Details

Time bar (total: 11.8s)

analyze80.0ms (0.7%)

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

Compiled 10 to 7 computations (30% saved)

sample3.9s (33.1%)

Results
2.1s2090×body2048valid
632.0ms3349×body256valid
540.0ms1115×body1024valid
462.0ms1579×body512valid
96.0ms123×body4096valid

preprocess69.0ms (0.6%)

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)

simplify118.0ms (1%)

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
33.3b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(cos.f64 x)
✓1.2b
(-.f64 1 (cos.f64 x))
✓18.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 20 to 9 computations (55% saved)

series10.0ms (0.1%)

Counts
3 → 20
Calls

9 calls:

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

rewrite82.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
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 exp.f64 (log.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 +.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 exp.f64 (log1p.f64 (neg.f64 (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 -.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 exp.f64 (log.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 x)))))))

simplify79.0ms (0.7%)

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)))

eval51.0ms (0.4%)

Compiler

Compiled 1358 to 795 computations (41.5% saved)

prune62.0ms (0.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New8517102
Fresh000
Picked011
Done000
Total8518103
Error
0.0b
Counts
103 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
▶19.7b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
32.3b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
33.3b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
▶32.7b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
▶18.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
29.5b
1/2
▶47.0b
(/.f64 (-.f64 1 1) (*.f64 x x))
33.3b
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
33.3b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
18.7b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
▶32.9b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
32.4b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
30.2b
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
33.4b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
33.4b
(/.f64 (/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x)))) (*.f64 x x))
30.4b
(fma.f64 -1/24 (*.f64 x x) 1/2)
32.4b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
✓33.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 417 to 286 computations (31.4% saved)

localize55.0ms (0.5%)

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))
✓0.3b
(+.f64 1 (cos.f64 x))
✓18.0b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 43 to 15 computations (65.1% saved)

series11.0ms (0.1%)

Counts
4 → 44
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
2.0ms
x
@inf
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
1.0ms
x
@0
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
1.0ms
x
@-inf
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
1.0ms
x
@inf
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))

rewrite208.0ms (1.8%)

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

simplify63.0ms (0.5%)

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)))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓17.7b
(/.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))

rewrite39.0ms (0.3%)

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)))))

simplify6.0ms (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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
✓0.2b
(/.f64 (-.f64 1 (cos.f64 x)) x)
✓0.5b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.2b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series5.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite171.0ms (1.5%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0936
119833
2274133
Stop Event
1×node limit
Counts
3 → 199
Calls
Call 1
Inputs
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 (-.f64 1 (cos.f64 x)) x)
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) 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x)) x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 2)) (cbrt.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))) (sqrt.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (/.f64 (neg.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))))))))

simplify76.0ms (0.6%)

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

Useful iterations: 3 (0.0ms)

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

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.1b
(*.f64 (cos.f64 x) (pow.f64 x -2))
✓19.8b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
Compiler

Compiled 24 to 14 computations (41.7% saved)

series17.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
11.0ms
x
@inf
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
2.0ms
x
@-inf
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
1.0ms
x
@0
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
1.0ms
x
@0
(*.f64 (cos.f64 x) (pow.f64 x -2))
1.0ms
x
@inf
(*.f64 (cos.f64 x) (pow.f64 x -2))

rewrite82.0ms (0.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0724
116021
2216221
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
(*.f64 (cos.f64 x) (pow.f64 x -2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 1 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4))) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) (fma.f64 (neg.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (/.f64 1 x))) (*.f64 (sqrt.f64 (cos.f64 x)) (/.f64 1 x)) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (+.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6))) (/.f64 1 (+.f64 (pow.f64 x -4) (+.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)) (*.f64 (pow.f64 x -4) (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4))) (/.f64 1 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) (*.f64 (sqrt.f64 (cos.f64 x)) (/.f64 1 x))) (-.f64 (/.f64 1 x) (*.f64 (sqrt.f64 (cos.f64 x)) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (cos.f64 x)) 1) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -4) (+.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)) (*.f64 (pow.f64 x -4) (cos.f64 x)))) (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))) (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6))) (+.f64 (pow.f64 x -4) (+.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)) (*.f64 (pow.f64 x -4) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4))) (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -6) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))) (neg.f64 (+.f64 (pow.f64 x -4) (+.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)) (*.f64 (pow.f64 x -4) (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -4) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))) (neg.f64 (*.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -6) (pow.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) 3)) (+.f64 (pow.f64 x -4) (-.f64 (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))) (*.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -4) (*.f64 (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))) (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -4)) (cbrt.f64 (pow.f64 x -2)) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 1 x) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x -2) (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (/.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x -6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))))

