Details

Time bar (total: 9.5s)

analyze116.0ms (1.2%)

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

Compiled 10 to 7 computations (30% saved)

sample3.3s (34.5%)

Results
1.8s2025×body2048valid
607.0ms3450×body256valid
421.0ms1102×body1024valid
379.0ms1563×body512valid
81.0ms116×body4096valid

preprocess53.0ms (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)

simplify42.0ms (0.4%)

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
35.7b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.7b
(-.f64 1 (cos.f64 x))
✓17.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite77.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
115218
2213518
Stop Event
1×node limit
Counts
2 → 62
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(-.f64 1 (cos.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (neg.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))))

simplify54.0ms (0.6%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
037218
191216
2217214
3656212
42571212
55901212
Stop Event
1×node limit
Counts
78 → 79
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(fma.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 6)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))))

eval24.0ms (0.3%)

Compiler

Compiled 1062 to 636 computations (40.1% saved)

prune32.0ms (0.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New601979
Fresh000
Picked011
Done000
Total602080
Error
0.0b
Counts
80 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
35.7b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
▶35.2b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
35.6b
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
✓35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
47.9b
(-.f64 (+.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1)
27.7b
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
35.0b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
▶28.0b
(fma.f64 -1/24 (*.f64 x x) 1/2)
▶17.9b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
35.7b
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))
27.1b
1/2
35.7b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
34.6b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
35.7b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
▶34.6b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
▶35.8b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
28.0b
(+.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)))))
27.7b
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
35.1b
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
35.7b
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
Compiler

Compiled 455 to 344 computations (24.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.5b
(+.f64 1 (cos.f64 x))
✓17.2b
(/.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)

series8.0ms (0.1%)

Counts
4 → 44
Calls

12 calls:

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

rewrite86.0ms (0.9%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122830
2354030
Stop Event
1×node limit
Counts
4 → 182
Calls
Call 1
Inputs
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(+.f64 1 (cos.f64 x))
(*.f64 (sin.f64 x) (sin.f64 x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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(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 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((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1) (+.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) (#(struct:change 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1/2 (cos.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 (cos.f64 (+.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 (+.f64 x x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (cos.f64 x) 2) 3)) (+.f64 1 (+.f64 (pow.f64 (pow.f64 (cos.f64 x) 2) 2) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 3)) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 2) (*.f64 1/2 (*.f64 (cos.f64 (+.f64 x x)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (cos.f64 x) 2) 2)) (+.f64 1 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) 2)) (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2))) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (/.f64 1 (/.f64 1 (tan.f64 (/.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (/.f64 1 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 (neg.f64 (cos.f64 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) 1) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) 1) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (neg.f64 (cos.f64 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))))

simplify74.0ms (0.8%)

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)))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 13 to 7 computations (46.2% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite52.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

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

simplify162.0ms (1.7%)

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

Useful iterations: 1 (0.0ms)

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

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))
✓0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
✓0.6b
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
1.7b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series9.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite109.0ms (1.1%)

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

Useful iterations: 1 (0.0ms)

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

simplify100.0ms (1%)

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))

localize118.0ms (1.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (-.f64 1 (cos.f64 x)))
✓0.1b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
✓0.1b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
1.7b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 31 to 19 computations (38.7% saved)

series8.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@0
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
1.0ms
x
@-inf
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
1.0ms
x
@inf
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
1.0ms
x
@0
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
1.0ms
x
@0
(sqrt.f64 (-.f64 1 (cos.f64 x)))

rewrite73.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
913×pow1_binary64
851×add-log-exp_binary64
850×log1p-expm1-u_binary64
850×expm1-log1p-u_binary64
832×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0933
119231
2233331
Stop Event
1×node limit
Counts
3 → 90
Calls
Call 1
Inputs
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(sqrt.f64 (-.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (/.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (*.f64 (cbrt.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 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 x (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 1 (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (*.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))))) (*.f64 (neg.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) 1) (*.f64 (neg.f64 x) (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (sqrt.f64 (-.f64 1 (cos.f64 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.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 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) 1) (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) (pow.f64 (-.f64 1 (cos.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (sqrt.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1/2))))))

