f64 1))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 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 (-.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 (*.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 1/2 (*.f64 x x) (*.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)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (fma.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 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 1/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 1 (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 1) (fma.f64 (pow.f64 x 6) -1/720 (*.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 (*.f64 (pow.f64 x 6) -1/720))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/24 1) (fma.f64 (pow.f64 x 6) -1/720 (*.f64 (*.f64 x x) -1/2)))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(exp.f64 1)
(E.f64)
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (exp.f64 1))
(fma.f64 -1/2 (*.f64 (*.f64 x x) (E.f64)) (E.f64))
(*.f64 (fma.f64 x (*.f64 x -1/2) 1) (E.f64))
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 4))) (exp.f64 1)))
(fma.f64 -1/2 (*.f64 (*.f64 x x) (E.f64)) (fma.f64 1/6 (*.f64 (pow.f64 x 4) (E.f64)) (E.f64)))
(fma.f64 (pow.f64 x 4) (*.f64 (E.f64) 1/6) (*.f64 (fma.f64 x (*.f64 x -1/2) 1) (E.f64)))
(*.f64 (E.f64) (+.f64 (fma.f64 x (*.f64 x -1/2) 1) (*.f64 (pow.f64 x 4) 1/6)))
(+.f64 (*.f64 -1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (*.f64 -31/720 (*.f64 (exp.f64 1) (pow.f64 x 6))) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 4))) (exp.f64 1))))
(fma.f64 -1/2 (*.f64 (*.f64 x x) (E.f64)) (fma.f64 -31/720 (*.f64 (pow.f64 x 6) (E.f64)) (fma.f64 1/6 (*.f64 (pow.f64 x 4) (E.f64)) (E.f64))))
(+.f64 (*.f64 (fma.f64 x (*.f64 x -1/2) 1) (E.f64)) (*.f64 (E.f64) (+.f64 (*.f64 (pow.f64 x 4) 1/6) (*.f64 (pow.f64 x 6) -31/720))))
(fma.f64 (pow.f64 x 6) (*.f64 (E.f64) -31/720) (*.f64 (E.f64) (+.f64 (fma.f64 x (*.f64 x -1/2) 1) (*.f64 (pow.f64 x 4) 1/6))))
(*.f64 (E.f64) (+.f64 (+.f64 (*.f64 (pow.f64 x 4) 1/6) (*.f64 (pow.f64 x 6) -31/720)) (fma.f64 x (*.f64 x -1/2) 1)))
(*.f64 (E.f64) (+.f64 (fma.f64 x (*.f64 x -1/2) 1) (+.f64 (*.f64 (pow.f64 x 4) 1/6) (*.f64 (pow.f64 x 6) -31/720))))

eval226.0ms (1.7%)

Compiler

Compiled 10067 to 5751 computations (42.9% saved)

prune103.0ms (0.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New62112633
Fresh13114
Picked101
Done325
Total63815653
Error
0.0b
Counts
653 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
29.7b
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
✓33.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
16.6b
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
▶32.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
✓45.8b
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
▶16.3b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
▶16.3b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
33.4b
(-.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))))
33.5b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
▶29.8b
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
48.9b
0
29.0b
1/2
▶33.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
33.0b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
45.8b
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
Compiler

Compiled 326 to 213 computations (34.7% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sin.f64 x)
✓0.2b
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
✓15.8b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series6.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite71.0ms (0.5%)

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
0931
120131
2280231
Stop Event
1×node limit
Counts
3 → 114
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))
(sin.f64 x)
Outputs
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(*.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))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sin.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sin.f64 (exp.f64 (log1p.f64 x))) (cos.f64 1)) (*.f64 (cos.f64 (exp.f64 (log1p.f64 x))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 x))) 2)) (cbrt.f64 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 x)))) (sqrt.f64 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sin.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sin.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 x)) 1) 1))))))

simplify66.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
989×distribute-rgt-out_binary64
851×fma-def_binary64
696×associate-*r*_binary64
691×unswap-sqr_binary64
272×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
058520
1149518
2366516
31128514
43744514
57794514
Stop Event
1×node limit
Counts
142 → 140
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)))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/40320 (pow.f64 x 6) (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) (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) (/.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) (/.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) (/.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) (/.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) (/.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) (/.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) (/.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) (/.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 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2))
(*.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)))))
(*.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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 (*.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 (/.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))))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 -1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 1/120 (pow.f64 x 5) (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 -1/5040 (pow.f64 x 7) x)))
(fma.f64 1/120 (pow.f64 x 5) (fma.f64 -1/5040 (pow.f64 x 7) (fma.f64 -1/6 (pow.f64 x 3) x)))