simplify101.0ms (0.9%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
036278
182276
2191274
3536272
41830272
54141272
Stop Event
1×node limit
Counts
75 → 70
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (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 1 (*.f64 x x)) (fma.f64 (*.f64 x 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 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 -1/2)) (/.f64 -1 (*.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 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
0.3b
(+.f64 1 (cos.f64 x))
✓0.6b
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
✓18.0b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
Compiler

Compiled 57 to 22 computations (61.4% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite68.0ms (0.6%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01140
125618
2393418
Stop Event
1×node limit
Counts
2 → 93
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) 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x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 -1 (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (tan.f64 (/.f64 x 2)))) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (sin.f64 x)) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 (sin.f64 x) 4))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (/.f64 -1 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))))

simplify99.0ms (0.8%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
045394
1101392
2241342
3754340
43326340
Stop Event
1×node limit
Counts
117 → 114
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 (cos.f64 x) 1) (pow.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

eval547.0ms (4.7%)

Compiler

Compiled 14333 to 8137 computations (43.2% saved)

prune208.0ms (1.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New77413787
Fresh11112
Picked101
Done415
Total79015805
Error
0b
Counts
805 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
19.9b
(/.f64 (/.f64 1 (/.f64 (-.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
▶30.4b
(fma.f64 x (*.f64 -1/24 x) 1/2)
32.9b
(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) 3) -1)
32.3b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓33.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
33.3b
(pow.f64 (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x)) -1)
33.3b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
▶18.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
▶32.7b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
▶33.3b
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
29.5b
1/2
32.3b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
19.0b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
▶32.9b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
46.4b
0
Compiler

Compiled 303 to 216 computations (28.7% saved)

localize36.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
✓18.0b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series8.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite92.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

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

simplify83.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 13 to 9 computations (30.8% saved)

series6.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(fma.f64 x (*.f64 -1/24 x) 1/2)
1.0ms
x
@-inf
(*.f64 -1/24 x)
1.0ms
x
@0
(*.f64 -1/24 x)
1.0ms
x
@inf
(*.f64 -1/24 x)
1.0ms
x
@0
(fma.f64 x (*.f64 -1/24 x) 1/2)

rewrite58.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

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

simplify172.0ms (1.5%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
08105
11587
22787
35187
411487
533787
6128287
7217987
8234387
9252787
10273587
11303487
12342587
13390487
14447287
15516287
16599787
17638987
18667987
19695787
20702987
21706387
Stop Event
1×node limit
Counts
44 → 37
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
✓0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
✓0.5b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
1.2b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series6.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite91.0ms (0.8%)

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

Useful iterations: 1 (0.0ms)

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

simplify65.0ms (0.5%)

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

Useful iterations: 3 (0.0ms)

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

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(-.f64 (+.f64 1 (cos.f64 x)) 1)
0.3b
(+.f64 1 (cos.f64 x))
✓1.2b
(-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1))
✓18.2b
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
Compiler

Compiled 38 to 23 computations (39.5% saved)

series107.0ms (0.9%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
105.0ms
x
@0
(-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1))
0.0ms
x
@0
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
0.0ms
x
@inf
(-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1))
0.0ms
x
@inf
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
0.0ms
x
@0
(-.f64 (+.f64 1 (cos.f64 x)) 1)