simplify140.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
792×times-frac_binary64
706×associate-/l*_binary64
591×associate-/r*_binary64
356×associate-*l/_binary64
244×associate-/r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
078667
1218572
2635418
32732418
Stop Event
1×node limit
Counts
118 → 114
Calls
Call 1
Inputs
(pow.f64 (sqrt.f64 1/2) 2)
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (pow.f64 (sqrt.f64 1/2) 2))
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2304 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 2))) 1/720) (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (pow.f64 (sqrt.f64 1/2) 2)))
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2304 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 2))) 1/720) (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (+.f64 (*.f64 (+.f64 (*.f64 -1 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2))))) (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6)) (pow.f64 (sqrt.f64 1/2) 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 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (sqrt.f64 1/2))) (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (sqrt.f64 1/2))) (+.f64 (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2))) (*.f64 -1/2 (/.f64 (*.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6)) (sqrt.f64 1/2))))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 5)) (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 7)) (sqrt.f64 1/2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 5)) (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
Outputs
(pow.f64 (sqrt.f64 1/2) 2)
1/2
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (pow.f64 (sqrt.f64 1/2) 2))
(fma.f64 -1/24 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 2))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2304 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 2))) 1/720) (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (pow.f64 (sqrt.f64 1/2) 2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 (+.f64 (/.f64 1/2304 (pow.f64 (sqrt.f64 1/2) 2)) (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2))) (pow.f64 x 4) (pow.f64 (sqrt.f64 1/2) 2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 (-.f64 13/5760 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4) 1/2))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2304 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 2))) 1/720) (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (+.f64 (*.f64 (+.f64 (*.f64 -1 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2))))) (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6)) (pow.f64 (sqrt.f64 1/2) 2))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 (+.f64 (/.f64 1/2304 (pow.f64 (sqrt.f64 1/2) 2)) (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2))) (pow.f64 x 4) (fma.f64 (fma.f64 -1 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6) (pow.f64 (sqrt.f64 1/2) 2))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 (-.f64 13/5760 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4) (fma.f64 (-.f64 (*.f64 -1/48 (-.f64 1/360 (/.f64 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2) 1/2))) (fma.f64 -1/48 (-.f64 1/360 (/.f64 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2) 1/2)) 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 (pow.f64 x 6) -1/40320 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))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (*.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2))))
(fma.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 -1/48 (*.f64 (/.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (sqrt.f64 1/2))) (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 4))) (*.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (*.f64 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 x 4)) (*.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)) (*.f64 (/.f64 1/3840 (sqrt.f64 1/2)) (pow.f64 x 4))))
(+.f64 (fma.f64 -1/48 (*.f64 (/.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2)) (/.f64 (pow.f64 x 4) (/.f64 (sqrt.f64 1/2) 1/3840)))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 4)) (sqrt.f64 1/2))) (+.f64 (*.f64 -1/48 (/.f64 (pow.f64 x 2) (sqrt.f64 1/2))) (*.f64 -1/2 (/.f64 (*.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6)) (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 4))) (fma.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)) (/.f64 (*.f64 -1/2 (*.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 6))) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (*.f64 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 x 4)) (fma.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)) (*.f64 -1/2 (/.f64 (fma.f64 -1/48 (-.f64 1/360 (/.f64 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2) 1/2)) 1/40320) (/.f64 (sqrt.f64 1/2) (pow.f64 x 6)))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (/.f64 1/3840 (sqrt.f64 1/2)) (pow.f64 x 4)) (fma.f64 -1/48 (/.f64 (*.f64 x x) (sqrt.f64 1/2)) (*.f64 (/.f64 -1/645120 (sqrt.f64 1/2)) (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/48 (*.f64 (/.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2)) (+.f64 (/.f64 (pow.f64 x 4) (/.f64 (sqrt.f64 1/2) 1/3840)) (/.f64 (pow.f64 x 6) (/.f64 (sqrt.f64 1/2) -1/645120))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))
(fma.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 5)) (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 5))) (fma.f64 (sqrt.f64 1/2) x (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))
(fma.f64 1/2 (*.f64 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 x 5)) (fma.f64 (sqrt.f64 1/2) x (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))
(fma.f64 (sqrt.f64 1/2) x (fma.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)) (*.f64 (/.f64 1/3840 (sqrt.f64 1/2)) (pow.f64 x 5))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (pow.f64 x 7)) (sqrt.f64 1/2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 x 5)) (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
(fma.f64 -1/2 (/.f64 (+.f64 1/40320 (*.f64 -1/48 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 7))) (fma.f64 1/2 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 5))) (fma.f64 (sqrt.f64 1/2) x (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
(fma.f64 -1/2 (/.f64 (fma.f64 -1/48 (-.f64 1/360 (/.f64 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2) 1/2)) 1/40320) (/.f64 (sqrt.f64 1/2) (pow.f64 x 7))) (fma.f64 1/2 (*.f64 (/.f64 (-.f64 1/720 (pow.f64 (/.f64 -1/48 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 x 5)) (fma.f64 (sqrt.f64 1/2) x (*.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
(+.f64 (fma.f64 (sqrt.f64 1/2) x (fma.f64 -1/48 (/.f64 (pow.f64 x 3) (sqrt.f64 1/2)) (*.f64 (/.f64 1/3840 (sqrt.f64 1/2)) (pow.f64 x 5)))) (*.f64 (/.f64 -1/645120 (sqrt.f64 1/2)) (pow.f64 x 7)))