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite39.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
431×pow1_binary64
421×add-sqr-sqrt_binary64
410×*-un-lft-identity_binary64
402×add-log-exp_binary64
402×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11027
211487
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) -1/24)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24)) (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x -1/24))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/24))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -25/24)))))))

simplify173.0ms (1.3%)

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 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.1b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
✓0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 28 to 16 computations (42.9% saved)

series4.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite95.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
117921
2256721
Stop Event
1×node limit
Counts
2 → 211
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) x)
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (cos.f64 x) x))) (sqrt.f64 (/.f64 (cos.f64 x) x)) (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 x)) (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (neg.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 x) 1 (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (/.f64 1 (neg.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) x) 1))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) 1 (*.f64 (/.f64 (cos.f64 x) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 x) 1 (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (/.f64 1 (neg.f64 x)) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 1 x) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 x)) (cos.f64 x) (*.f64 (/.f64 1 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 x) 1 (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (/.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 2) (/.f64 x (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (/.f64 x (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (neg.f64 x) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) 1) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) -1) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) -1) (pow.f64 (neg.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (neg.f64 (-.f64 1 (cos.f64 x)))) (pow.f64 (neg.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (/.f64 (-.f64 1 (cos.f64 x)) x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (neg.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x (-.f64 1 (cos.f64 x))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) x)) 1) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 x) -1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 1 x) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -3/2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -3/2) (pow.f64 x -1/2) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 4) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 5) (/.f64 1 (cbrt.f64 x)) (neg.f64 (/.f64 (/.f64 (cos.f64 x) x) x)))))))

simplify62.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
506×unswap-sqr_binary64
492×fma-def_binary64
476×distribute-lft-out_binary64
422×associate-/l/_binary64
397×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041206
1107204
2254202
3701200
42591200
55045200
67631200
Stop Event
1×node limit
Counts
227 → 226
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)))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
(*.f64 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 x (fma.f64 x (*.f64 x -1/24) 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 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (fma.f64 -1/40320 (pow.f64 x 7) (*.f64 1/2 x))))
(fma.f64 1/2 x (fma.f64 1/720 (pow.f64 x 5) (fma.f64 -1/24 (pow.f64 x 3) (*.f64 -1/40320 (pow.f64 x 7)))))
(fma.f64 -1/40320 (pow.f64 x 7) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (*.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))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 1/720 (*.f64 x x) -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 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 x (*.f64 x -1/24) 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(fma.f64 (*.f64 x x) (fma.f64 1/720 (*.f64 x x) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
2.1b
(-.f64 1 (cos.f64 x))
✓16.3b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
Compiler

Compiled 21 to 13 computations (38.1% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite48.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
802×pow1_binary64
748×add-log-exp_binary64
746×log1p-expm1-u_binary64
746×expm1-log1p-u_binary64
733×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
116912
2200412
Stop Event
1×node limit
Counts
1 → 19
Calls
Call 1
Inputs
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (pow.f64 x -2)) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 x -2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x)) 2)))) (#(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 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))))

simplify49.0ms (0.4%)

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
31 → 28
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))

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓15.3b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))
Compiler

Compiled 34 to 18 computations (47.1% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite66.0ms (0.5%)

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 (*.f64 x 1/2))) (*.f64 (cbrt.f64 x) x)) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (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 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 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)) (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) (*.f64 -2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -2 (log.f64 x)) (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) 1) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (sin.f64 x)) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (sin.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (neg.f64 (tan.f64 (*.f64 x 1/2)))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (*.f64 x 1/2)) x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))) 2)) (cbrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -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)) (*.f64 (pow.f64 x -2) (sin.f64 x)))))) (sqrt.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 x -2) (sin.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1) (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) 1)))))))

simplify73.0ms (0.6%)

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)))

eval303.0ms (2.3%)

Compiler

Compiled 12633 to 7348 computations (41.8% saved)

prune197.0ms (1.5%)

Pruning

22 alts after pruning (15 fresh and 7 done)