rewrite153.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
449×log-prod_binary64
425×prod-diff_binary64
311×fma-def_binary64
292×pow-prod-down_binary64
249×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0939
121521
2346221
Stop Event
1×node limit
Counts
3 → 194
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
(-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1))
(-.f64 (+.f64 1 (cos.f64 x)) 1)
Outputs
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x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (cos.f64 x) 2) (expm1.f64 (*.f64 2 (log1p.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 3 (log1p.f64 (cos.f64 x)))) (+.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (+.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 3 (log1p.f64 (cos.f64 x)))) (+.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (-.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 2 (log1p.f64 (cos.f64 x)))) (+.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 3 (log1p.f64 (cos.f64 x))))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (+.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 2 (log1p.f64 (cos.f64 x))))) (neg.f64 (+.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (cos.f64 x) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 (cos.f64 x) -1) 2) (+.f64 (cos.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (cos.f64 x) -1) 2)) (-.f64 1 (+.f64 (cos.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 x) 2) 1/2)))) (#(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 pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (+.f64 (cos.f64 x) 2)) (expm1.f64 (*.f64 3 (log1p.f64 (cos.f64 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (cos.f64 x) 2) (expm1.f64 (*.f64 2 (log1p.f64 (cos.f64 x))))) -1)))) (#(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 log.f64 (+.f64 1 (expm1.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 cos.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (cos.f64 x)) (hypot.f64 (cos.f64 x) (sqrt.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (hypot.f64 (cos.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (cos.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (cos.f64 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (cos.f64 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (cos.f64 x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 x) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (+.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (pow.f64 (cos.f64 x) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (cbrt.f64 (cos.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 3 (log1p.f64 (cos.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (+.f64 (cos.f64 x) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (cos.f64 x)))) (/.f64 1 (+.f64 (cos.f64 x) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 x) -1)) 2) (cbrt.f64 (+.f64 (cos.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (cos.f64 x) -1)) (sqrt.f64 (+.f64 (cos.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (cos.f64 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (cos.f64 x)) 1) (-.f64 (sqrt.f64 (cos.f64 x)) 1) 1)))))

simplify64.0ms (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
049342
1118338
2288334
3889330
43464330
56859330
Stop Event
1×node limit
Counts
230 → 219
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)
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)))
(-.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 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)))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.1b
(/.f64 (/.f64 (cos.f64 x) x) x)
✓0.1b
(/.f64 (cos.f64 x) x)
✓23.4b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Compiler

Compiled 28 to 10 computations (64.3% saved)

series3.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite113.0ms (1%)

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 (cos.f64 x) x)
(/.f64 (/.f64 (cos.f64 x) x) x)
Outputs
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simplify60.0ms (0.5%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
050331
1121325
2293323
3829321
43022321
56182321
Stop Event
1×node limit
Counts
308 → 306
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (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 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (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 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(fma.f64 -1/2 x (/.f64 1 x))
(fma.f64 x -1/2 (/.f64 1 x))
(+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 -1/2 x (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 5) (+.f64 (/.f64 1 x) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 x -1/2 (fma.f64 -1/720 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x -1/2 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 -1/720 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x (fma.f64 x (*.f64 x 1/24) -1/2) (fma.f64 -1/720 (pow.f64 x 5) (/.f64 1 x)))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(+.f64 (/.f64 1 (*.f64 x x)) -1/2)
(+.f64 -1/2 (/.f64 1 (*.f64 x x)))
(+.f64 -1/2 (/.f64 (/.f64 1 x) x))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(+.f64 (fma.f64 1/24 (*.f64 x x) (/.f64 1 (*.f64 x x))) -1/2)
(+.f64 -1/2 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 (*.f64 x x)) (fma.f64 x (*.f64 x 1/24) -1/2))
(+.f64 -1/2 (fma.f64 x (*.f64 x 1/24) (/.f64 (/.f64 1 x) x)))
(-.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 -1/2 (fma.f64 (pow.f64 x 4) -1/720 (fma.f64 (*.f64 x x) 1/24 (/.f64 1 (*.f64 x x)))))
(+.f64 -1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 (/.f64 1 (*.f64 x x)))))
(+.f64 -1/2 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 (/.f64 (/.f64 1 x) x))))
(/.f64 (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))

eval737.0ms (6.3%)

Compiler

Compiled 18951 to 10255 computations (45.9% saved)

prune502.0ms (4.3%)

Pruning

21 alts after pruning (16 fresh and 5 done)