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(cbrt.f64 (-.f64 1 (cos.f64 x)))
✓0.4b
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
1.7b
(-.f64 1 (cos.f64 x))
✓17.2b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
Compiler

Compiled 36 to 21 computations (41.7% saved)

series11.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
2.0ms
x
@-inf
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
1.0ms
x
@0
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
1.0ms
x
@-inf
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
1.0ms
x
@0
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))

rewrite77.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
121726
2255126
Stop Event
1×node limit
Counts
3 → 162
Calls
Call 1
Inputs
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(cbrt.f64 (-.f64 1 (cos.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (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))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 4)) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.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 (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 (cbrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 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)))))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/6) (pow.f64 (-.f64 1 (cos.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))) 2)) (cbrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))) (sqrt.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1) 1))))))

simplify62.0ms (0.6%)

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

Useful iterations: 3 (0.0ms)

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

eval575.0ms (6%)

Compiler

Compiled 14717 to 8676 computations (41% saved)

prune254.0ms (2.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New84915864
Fresh14014
Picked101
Done415
Total86816884
Error
0b
Counts
884 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
35.7b
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
▶47.9b
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
35.2b
(pow.f64 (/.f64 x (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x))) -1)
27.1b
1/2
18.3b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
18.8b
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
28.1b
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
34.6b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
35.2b
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
▶35.2b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
✓35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
34.9b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
▶28.0b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
▶17.7b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
34.6b
(/.f64 (/.f64 1 x) (/.f64 x (-.f64 1 (cos.f64 x))))
▶35.7b
(/.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1) (*.f64 x x))
Compiler

Compiled 375 to 266 computations (29.1% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
✓17.2b
(/.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
5.0ms
x
@-inf
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
1.0ms
x
@inf
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
1.0ms
x
@0
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
0.0ms
x
@inf
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))
0.0ms
x
@-inf
(*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))

rewrite68.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

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

simplify67.0ms (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))))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

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

simplify177.0ms (1.9%)

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

Useful iterations: 0 (0.0ms)

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

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 x (/.f64 x (-.f64 1 (cos.f64 x))))
✓0.1b
(/.f64 x (-.f64 1 (cos.f64 x)))
✓0.6b
(/.f64 1 (*.f64 x (/.f64 x (-.f64 1 (cos.f64 x)))))
1.7b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 33 to 18 computations (45.5% saved)

series5.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite80.0ms (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 log1p.f64 (expm1.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (/.f64 x (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (-.f64 1 (cos.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (-.f64 1 (cos.f64 x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 2) (cbrt.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 x x)) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x x)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) x) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (neg.f64 x)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) 1) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 x (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 x (-.f64 1 (cos.f64 x))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x)))))))))

simplify81.0ms (0.9%)

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))))

localize30.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓1.5b
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
1.7b
(-.f64 1 (cos.f64 x))
17.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 42 to 21 computations (50% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite114.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
729×prod-diff_binary64
462×log-prod_binary64
460×fma-def_binary64
259×pow2_binary64
253×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0918
121312
2329012
Stop Event
1×node limit
Counts
1 → 152
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
Outputs
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(fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) 2) (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) 2) (*.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1)) 1) -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))) (pow.f64 x -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) (*.f64 (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 1) -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))) (pow.f64 x -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1) 2) (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3)) (/.f64 1 (fma.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 1) 2) -1) (/.f64 1 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 2)) (/.f64 1 (-.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1)) 2) (cbrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1)) (sqrt.f64 (fma.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 1) (-.f64 (hypot.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 1) (-.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 1) 1)))))

simplify64.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
025148
158146
2130144
3356142
41285142
53563142
66488142
Stop Event
1×node limit
Counts
164 → 160
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (-.f64 1 (cos.f64 x)))
✓0.1b
(pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)
1.7b
(-.f64 1 (cos.f64 x))
✓17.2b
(/.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1) (*.f64 x x))
Compiler