PrunedKeptTotal
New67113684
Fresh628
Picked011
Done066
Total67722699
Error
0b
Counts
699 → 22
Alt Table
Click to see full alt table
StatusErrorProgram
▶32.7b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓29.8b
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
15.5b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
32.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
48.9b
0
▶28.6b
(*.f64 (sin.f64 x) (/.f64 1/2 x))
44.8b
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
33.5b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
✓33.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
32.7b
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
✓32.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
✓45.8b
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
✓16.3b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
✓16.3b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
45.8b
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
29.0b
1/2
32.8b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
✓33.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
29.7b
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
▶0.5b
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
▶29.1b
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
▶33.2b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 382 to 252 computations (34% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.1b
(/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x))
✓0.1b
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
✓0.4b
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
Compiler

Compiled 37 to 23 computations (37.8% saved)

series9.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite121.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
594×log-prod_binary64
464×exp-prod_binary64
306×pow-prod-down_binary64
268×pow2_binary64
233×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
120138
2292338
Stop Event
1×node limit
Counts
3 → 162
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
(/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x))
Outputs
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simplify101.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
792×fma-def_binary64
585×associate-*l*_binary64
506×unswap-sqr_binary64
463×associate-*r*_binary64
440×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
062658
1150654
2362650
31074646
44205646
57964646
Stop Event
1×node limit
Counts
198 → 189
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)))
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 2 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (*.f64 -1/360 (pow.f64 x 5))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 -1/360 (pow.f64 x 5)) (*.f64 -1/15120 (pow.f64 x 7)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.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))))
(+.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)))
(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)))
(/.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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x 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))))
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 (*.f64 x x) 1/24))
(fma.f64 (*.f64 x x) 1/24 1/2)
(fma.f64 x (*.f64 x 1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/240)))
(+.f64 (fma.f64 (*.f64 x x) 1/24 1/2) (*.f64 (pow.f64 x 4) 1/240))
(fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) 1/240 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/240) 1/24) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/240 1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (fma.f64 17/40320 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/240))))
(+.f64 (fma.f64 (*.f64 x x) 1/24 1/2) (fma.f64 (pow.f64 x 4) 1/240 (*.f64 (pow.f64 x 6) 17/40320)))
(+.f64 1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 6) 17/40320 (*.f64 (pow.f64 x 4) 1/240))))
(fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) 1/240 (fma.f64 (pow.f64 x 6) 17/40320 1/2)))
(fma.f64 (pow.f64 x 6) 17/40320 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/240 1/24) 1/2))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x)))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) x)
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 2 x))
(fma.f64 -1/6 (pow.f64 x 3) (*.f64 x 2))
(fma.f64 x 2 (*.f64 -1/6 (pow.f64 x 3)))
(*.f64 x (fma.f64 x (*.f64 x -1/6) 2))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (*.f64 -1/360 (pow.f64 x 5))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 2 x (*.f64 -1/360 (pow.f64 x 5))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 x 2 (*.f64 -1/360 (pow.f64 x 5))))
(fma.f64 x 2 (fma.f64 -1/6 (pow.f64 x 3) (*.f64 -1/360 (pow.f64 x 5))))
(fma.f64 x 2 (fma.f64 -1/360 (pow.f64 x 5) (*.f64 -1/6 (pow.f64 x 3))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 2 x) (+.f64 (*.f64 -1/360 (pow.f64 x 5)) (*.f64 -1/15120 (pow.f64 x 7)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 2 x (fma.f64 -1/360 (pow.f64 x 5) (*.f64 -1/15120 (pow.f64 x 7)))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 x 2 (fma.f64 -1/15120 (pow.f64 x 7) (*.f64 -1/360 (pow.f64 x 5)))))
(fma.f64 x 2 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 -1/360 (pow.f64 x 5) (*.f64 -1/15120 (pow.f64 x 7)))))
(fma.f64 -1/360 (pow.f64 x 5) (fma.f64 x 2 (fma.f64 -1/6 (pow.f64 x 3) (*.f64 -1/15120 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (*.f64 x -1/6) 2) (fma.f64 -1/360 (pow.f64 x 5) (*.f64 -1/15120 (pow.f64 x 7))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 x (*.f64 x (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))))

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
Compiler

Compiled 17 to 12 computations (29.4% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite78.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
563×pow1_binary64
526×add-log-exp_binary64
526×log1p-expm1-u_binary64
526×expm1-log1p-u_binary64
514×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
077
11441
217341
Stop Event
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 1/2)))))

simplify12.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112
Stop Event
1×saturated
Counts
13 → 1
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
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