PrunedKeptTotal
New88910899
Fresh369
Picked011
Done145
Total89321914
Error
0b
Counts
914 → 21
Alt Table
Click to see full alt table
StatusErrorProgram
19.1b
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))
32.7b
(/.f64 1 (/.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x)))
32.7b
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
▶32.7b
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
13.8b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
✓32.9b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
47.9b
(/.f64 1 (*.f64 x (/.f64 x (*.f64 x (*.f64 1/2 x)))))
✓33.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
▶33.3b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
✓18.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
33.4b
(/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3))
✓32.7b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
✓33.3b
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
29.5b
1/2
32.3b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
19.0b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
▶30.4b
(-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)
▶30.4b
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
▶12.6b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
32.3b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
46.4b
0
Compiler

Compiled 402 to 297 computations (26.1% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
✓0.1b
(*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
✓0.3b
(*.f64 1/6 x)
✓0.4b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
Compiler

Compiled 49 to 37 computations (24.5% saved)

series16.0ms (0.1%)

Counts
4 → 27
Calls

12 calls:

TimeVariablePointExpression
8.0ms
x
@-inf
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
1.0ms
x
@inf
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
1.0ms
x
@0
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
1.0ms
x
@inf
(*.f64 1/6 x)
1.0ms
x
@-inf
(*.f64 1/6 x)

rewrite96.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
568×log-prod_binary64
388×pow-prod-down_binary64
349×fma-def_binary64
291×pow2_binary64
205×pow1/3_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01137
124537
2330731
Stop Event
1×node limit
Counts
4 → 203
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(*.f64 1/6 x)
(*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 1 (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2))) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -1/2) (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x (*.f64 x 1/6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) 1) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) -2) (/.f64 (/.f64 1 x) (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) 2)) (/.f64 1 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) 2)) (/.f64 (pow.f64 x -1/2) (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 1/6 (/.f64 2 x)) -1/2) (/.f64 (/.f64 1 x) (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))) (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x 1/6 (/.f64 2 x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) 1/216 (pow.f64 (/.f64 2 x) 3))) (fma.f64 (*.f64 x x) 1/36 (fma.f64 4 (pow.f64 x -2) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (-.f64 (*.f64 (*.f64 x x) 1/36) (*.f64 4 (pow.f64 x -2)))) (-.f64 (*.f64 x 1/6) (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2)) -2) (/.f64 1 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x (*.f64 x 1/6) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/6) 2) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/6) 2)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 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(pow.f64 (exp.f64 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 2 x)) (+.f64 1 (expm1.f64 (*.f64 x 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 2 x))) (+.f64 1 (expm1.f64 (*.f64 x 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/6 (/.f64 2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/6 (/.f64 2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 x 1/6 (/.f64 2 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/6) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 2 x) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/6 (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/6 x (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/6) 1 (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (/.f64 1 x) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 2 (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 x) 1 (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 2 x)) (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (cbrt.f64 (/.f64 2 x)) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/6)) (cbrt.f64 (*.f64 (*.f64 x x) 1/36)) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/36)) (cbrt.f64 (*.f64 x 1/6)) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/6) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (cbrt.f64 (/.f64 1 x)) 2) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 2 x)) (sqrt.f64 (/.f64 2 x)) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/6)) (sqrt.f64 (*.f64 x 1/6)) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/6) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) 2) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (cbrt.f64 (pow.f64 x -2))) (cbrt.f64 (/.f64 1 x)) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (pow.f64 x -1/2)) (pow.f64 x -1/2) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 2 x))))))