Compiled 39 to 24 computations (38.5% saved)

series7.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite101.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
993×pow1_binary64
929×add-log-exp_binary64
927×log1p-expm1-u_binary64
927×expm1-log1p-u_binary64
107×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01039
121627
2284027
Stop Event
1×node limit
Counts
3 → 97
Calls
Call 1
Inputs
(/.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1) (*.f64 x x))
(pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)
(/.f64 1 (-.f64 1 (cos.f64 x)))
Outputs
((#(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 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (/.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 (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 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.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 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 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 (cbrt.f64 (pow.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 log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.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 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (/.f64 (cos.f64 x) 1))))) (#(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 (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) 3) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.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 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))))) (#(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 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) -1) (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) -1) (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (-.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 -1 (neg.f64 (/.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 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2))))) (#(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) (+.f64 1 (cos.f64 x))))))))) (#(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 /.f64 (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2))) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) -1) (pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))))))

simplify70.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
050324
1120322
2289320
3829318
43058318
56687318
Stop Event
1×node limit
Counts
125 → 122
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (*.f64 1/720 (pow.f64 x 4)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 1/2 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 x (*.f64 1/2 x))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(*.f64 x (*.f64 x (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 1/720 (pow.f64 x 4) 1/2))))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (/.f64 2 (*.f64 x x)) (fma.f64 x (*.f64 x 1/120) 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (/.f64 2 (*.f64 x x))))
(+.f64 (*.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (*.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(fma.f64 1/120 (*.f64 x x) (+.f64 1/6 (fma.f64 1/3024 (pow.f64 x 4) (/.f64 2 (*.f64 x x)))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 (*.f64 x x) 1/120 1/6))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x))) (fma.f64 x (*.f64 x 1/120) 1/6))
(+.f64 1/6 (fma.f64 x (*.f64 x 1/120) (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (*.f64 x x)))))

eval291.0ms (3.1%)

Compiler

Compiled 11589 to 7380 computations (36.3% saved)

prune109.0ms (1.1%)

Pruning

19 alts after pruning (16 fresh and 3 done)

PrunedKeptTotal
New65612668
Fresh6410
Picked101
Done235
Total66519684
Error
0b
Counts
684 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
▶35.2b
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
▶13.3b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
35.7b
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
✓47.9b
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
12.2b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
35.7b
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
✓35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
44.7b
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
34.9b
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
✓28.0b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
▶28.0b
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
17.8b
(pow.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) -1)
27.1b
1/2
18.3b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
35.2b
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
▶34.6b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
▶0.1b
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
35.1b
(*.f64 (/.f64 (/.f64 1 x) x) (-.f64 1 (cos.f64 x)))
35.7b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
Compiler

Compiled 422 to 310 computations (26.5% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 33 to 18 computations (45.5% saved)

series5.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
1.0ms
x
@-inf
(/.f64 (sin.f64 x) x)
1.0ms
x
@inf
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
1.0ms
x
@0
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
0.0ms
x
@0
(/.f64 (sin.f64 x) x)

rewrite73.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
541×log-prod_binary64
406×exp-prod_binary64
353×pow-prod-down_binary64
263×pow2_binary64
199×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0932
119732
2275232
Stop Event
1×node limit
Counts
3 → 155
Calls
Call 1
Inputs
(/.f64 (tan.f64 (*.f64 x 1/2)) x)
(/.f64 (sin.f64 x) x)
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 2) (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (tan.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (tan.f64 (*.f64 x 1/2)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))) (sqrt.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))) (#(struct:change #<rule 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2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (pow.f64 x -2))) 1) 1))))))