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 x)
✓0.2b
(*.f64 (sin.f64 x) (/.f64 1/2 x))
Compiler

Compiled 14 to 8 computations (42.9% saved)

series4.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite72.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
624×pow1_binary64
580×add-log-exp_binary64
580×log1p-expm1-u_binary64
580×expm1-log1p-u_binary64
569×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11289
215679
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (/.f64 1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sin.f64 x) (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 x) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (*.f64 (sin.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sin.f64 x) 1/2)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 1/2) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 1/2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 1/2) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1/2 (sin.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) -1/2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sin.f64 x) (/.f64 1/2 x))))))))

simplify114.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
704×fma-def_binary64
646×associate-/l/_binary64
571×*-commutative_binary64
477×sqr-pow_binary64
326×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
024124
154122
2120120
3333118
41188118
53042118
63998118
76107118
86337118
96680118
107076118
117520118
Stop Event
1×node limit
Counts
32 → 28
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/12 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (*.f64 -1/10080 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/12 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/12 (*.f64 x x)))
(fma.f64 -1/12 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/12 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (*.f64 1/240 (pow.f64 x 4))))
(fma.f64 -1/12 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (+.f64 (*.f64 -1/10080 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (fma.f64 -1/10080 (pow.f64 x 6) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) (*.f64 -1/10080 (pow.f64 x 6)))))
(fma.f64 -1/10080 (pow.f64 x 6) (fma.f64 -1/12 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) 1/2)))
(fma.f64 x (fma.f64 -1/10080 (pow.f64 x 5) (*.f64 -1/12 x)) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(fma.f64 x (*.f64 x (fma.f64 (pow.f64 x 4) -1/10080 -1/12)) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))
(*.f64 1/2 (/.f64 (sin.f64 x) x))

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.1b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
2.1b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 28 to 16 computations (42.9% saved)

series5.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite96.0ms (0.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0824
118321
2270821
Stop Event
1×node limit
Counts
2 → 131
Calls
Call 1
Inputs
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) -2) (/.f64 x (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 2)) (cbrt.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) 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simplify81.0ms (0.6%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
043199
1104195
2241193
3682191
42502191
54938191
67594191
Stop Event
1×node limit
Counts
147 → 147
Calls
Call 1
Inputs
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(fma.f64 1/6 x (/.f64 2 x))
(fma.f64 x 1/6 (/.f64 2 x))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 1/6 x (/.f64 2 x)))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))
(fma.f64 x 1/6 (fma.f64 1/120 (pow.f64 x 3) (/.f64 2 x)))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
(fma.f64 1/120 (pow.f64 x 3) (+.f64 (fma.f64 1/6 x (/.f64 2 x)) (*.f64 1/3024 (pow.f64 x 5))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x))))
(fma.f64 x 1/6 (fma.f64 1/120 (pow.f64 x 3) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x))))
(fma.f64 x (fma.f64 1/120 (*.f64 x x) 1/6) (fma.f64 1/3024 (pow.f64 x 5) (/.f64 2 x)))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 x -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 x (*.f64 x -1/24) 1/2)))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.1b
(/.f64 (cos.f64 x) x)
✓0.1b
(/.f64 (/.f64 (cos.f64 x) x) x)
✓21.3b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 28 to 10 computations (64.3% saved)

series10.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
2.0ms
x
@0
(/.f64 (/.f64 (cos.f64 x) x) x)
2.0ms
x
@inf
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
1.0ms
x
@-inf
(/.f64 (cos.f64 x) x)
1.0ms
x
@0
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))

rewrite166.0ms (1.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0830
118830
2279130
Stop Event
1×node limit
Counts
3 → 280
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (/.f64 (cos.f64 x) x) x)
(/.f64 (cos.f64 x) x)
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (cos.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (*.f64 (cbrt.f64 (cos.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 2) (cbrt.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 (cos.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) (sqrt.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cos.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (cos.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 x)) 1) (/.f64 (sqrt.f64 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 x) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (cos.f64 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (cos.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (cos.f64 x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (cos.f64 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 x) x)) 1))))))