simplify48.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
642×associate-*r/_binary64
607×associate-*l/_binary64
413×unswap-sqr_binary64
385×fma-neg_binary64
358×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047315
1112313
2263311
3710309
43013309
Stop Event
1×node limit
Counts
230 → 226
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 1/288 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/3456 (pow.f64 x 6)) (*.f64 1/288 (pow.f64 x 4)))))
(/.f64 6 (pow.f64 x 2))
(-.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 10368 (/.f64 1 (pow.f64 x 8))) (*.f64 72 (/.f64 1 (pow.f64 x 4)))))
(/.f64 6 (pow.f64 x 2))
(-.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 10368 (/.f64 1 (pow.f64 x 8))) (*.f64 72 (/.f64 1 (pow.f64 x 4)))))
2
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(*.f64 1/6 (pow.f64 x 2))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(/.f64 2 x)
(*.f64 1/6 x)
(*.f64 1/6 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 1/288 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/288 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/288 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/288 -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/3456 (pow.f64 x 6)) (*.f64 1/288 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/3456 (pow.f64 x 6) (*.f64 1/288 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/288 (pow.f64 x 4) (*.f64 -1/3456 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/3456 (pow.f64 x 6) (*.f64 1/288 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/288 (pow.f64 x 4) (fma.f64 -1/3456 (pow.f64 x 6) 1/2)))
(fma.f64 1/288 (pow.f64 x 4) (fma.f64 -1/3456 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(/.f64 6 (pow.f64 x 2))
(/.f64 6 (*.f64 x x))
(-.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 6 (*.f64 x x)) (/.f64 72 (pow.f64 x 4)))
(+.f64 (/.f64 6 (*.f64 x x)) (/.f64 -72 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 6 (*.f64 x x)) (-.f64 (/.f64 864 (pow.f64 x 6)) (/.f64 72 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 864 (pow.f64 x 6))) (/.f64 -72 (pow.f64 x 4)))
(-.f64 (/.f64 864 (pow.f64 x 6)) (-.f64 (/.f64 72 (pow.f64 x 4)) (/.f64 6 (*.f64 x x))))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (/.f64 -72 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 -72 (pow.f64 x 4))) (/.f64 864 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 10368 (/.f64 1 (pow.f64 x 8))) (*.f64 72 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 6 (*.f64 x x)) (-.f64 (/.f64 864 (pow.f64 x 6)) (+.f64 (/.f64 72 (pow.f64 x 4)) (/.f64 10368 (pow.f64 x 8)))))
(-.f64 (+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 864 (pow.f64 x 6))) (/.f64 -72 (pow.f64 x 4))) (/.f64 10368 (pow.f64 x 8)))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (-.f64 (/.f64 -72 (pow.f64 x 4)) (/.f64 10368 (pow.f64 x 8)))))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (+.f64 (/.f64 -72 (pow.f64 x 4)) (/.f64 -10368 (pow.f64 x 8)))))
(/.f64 6 (pow.f64 x 2))
(/.f64 6 (*.f64 x x))
(-.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 6 (*.f64 x x)) (/.f64 72 (pow.f64 x 4)))
(+.f64 (/.f64 6 (*.f64 x x)) (/.f64 -72 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (*.f64 72 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 6 (*.f64 x x)) (-.f64 (/.f64 864 (pow.f64 x 6)) (/.f64 72 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 864 (pow.f64 x 6))) (/.f64 -72 (pow.f64 x 4)))
(-.f64 (/.f64 864 (pow.f64 x 6)) (-.f64 (/.f64 72 (pow.f64 x 4)) (/.f64 6 (*.f64 x x))))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (/.f64 -72 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 -72 (pow.f64 x 4))) (/.f64 864 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 6 (/.f64 1 (pow.f64 x 2))) (*.f64 864 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 10368 (/.f64 1 (pow.f64 x 8))) (*.f64 72 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 6 (*.f64 x x)) (-.f64 (/.f64 864 (pow.f64 x 6)) (+.f64 (/.f64 72 (pow.f64 x 4)) (/.f64 10368 (pow.f64 x 8)))))
(-.f64 (+.f64 (+.f64 (/.f64 6 (*.f64 x x)) (/.f64 864 (pow.f64 x 6))) (/.f64 -72 (pow.f64 x 4))) (/.f64 10368 (pow.f64 x 8)))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (-.f64 (/.f64 -72 (pow.f64 x 4)) (/.f64 10368 (pow.f64 x 8)))))
(+.f64 (/.f64 6 (*.f64 x x)) (+.f64 (/.f64 864 (pow.f64 x 6)) (+.f64 (/.f64 -72 (pow.f64 x 4)) (/.f64 -10368 (pow.f64 x 8)))))
2
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 2)
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/6)
(*.f64 x (*.f64 x 1/6))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/6)
(*.f64 x (*.f64 x 1/6))
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(+.f64 2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) 1/6 2)
(fma.f64 x (*.f64 x 1/6) 2)
(/.f64 2 x)
(*.f64 1/6 x)
(*.f64 x 1/6)
(*.f64 1/6 x)
(*.f64 x 1/6)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (*.f64 -1/24 x))
0.3b
(*.f64 -1/24 x)
Compiler