simplify65.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
055492
1128486
2307480
3896474
43356474
56502474
Stop Event
1×node limit
Counts
183 → 179
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
1
(+.f64 1 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
Outputs
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 1/24 (*.f64 x x)))
(fma.f64 1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 (fma.f64 1/24 (*.f64 x x) 1/2) (*.f64 1/240 (pow.f64 x 4)))
(fma.f64 1/24 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (fma.f64 17/40320 (pow.f64 x 6) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 (fma.f64 1/24 (*.f64 x x) 1/2) (fma.f64 17/40320 (pow.f64 x 6) (*.f64 1/240 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) (*.f64 17/40320 (pow.f64 x 6)))))
(fma.f64 1/24 (*.f64 x x) (fma.f64 1/240 (pow.f64 x 4) (fma.f64 17/40320 (pow.f64 x 6) 1/2)))
(fma.f64 1/240 (pow.f64 x 4) (fma.f64 17/40320 (pow.f64 x 6) (fma.f64 1/24 (*.f64 x x) 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x))))
1
(+.f64 1 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -1/6))
(fma.f64 (*.f64 x x) -1/6 1)
(fma.f64 x (*.f64 x -1/6) 1)
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/120)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/6 (*.f64 (pow.f64 x 4) 1/120)))
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 1))
(fma.f64 (pow.f64 x 4) 1/120 (fma.f64 x (*.f64 x -1/6) 1))
(+.f64 1 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (*.f64 -1/5040 (pow.f64 x 6)) (*.f64 1/120 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/6 (*.f64 x x) (fma.f64 -1/5040 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/120))))
(+.f64 (fma.f64 (*.f64 x x) -1/6 1) (fma.f64 (pow.f64 x 4) 1/120 (*.f64 (pow.f64 x 6) -1/5040)))
(+.f64 1 (fma.f64 (pow.f64 x 6) -1/5040 (fma.f64 x (*.f64 x -1/6) (*.f64 (pow.f64 x 4) 1/120))))
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) 1/120 (fma.f64 (pow.f64 x 6) -1/5040 1)))
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/24))
(fma.f64 (*.f64 x x) -1/24 1/2)
(fma.f64 x (*.f64 x -1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/720)))
(+.f64 1/2 (fma.f64 (*.f64 x x) -1/24 (*.f64 (pow.f64 x 4) 1/720)))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 1/2))
(fma.f64 (pow.f64 x 4) 1/720 (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/720))))
(+.f64 (fma.f64 (*.f64 x x) -1/24 1/2) (fma.f64 (pow.f64 x 4) 1/720 (*.f64 (pow.f64 x 6) -1/40320)))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 (*.f64 (pow.f64 x 6) -1/40320))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 (fma.f64 (pow.f64 x 6) -1/40320 1/2)))
(fma.f64 (pow.f64 x 4) 1/720 (fma.f64 (pow.f64 x 6) -1/40320 (fma.f64 x (*.f64 x -1/24) 1/2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (cos.f64 (*.f64 1/2 x)))) (/.f64 (sin.f64 x) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (*.f64 x x)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x)))) (*.f64 x x))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.4b
(*.f64 -1/24 (*.f64 x x))
✓1.5b
(-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1)
Compiler

Compiled 40 to 25 computations (37.5% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite58.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
816×pow1_binary64
769×add-log-exp_binary64
768×log1p-expm1-u_binary64
768×expm1-log1p-u_binary64
756×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
11787
223997
Stop Event
1×node limit
Counts
1 → 46
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 -1/24 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 -1/24 (*.f64 x x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/24 (*.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/24 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 -1/24 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/24 (*.f64 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 -1/24 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/24 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 -1/24 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) -1/24)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/24 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (pow.f64 (cbrt.f64 x) 2) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 -1/24 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/576)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/576)) (cbrt.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 -1/24)) (*.f64 x (sqrt.f64 -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) (+.f64 (*.f64 -1/24 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (*.f64 -1/24 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/24 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/24))) 1) (-.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/24))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/24 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 -1/24 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 -1/24 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) (+.f64 (*.f64 -1/24 (*.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 -1/24 (*.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) (+.f64 (*.f64 -1/24 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) (-.f64 1 (*.f64 (fma.f64 -1/24 (*.f64 x x) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) -1) (+.f64 (*.f64 -1/24 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) -1) (-.f64 (fma.f64 -1/24 (*.f64 x x) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) (+.f64 (*.f64 -1/24 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (*.f64 -1/24 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 -1/24 (*.f64 x x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 -1/24 (*.f64 x x) -1) (fma.f64 -1/24 (*.f64 x x) -1)) (fma.f64 -1/24 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 -1/24 (*.f64 x x) -1) (fma.f64 -1/24 (*.f64 x x) -1))) (-.f64 1 (fma.f64 -1/24 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/13824) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/13824))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -1/24 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/24 (*.f64 x x) 1) 2)) (cbrt.f64 (fma.f64 -1/24 (*.f64 x x) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/24))) (hypot.f64 1 (*.f64 x (sqrt.f64 -1/24))) -1)))))

simplify172.0ms (1.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533184
6125084
7212384
8228784
9247184
10267984
11297684
12337184
13385284
14441884
15510284
16593584
17632784
18661984
19689584
20696984
21700384
22794484
Stop Event
1×node limit
Counts
58 → 47
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))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
0.1b
(/.f64 (-.f64 1 (cos.f64 x)) x)
1.7b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 23 to 12 computations (47.8% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite51.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