simplify85.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
050331
1121325
2293323
3825321
42995321
56165321
Stop Event
1×node limit
Counts
308 → 306
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
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 (fma.f64 -1/40320 (pow.f64 x 6) (*.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))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(+.f64 (/.f64 1 (*.f64 x x)) -1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(+.f64 (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x))) -1/2)
(+.f64 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x))) -1/2)
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) -1/2))
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x)))) -1/2)
(+.f64 (fma.f64 (pow.f64 x 4) -1/720 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x)))) -1/2)
(+.f64 (fma.f64 x (*.f64 x 1/24) (/.f64 1 (*.f64 x x))) (fma.f64 (pow.f64 x 4) -1/720 -1/2))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 -1/2)))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(fma.f64 -1/2 x (/.f64 1 x))
(fma.f64 x -1/2 (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 -1/2 x (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 x (*.f64 x 1/24) -1/2) (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 x -1/2 (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 -1/720 (pow.f64 x 5) (fma.f64 x (fma.f64 x (*.f64 x 1/24) -1/2) (/.f64 1 x)))
(fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 -1/720 (pow.f64 x 5) (/.f64 1 x))))

eval996.0ms (7.7%)

Compiler

Compiled 16757 to 9258 computations (44.8% saved)

prune449.0ms (3.5%)

Pruning

24 alts after pruning (14 fresh and 10 done)

PrunedKeptTotal
New8207827
Fresh3710
Picked011
Done2911
Total82524849
Error
0b
Counts
849 → 24
Alt Table
Click to see full alt table
StatusErrorProgram
✓33.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
44.9b
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
✓32.7b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
✓29.8b
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
15.5b
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
29.0b
1/2
32.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
33.2b
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
48.9b
0
33.5b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
✓33.2b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
14.3b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
✓0.5b
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
32.7b
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
✓32.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
✓45.8b
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
✓16.3b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
✓16.3b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
32.8b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
32.7b
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
15.7b
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
29.1b
(*.f64 x (/.f64 1/2 x))
✓33.2b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
45.8b
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
Compiler

Compiled 271 to 187 computations (31% saved)

regimes253.0ms (1.9%)

Counts
52 → 1
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(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)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) 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)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(/.f64 (-.f64 1 (log.f64 (exp.f64 (cos.f64 x)))) (*.f64 x x))
(/.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)))
(/.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 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x 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))))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))
Outputs
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
Calls

3 calls:

169.0ms
x
17.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
16.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.5b1x
0.5b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 548 to 309 computations (43.6% saved)

regimes153.0ms (1.2%)

Counts
36 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(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)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
Outputs
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)
Calls

3 calls:

87.0ms
x
24.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
23.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b3x
0.5b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 348 to 206 computations (40.8% saved)

bsearch88.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
44.0ms
0.004206908263075869
13613.647418394847
44.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes154.0ms (1.2%)

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

3 calls:

89.0ms
x
26.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
21.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b3x
0.5b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.5b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 337 to 201 computations (40.4% saved)

bsearch110.0ms (0.8%)

Algorithm
2×binary-search
Steps
TimeLeftRight
68.0ms
0.004206908263075869
13613.647418394847
41.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes411.0ms (3.2%)

Counts
34 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
Outputs
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
Calls

3 calls:

269.0ms
x
45.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
29.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 326 to 195 computations (40.2% saved)

bsearch222.0ms (1.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
42.0ms
0.004206908263075869
13613.647418394847
179.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes153.0ms (1.2%)

Counts
28 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2)) (*.f64 x x))
Outputs
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))
Calls

3 calls:

83.0ms
x
30.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
28.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 261 to 154 computations (41% saved)

bsearch120.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
43.0ms
0.004206908263075869
13613.647418394847
77.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes312.0ms (2.4%)

Counts
26 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (/.f64 (/.f64 1 x) (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
Outputs
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Calls

3 calls:

174.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
77.0ms
x
26.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 234 to 141 computations (39.7% saved)

bsearch95.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
48.0ms
0.004206908263075869
13613.647418394847
46.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes111.0ms (0.8%)

Counts
19 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
Outputs
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
Calls

3 calls:

59.0ms
x
22.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
21.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.3b3x
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 154 to 93 computations (39.6% saved)

bsearch86.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
41.0ms
0.004206908263075869
13613.647418394847
45.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes104.0ms (0.8%)

Counts
17 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

57.0ms
x
20.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
18.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.4b3x
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 134 to 82 computations (38.8% saved)

bsearch91.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
44.0ms
0.004206908263075869
13613.647418394847
47.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes24.0ms (0.2%)