Compiled 19 to 13 computations (31.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

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

simplify171.0ms (1.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533184
6125084
7212384
8228784
9247184
10267984
11297684
12337184
13385284
14441884
15510284
16593584
17632784
18661984
19689584
20696984
21700384
22794484
Stop Event
1×node limit
Counts
23 → 13
Calls
Call 1
Inputs
(*.f64 -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))

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiled 32 to 24 computations (25% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite83.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
913×pow1_binary64
858×add-log-exp_binary64
858×log1p-expm1-u_binary64
858×expm1-log1p-u_binary64
845×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0914
11988
225538
Stop Event
1×node limit
Counts
1 → 43
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x -1/24)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x -1/24)) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x -1/24) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) -1) (/.f64 1 (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) 1) (-.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2)) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) -1) (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) -1) (-.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) 2) -1)) (neg.f64 (+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2) (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2)) (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3) 1/8) (+.f64 (*.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x (*.f64 x -1/24))) (-.f64 1/4 (*.f64 (*.f64 x (*.f64 x -1/24)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2) (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2))) (-.f64 1 (+.f64 (*.f64 x (*.f64 x -1/24)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x (*.f64 x -1/24))) 1/4) (-.f64 (*.f64 x (*.f64 x -1/24)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x -1/24) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) 2) (cbrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2)) -1)))))

simplify186.0ms (1.6%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
08105
11587
22787
35187
411487
533787
6128287
7217987
8234387
9252787
10273587
11303487
12342587
13390487
14447287
15516287
16599787
17638987
18667987
19695787
20702987
21706387
Stop Event
1×node limit
Counts
55 → 48
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(*.f64 -1/24 (pow.f64 x 2))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (*.f64 x x))
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)

localize48.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (-.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)
✓0.5b
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
1.2b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 45 to 28 computations (37.8% saved)

series6.0ms (0%)

Counts
3 → 28
Calls

9 calls:

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

rewrite102.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
481×log-prod_binary64
371×prod-exp_binary64
365×exp-prod_binary64
291×pow-prod-down_binary64
247×pow2_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0933
119633
2259030
Stop Event
1×node limit
Counts
3 → 140
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)
(/.f64 1 (-.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (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 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) (sqrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 x (neg.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (/.f64 1 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 x (-.f64 1 (cos.f64 x)))) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) -2) (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (/.f64 x (-.f64 1 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simplify198.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
604×fma-def_binary64
570×times-frac_binary64
502×distribute-lft-out_binary64
492×unswap-sqr_binary64
417×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054329
1130325
2307323
3833321
42973321
55699321
Stop Event
1×node limit
Counts
168 → 164
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 1/3024 (pow.f64 x 5)))))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 2 x)
(+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))
(fma.f64 1/6 x (/.f64 2 x))
(fma.f64 x 1/6 (/.f64 2 x))
(+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 1/6 x (/.f64 2 x)))
(fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))
(fma.f64 x 1/6 (fma.f64 1/120 (pow.f64 x 3) (/.f64 2 x)))
(+.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))))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 x (-.f64 1 (cos.f64 x)))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (fma.f64 1/3024 (pow.f64 x 4) (/.f64 2 (*.f64 x x)))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) (fma.f64 (pow.f64 x 4) 1/3024 1/6)))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 x (*.f64 x 1/120) 1/6))

localize89.0ms (0.8%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
✓0.5b
(/.f64 (cos.f64 x) (*.f64 x x))
✓19.8b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
Compiler

Compiled 27 to 10 computations (63% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite303.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
649×prod-diff_binary64
433×log-prod_binary64
268×pow-prod-down_binary64
239×pow2_binary64
219×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
118424
2261824
Stop Event
1×node limit
Counts
2 → 210
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 (cos.f64 x) (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (*.f64 (cos.f64 x) (neg.f64 (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))) (fma.f64 (*.f64 (cos.f64 x) (neg.f64 (pow.f64 x -2))) 1 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4)) (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (cos.f64 x))) (+.f64 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(#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2)) (sqrt.f64 (cos.f64 x))))) (fma.f64 (neg.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2))) (sqrt.f64 (cos.f64 x)) (*.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2)) (sqrt.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 (pow.f64 x -4)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2)) (sqrt.f64 (cos.f64 x))))) (fma.f64 (neg.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2))) (sqrt.f64 (cos.f64 x)) (*.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2)) (sqrt.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -4)) (pow.f64 (cbrt.f64 x) -2) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2)) (sqrt.f64 (cos.f64 x))))) (fma.f64 (neg.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 x -2))) (sqrt.f64 (cos.f64 x)) (*.f64 (*.f64 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#<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (cos.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (/.f64 (cos.f64 x) x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -6) (pow.f64 (cos.f64 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) (cos.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 x)) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 (cos.f64 x) x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (cos.f64 x))))))))