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

simplify63.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
025148
158146
2130144
3356142
41285142
53563142
66488142
Stop Event
1×node limit
Counts
52 → 49
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 1 x) (/.f64 1 x))
1.7b
(-.f64 1 (cos.f64 x))
✓17.8b
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
Compiler

Compiled 31 to 20 computations (35.5% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite114.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
877×pow1_binary64
818×add-log-exp_binary64
817×log1p-expm1-u_binary64
817×expm1-log1p-u_binary64
800×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0822
117416
2232816
Stop Event
1×node limit
Counts
2 → 61
Calls
Call 1
Inputs
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 (/.f64 1 x) (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -2) (*.f64 (pow.f64 x -2) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 x x) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (*.f64 (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 x)) (*.f64 (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 x)) (*.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (-.f64 1 (pow.f64 (cos.f64 x) 3))) (*.f64 x (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 x (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (pow.f64 x -2)) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 x -2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 x (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x -1/2) (/.f64 x (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 1 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 1 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 1 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (/.f64 1 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 1 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -2)))))))

simplify153.0ms (1.6%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
026232
158230
2130228
3356226
41285226
53562226
66490226
Stop Event
1×node limit
Counts
85 → 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 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))

localize138.0ms (1.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
✓0.3b
(*.f64 1/120 (pow.f64 x 3))
✓0.4b
(*.f64 1/6 x)
✓0.4b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
Compiler

Compiled 86 to 67 computations (22.1% saved)

series133.0ms (1.4%)

Counts
4 → 24
Calls

12 calls:

TimeVariablePointExpression
125.0ms
x
@inf
(*.f64 1/6 x)
1.0ms
x
@inf
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
1.0ms
x
@0
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
1.0ms
x
@-inf
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
1.0ms
x
@0
(*.f64 1/120 (pow.f64 x 3))

rewrite161.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
797×log-prod_binary64
691×fma-def_binary64
366×fma-neg_binary64
290×expm1-udef_binary64
290×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01650
136650
2485450
Stop Event
1×node limit
Counts
4 → 145
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 1/6 x)
(*.f64 1/120 (pow.f64 x 3))
(*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 x -1) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x 1/6 (/.f64 2 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 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x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) 2)) (cbrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) (*.f64 (*.f64 x 1/120) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x)))) (sqrt.f64 (fma.f64 x 1/6 (/.f64 2 x))) (*.f64 (*.f64 x 1/120) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 x 1/6 (/.f64 2 x)) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 (*.f64 x 1/120) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 x 1/6 (/.f64 2 x)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (*.f64 x 1/120) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (*.f64 x (cbrt.f64 1/120)) 2)) (*.f64 x (cbrt.f64 1/120)) (*.f64 x (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 (sqrt.f64 1/120) (pow.f64 x 3/2))) (*.f64 (sqrt.f64 1/120) (pow.f64 x 3/2)) (*.f64 x (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/120 (pow.f64 x 3)) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 x (fma.f64 x 1/6 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/120 (pow.f64 x 3)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x (fma.f64 x 1/6 (/.f64 2 x))))))))