Counts
15 → 1
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) -1/24) (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 1/2 x))
(fma.f64 -1/24 (*.f64 x x) 1/2)
Outputs
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
Calls

1 calls:

17.0ms
x
Results
ErrorSegmentsBranch
14.3b1x
Compiler

Compiled 100 to 62 computations (38% saved)

regimes28.0ms (0.2%)

Counts
11 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 (/.f64 1 x) (/.f64 x (*.f64 x (*.f64 1/2 x))))
(*.f64 (/.f64 (*.f64 x (*.f64 1/2 x)) x) (/.f64 1 x))
Outputs
0
(+.f64 (*.f64 (*.f64 x x) -1/24) 1/2)
0
Calls

1 calls:

24.0ms
x
Results
ErrorSegmentsBranch
16.0b3x
Compiler

Compiled 56 to 38 computations (32.1% saved)

bsearch46.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.004206908263075869
13613.647418394847
23.0ms
-977.7648518297204
-2.916185593453089e-7
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes18.0ms (0.1%)

Counts
7 → 3
Calls
Call 1
Inputs
1/2
1/2
0
1/2
1/2
(*.f64 x (/.f64 1/2 x))
(*.f64 (*.f64 1/2 x) (/.f64 1 x))
Outputs
0
1/2
0
Calls

1 calls:

13.0ms
x
Results
ErrorSegmentsBranch
16.0b3x
Compiler

Compiled 20 to 15 computations (25% saved)

bsearch172.0ms (1.3%)

Algorithm
2×binary-search
Steps
TimeLeftRight
43.0ms
7.094759442564294e+76
1.943739299060973e+80
129.0ms
-2.21145803279371e+81
-1.8499371439084775e+72
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes4.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
29.0b1x
Compiler

Compiled 5 to 4 computations (20% saved)

simplify117.0ms (0.9%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
073493
190493
297493
3102493
4104493
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 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))))
(if (<=.f64 x -8600510590539643/8796093022208) 0 (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) 0))
(if (<=.f64 x -2211458032793710004392549232526260092813034568107129702976144247826159473679925248) 0 (if (<=.f64 x 70947594425642941808021075578026866723060008370347527592575289155111826227200) 1/2 0))
1/2
Outputs
(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (/.f64 (/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 x 1/6) (*.f64 (/.f64 1 x) 2)))) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x)) (if (<=.f64 x 606279375551051/144115188075855872) (/.f64 (/.f64 1 x) (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 x 1/6) (*.f64 (/.f64 1 x) 2)))) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 1/2 (*.f64 (*.f64 x x) -1/24)) (*.f64 (/.f64 -1 x) (/.f64 1 (/.f64 (neg.f64 x) (-.f64 1 (cos.f64 x)))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x)) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 1/2 (*.f64 (*.f64 x x) -1/24)) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x)))) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 1/2 (*.f64 (*.f64 x x) -1/24)) (/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8600510590539643/8796093022208) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 1/2 (*.f64 (*.f64 x x) -1/24)) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(/.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/6) (*.f64 (/.f64 1 x) 2)))
(if (<=.f64 x -8600510590539643/8796093022208) 0 (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 (*.f64 (*.f64 x x) -1/24) 1/2) 0))
(if (<=.f64 x -8600510590539643/8796093022208) 0 (if (<=.f64 x 606279375551051/144115188075855872) (+.f64 1/2 (*.f64 (*.f64 x x) -1/24)) 0))
(if (<=.f64 x -2211458032793710004392549232526260092813034568107129702976144247826159473679925248) 0 (if (<=.f64 x 70947594425642941808021075578026866723060008370347527592575289155111826227200) 1/2 0))
1/2
Compiler

Compiled 344 to 243 computations (29.4% saved)

soundness296.0ms (2.3%)

Algorithm
2×egg-herbie
Rules
989×distribute-rgt-out_binary64
920×times-frac_binary64
877×distribute-lft-out_binary64
851×fma-def_binary64
696×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
068576
1158572
2393520
31256520
42457520
57247520
058520
1149518
2366516
31128514
43744514
57794514
Stop Event
1×node limit
1×node limit
Compiler

Compiled 313 to 240 computations (23.3% saved)

end193.0ms (1.5%)

Compiler

Compiled 333 to 220 computations (33.9% saved)

Profiling

Loading profile data...