simplify59.0ms (0.5%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
036278
182276
2191274
3536272
41830272
54141272
Stop Event
1×node limit
Counts
234 → 229
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) 1/2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2))) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 1/24 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 2)))) 1/2)
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (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 1 (*.f64 x x)) (fma.f64 (*.f64 x 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 (fma.f64 x (*.f64 x 1/24) (fma.f64 (pow.f64 x 4) -1/720 -1/2)) (/.f64 -1 (*.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 (cos.f64 x) (pow.f64 x 2))
(/.f64 (cos.f64 x) (*.f64 x x))

eval418.0ms (3.6%)

Compiler

Compiled 14531 to 9288 computations (36.1% saved)

prune202.0ms (1.7%)

Pruning

22 alts after pruning (14 fresh and 8 done)

PrunedKeptTotal
New7825787
Fresh2911
Picked011
Done279
Total78622808
Error
0b
Counts
808 → 22
Alt Table
Click to see full alt table
StatusErrorProgram
19.1b
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))
32.7b
(/.f64 1 (/.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x)))
32.7b
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
✓32.7b
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
45.2b
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
30.4b
(+.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)
✓33.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
✓33.3b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
✓18.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
33.4b
(/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3))
✓32.7b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
✓33.3b
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
29.5b
1/2
32.3b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
12.5b
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
19.0b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
45.1b
(/.f64 6 (*.f64 x x))
✓32.9b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
✓30.4b
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
32.2b
(/.f64 1 (*.f64 x (*.f64 (+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x)))) x)))
32.3b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
46.4b
0
Compiler

Compiled 227 to 165 computations (27.3% saved)

regimes144.0ms (1.2%)

Counts
46 → 3
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (/.f64 (-.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))) 3) -1)
(/.f64 (/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3))
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.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 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(pow.f64 (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x)) -1)
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(/.f64 1 (*.f64 x (*.f64 (+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x)))) x)))
(/.f64 1 (/.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x)))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(fma.f64 x (*.f64 -1/24 x) 1/2)
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 x (*.f64 1/2 x)))))
(+.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 6 (*.f64 x x))
1/2
0
1/2
Outputs
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2)
(*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))
Calls

3 calls:

96.0ms
x
15.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
13.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b3x
0.6b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.6b2(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 506 to 294 computations (41.9% saved)

bsearch58.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
34.0ms
2.479060632992062e-23
4.259081342341926e-23
24.0ms
-0.030539271847426327
-0.0006278002588575877
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes241.0ms (2.1%)

Counts
28 → 3
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(/.f64 1 (*.f64 x (*.f64 (+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x)))) x)))
(/.f64 1 (/.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x)))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(/.f64 (-.f64 1 (-.f64 (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
(-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(fma.f64 x (*.f64 -1/24 x) 1/2)
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 x (*.f64 1/2 x)))))
(+.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 6 (*.f64 x x))
1/2
0
1/2
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

206.0ms
x
14.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
12.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.7b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 273 to 175 computations (35.9% saved)

bsearch46.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
21.0ms
4.259081342341926e-23
3744111.346643993
25.0ms
-0.030539271847426327
-0.0006278002588575877
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes11.0ms (0.1%)

Counts
13 → 1
Calls
Call 1
Inputs
(fma.f64 x (*.f64 -1/24 x) 1/2)
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 1 (*.f64 x (/.f64 x (*.f64 x (*.f64 1/2 x)))))
(+.f64 (+.f64 (*.f64 x (*.f64 x -1/24)) 3/2) -1)
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 6 (*.f64 x x))
1/2
0
1/2
Outputs
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
Calls