simplify61.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
649×fma-neg_binary64
469×associate-*r/_binary64
458×associate-*l/_binary64
446×unswap-sqr_binary64
356×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
052369
1126355
2279353
3750351
43036351
57344351
Stop Event
1×node limit
Counts
169 → 168
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 1/17280 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(/.f64 120 (pow.f64 x 4))
(-.f64 (*.f64 120 (/.f64 1 (pow.f64 x 4))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4)))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (+.f64 (*.f64 192000 (/.f64 1 (pow.f64 x 10))) (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4))))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(/.f64 120 (pow.f64 x 4))
(-.f64 (*.f64 120 (/.f64 1 (pow.f64 x 4))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4)))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (+.f64 (*.f64 192000 (/.f64 1 (pow.f64 x 10))) (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4))))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
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 1/120 (pow.f64 x 4))))
(*.f64 1/120 (pow.f64 x 4))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4)))
(+.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 1/120 (pow.f64 x 4))))
(*.f64 1/120 (pow.f64 x 4))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4)))
(+.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 1/120 (pow.f64 x 4))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.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 1/17280 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/17280 (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 1/17280 (pow.f64 x 6)))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 1/17280 (pow.f64 x 6) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/720 -1/24) (fma.f64 1/17280 (pow.f64 x 6) 1/2))
(/.f64 120 (pow.f64 x 4))
(-.f64 (*.f64 120 (/.f64 1 (pow.f64 x 4))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 -2400 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4)))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6))))
(+.f64 (/.f64 120 (pow.f64 x 4)) (-.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 2400 (pow.f64 x 6))))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 -2400 (pow.f64 x 6))))
(-.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 120 (pow.f64 x 4))))
(-.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 -19200 (pow.f64 x 8))))
(-.f64 (+.f64 (*.f64 192000 (/.f64 1 (pow.f64 x 10))) (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4))))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 192000 (pow.f64 x 10)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6)))))
(+.f64 (+.f64 (/.f64 120 (pow.f64 x 4)) (-.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 2400 (pow.f64 x 6)))) (/.f64 192000 (pow.f64 x 10)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (+.f64 (/.f64 192000 (pow.f64 x 10)) (/.f64 -2400 (pow.f64 x 6)))))
(+.f64 (-.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 120 (pow.f64 x 4)))) (/.f64 192000 (pow.f64 x 10)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 -2400 (pow.f64 x 6)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 192000 (pow.f64 x 10)))))
(/.f64 120 (pow.f64 x 4))
(-.f64 (*.f64 120 (/.f64 1 (pow.f64 x 4))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 -2400 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4)))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6))))
(+.f64 (/.f64 120 (pow.f64 x 4)) (-.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 2400 (pow.f64 x 6))))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 -2400 (pow.f64 x 6))))
(-.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 120 (pow.f64 x 4))))
(-.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 -19200 (pow.f64 x 8))))
(-.f64 (+.f64 (*.f64 192000 (/.f64 1 (pow.f64 x 10))) (+.f64 (*.f64 19200 (/.f64 1 (pow.f64 x 8))) (*.f64 120 (/.f64 1 (pow.f64 x 4))))) (*.f64 2400 (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 192000 (pow.f64 x 10)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 120 (pow.f64 x 4)) (/.f64 2400 (pow.f64 x 6)))))
(+.f64 (+.f64 (/.f64 120 (pow.f64 x 4)) (-.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 2400 (pow.f64 x 6)))) (/.f64 192000 (pow.f64 x 10)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (+.f64 (/.f64 192000 (pow.f64 x 10)) (/.f64 -2400 (pow.f64 x 6)))))
(+.f64 (-.f64 (/.f64 19200 (pow.f64 x 8)) (-.f64 (/.f64 2400 (pow.f64 x 6)) (/.f64 120 (pow.f64 x 4)))) (/.f64 192000 (pow.f64 x 10)))
(+.f64 (/.f64 120 (pow.f64 x 4)) (+.f64 (/.f64 -2400 (pow.f64 x 6)) (+.f64 (/.f64 19200 (pow.f64 x 8)) (/.f64 192000 (pow.f64 x 10)))))
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))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)
(*.f64 1/120 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) 1/120)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4)))
(fma.f64 1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/120))
(fma.f64 (*.f64 x x) 1/6 (*.f64 (pow.f64 x 4) 1/120))
(fma.f64 x (*.f64 x 1/6) (*.f64 (pow.f64 x 4) 1/120))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) 1/120 1/6)))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x 1/120) 1/6)))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)
(*.f64 1/120 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) 1/120)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/120 (pow.f64 x 4)))
(fma.f64 1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) 1/120))
(fma.f64 (*.f64 x x) 1/6 (*.f64 (pow.f64 x 4) 1/120))
(fma.f64 x (*.f64 x 1/6) (*.f64 (pow.f64 x 4) 1/120))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) 1/120 1/6)))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x 1/120) 1/6)))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/120 (pow.f64 x 4))))
(fma.f64 1/6 (*.f64 x x) (+.f64 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 x (*.f64 x 1/120) 1/6) 2)

eval557.0ms (5.9%)

Compiler

Compiled 12510 to 7967 computations (36.3% saved)

prune110.0ms (1.2%)

Pruning

18 alts after pruning (11 fresh and 7 done)

PrunedKeptTotal
New6866692
Fresh6511
Picked011
Done167
Total69318711
Error
0b
Counts
711 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
27.1b
1/2
✓35.2b
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
✓13.3b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
34.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
35.7b
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
✓35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
✓28.0b
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
✓28.0b
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
✓34.6b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
✓0.1b
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
12.2b
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
48.6b
(/.f64 120 (pow.f64 x 4))
35.7b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
44.7b
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
44.6b
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
0.1b
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
35.7b
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
18.3b
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
Compiler

Compiled 199 to 142 computations (28.6% saved)

regimes74.0ms (0.8%)