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
12.5b1x
Compiler

Compiled 86 to 59 computations (31.4% saved)

regimes23.0ms (0.2%)

Counts
7 → 3
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
(/.f64 (-.f64 1 1) (*.f64 x x))
(/.f64 6 (*.f64 x x))
1/2
0
1/2
Outputs
(/.f64 6 (*.f64 x x))
(+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2)
(/.f64 1 (*.f64 x (*.f64 x 1/6)))
Calls

1 calls:

22.0ms
x
Results
ErrorSegmentsBranch
12.5b3x
Compiler

Compiled 32 to 22 computations (31.3% saved)

bsearch46.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
21.0ms
4.259081342341926e-23
3744111.346643993
25.0ms
-97919.52281259478
-0.030539271847426327
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes11.0ms (0.1%)

Accuracy

Total -47.9b remaining (-342.9%)

Threshold costs -47.9b (-342.9%)

Counts
3 → 3
Calls
Call 1
Inputs
1/2
0
1/2
Outputs
0
1/2
0
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
14.0b3x
Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch125.0ms (1.1%)

Algorithm
2×binary-search
Steps
TimeLeftRight
46.0ms
2.0905127883141194e+76
1.2417956958871213e+82
79.0ms
-7.14495020679171e+77
-2.8562813184289223e+76
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
058179
175179
279179
381179
482179
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -563350131966916544/18446744073709551616) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (if (<=.f64 x 8435806199350588/340282366920938463463374607431768211456) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))
(if (<=.f64 x -563350131966916544/18446744073709551616) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 14492902800809184/340282366920938463463374607431768211456) (-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
(if (<=.f64 x -841122296240041/8589934592) (/.f64 6 (*.f64 x x)) (if (<=.f64 x 14492902800809184/340282366920938463463374607431768211456) (+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2) (/.f64 1 (*.f64 x (*.f64 x 1/6)))))
(if (<=.f64 x -714495020679170962952210243872384574278329453264750510612868470944099444195328) 0 (if (<=.f64 x 20905127883141194237284662543316603017423104551690132447462289461176812175360) 1/2 0))
1/2
Outputs
(if (<=.f64 x -563350131966916544/18446744073709551616) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (if (<=.f64 x 8435806199350588/340282366920938463463374607431768211456) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))
(if (<=.f64 x -8802345811983071/288230376151711744) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2))) (if (<=.f64 x 2108951549837647/85070591730234615865843651857942052864) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) 1/2) (*.f64 (sin.f64 x) (*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 x -2)))))
(if (<=.f64 x -563350131966916544/18446744073709551616) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 14492902800809184/340282366920938463463374607431768211456) (-.f64 (+.f64 1 (fma.f64 x (*.f64 -1/24 x) 1/2)) 1) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -8802345811983071/288230376151711744) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 452903212525287/10633823966279326983230456482242756608) (+.f64 (+.f64 1 (fma.f64 x (*.f64 x -1/24) 1/2)) -1) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 1 (+.f64 (*.f64 1/6 (*.f64 x x)) 2))
(/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/6) 2))
(if (<=.f64 x -841122296240041/8589934592) (/.f64 6 (*.f64 x x)) (if (<=.f64 x 14492902800809184/340282366920938463463374607431768211456) (+.f64 (*.f64 x (*.f64 -1/24 x)) 1/2) (/.f64 1 (*.f64 x (*.f64 x 1/6)))))
(if (<=.f64 x -841122296240041/8589934592) (/.f64 6 (*.f64 x x)) (if (<=.f64 x 452903212525287/10633823966279326983230456482242756608) (+.f64 1/2 (*.f64 x (*.f64 x -1/24))) (/.f64 1 (*.f64 x (*.f64 x 1/6)))))
(if (<=.f64 x -714495020679170962952210243872384574278329453264750510612868470944099444195328) 0 (if (<=.f64 x 20905127883141194237284662543316603017423104551690132447462289461176812175360) 1/2 0))
1/2
Compiler

Compiled 129 to 92 computations (28.7% saved)

soundness102.0ms (0.9%)

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
Compiler

Compiled 170 to 140 computations (17.6% saved)

end77.0ms (0.7%)

Compiler

Compiled 124 to 85 computations (31.5% saved)

Profiling

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