Counts
53 → 1
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
(/.f64 120 (pow.f64 x 4))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(*.f64 (/.f64 (/.f64 1 x) x) (-.f64 1 (cos.f64 x)))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.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 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
(pow.f64 (/.f64 x (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x))) -1)
(/.f64 (pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1) (*.f64 x x))
(-.f64 (+.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(/.f64 (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 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3) (*.f64 x x))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(/.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3) (*.f64 x x))
(pow.f64 (/.f64 (*.f64 x x) (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x))) -1)
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
(+.f64 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 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))
Outputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
Calls

3 calls:

33.0ms
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
0.1b1x
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 582 to 346 computations (40.5% saved)

regimes41.0ms (0.4%)

Counts
32 → 1
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
(/.f64 120 (pow.f64 x 4))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(*.f64 (/.f64 (/.f64 1 x) x) (-.f64 1 (cos.f64 x)))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.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 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
Outputs
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
Calls

3 calls:

17.0ms
x
10.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
6.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b1x
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.1b1(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 322 to 195 computations (39.4% saved)

regimes85.0ms (0.9%)

Counts
31 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
(/.f64 120 (pow.f64 x 4))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(*.f64 (/.f64 (/.f64 1 x) x) (-.f64 1 (cos.f64 x)))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.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 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))
Calls

3 calls:

45.0ms
x
16.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
16.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 311 to 188 computations (39.5% saved)

bsearch49.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
5.0695251275149014e-8
0.019470802749832723
25.0ms
-3633426.229666276
-2.237237663846165e-11
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes73.0ms (0.8%)

Counts
29 → 3
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
(/.f64 120 (pow.f64 x 4))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) x)) x)
(*.f64 (/.f64 (/.f64 1 x) x) (-.f64 1 (cos.f64 x)))
(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
(/.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 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 (/.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 1 (*.f64 x (*.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (*.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/120 (pow.f64 x 3)) (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x))))))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
Outputs
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Calls

3 calls:

40.0ms
x
13.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
12.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Results
ErrorSegmentsBranch
0.2b3x
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
0.9b3(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 291 to 178 computations (38.8% saved)

bsearch46.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
21.0ms
5.0695251275149014e-8
0.019470802749832723
25.0ms
-3633426.229666276
-2.237237663846165e-11
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes10.0ms (0.1%)

Counts
12 → 1
Calls
Call 1
Inputs
1/2
1/2
1/2
1/2
(+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2)
(/.f64 (/.f64 (*.f64 1/2 (*.f64 x x)) x) x)
(/.f64 1 (*.f64 x (/.f64 x (*.f64 1/2 (*.f64 x x)))))
(+.f64 (-.f64 (+.f64 1 (*.f64 -1/24 (*.f64 x x))) 1) 1/2)
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 -1/24 (*.f64 x x)) (*.f64 -1/24 (*.f64 x x))) 1/4) (-.f64 (*.f64 -1/24 (*.f64 x x)) 1/2))
(/.f64 120 (pow.f64 x 4))
(fma.f64 -1/24 (*.f64 x x) 1/2)
Outputs
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
Calls

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
12.2b1x
Compiler

Compiled 90 to 58 computations (35.6% saved)

regimes8.0ms (0.1%)

Accuracy

Total -18.2b remaining (-67%)

Threshold costs -18.2b (-67%)

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

1 calls:

6.0ms
x
Results
ErrorSegmentsBranch
27.1b1x
Compiler

Compiled 45 to 29 computations (35.6% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
042149
156149
265149
372149
476149
577149
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
1/2
Outputs
(*.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 (sin.f64 x) x))
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (-.f64 (pow.f64 x -2) (/.f64 (/.f64 (cos.f64 x) x) x))))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 (*.f64 -1/24 (*.f64 x x)) 1/2) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(if (<=.f64 x -1950680853605655/536870912) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x) (if (<=.f64 x 7660849774797387/151115727451828646838272) (+.f64 1/2 (*.f64 -1/24 (*.f64 x x))) (/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)))
(/.f64 1 (*.f64 x (+.f64 (*.f64 1/6 x) (*.f64 2 (/.f64 1 x)))))
(/.f64 1 (*.f64 x (+.f64 (*.f64 x 1/6) (*.f64 2 (/.f64 1 x)))))
1/2
Compiler

Compiled 106 to 72 computations (32.1% saved)

soundness0.0ms (0%)

end59.0ms (0.6%)

Compiler

Compiled 101 to 63 computations (37.6% saved)

Profiling

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