Details

Time bar (total: 4.6s)

analyze327.0ms (7.1%)

Algorithm
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
78.1%21.9%0%13
78.1%21.8%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample2.8s (61.7%)

Results
1.4s2061×body2048valid
454.0ms1133×body1024valid
435.0ms1588×body512valid
256.0ms2593×body128valid
167.0ms768×body256valid
73.0ms113×body4096valid
Compiler

Compiled 20 to 14 computations (30% saved)

preprocess30.0ms (0.7%)

Algorithm
egg-herbie
Rules
424×fma-def_binary64
293×fma-neg_binary64
86×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512712
619212
731712
862112
9114012
10170012
11182912
011
Stop Event
saturated
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 9 to 6 computations (33.3% saved)

simplify18.0ms (0.4%)

Algorithm
egg-herbie
Rules
424×fma-def_binary64
293×fma-neg_binary64
86×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47312
512712
619212
731712
862112
9114012
10170012
11182912
Stop Event
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))

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.6b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
2.6b
(-.f64 1 (cos.f64 x))
13.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series3.0ms (0.1%)

Counts
2 → 16
Calls

6 calls:

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

rewrite47.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
818×log1p-expm1-u_binary64
818×expm1-log1p-u_binary64
78×add-sqr-sqrt_binary64
75×*-un-lft-identity_binary64
75×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
115218
2213018
Stop Event
node limit
Counts
2 → 66
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 (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 (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 (*.f64 x x) (-.f64 1 (cos.f64 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 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 expm1.f64 (log1p.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 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 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))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))))

simplify33.0ms (0.7%)

Algorithm
egg-herbie
Rules
588×associate-*l*_binary64
468×fma-def_binary64
434×associate-*r*_binary64
413×unswap-sqr_binary64
387×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035224
197220
2266214
3901212
44446212
Stop Event
node limit
Counts
82 → 83
Calls
Call 1
Inputs
1/2
(-.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (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 (-.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 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.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)))
(+.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 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (*.f64 1/24 (*.f64 x x)))
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (pow.f64 x 2))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/40320 (pow.f64 x 6) (*.f64 1/24 (*.f64 x x))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (*.f64 x x) (*.f64 1/40320 (pow.f64 x 6))))
(+.f64 1/2 (fma.f64 1/720 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/24 (*.f64 (pow.f64 x 6) -1/40320))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 6) -1/40320 (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 (*.f64 1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
(+.f64 (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -1/24)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 1/40320 (pow.f64 x 8))))
(-.f64 (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))) (fma.f64 1/24 (pow.f64 x 4) (*.f64 1/40320 (pow.f64 x 8))))
(+.f64 (fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24))) (*.f64 -1/40320 (pow.f64 x 8)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -1/24 (*.f64 (pow.f64 x 8) -1/40320))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1/40320)))

prune88.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New75883
Fresh000
Picked101
Done000
Total76884
Error
0.0b
Counts
84 → 8
Alt Table
StatusErrorProgram
29.7b
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))) (*.f64 x x))
29.3b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
29.0b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
29.1b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
33.7b
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
28.9b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
14.3b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
14.3b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 1343 to 834 computations (37.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
0.5b
(+.f64 1 (cos.f64 x))
13.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series7.0ms (0.2%)

Counts
4 → 40
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)))

rewrite64.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
456×prod-diff_binary64
195×expm1-udef_binary64
195×log1p-udef_binary64
120×add-sqr-sqrt_binary64
116×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122830
2352130
Stop Event
node limit
Counts
4 → 145
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 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 x x)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (pow.f64 x 4))) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (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 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 expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (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)) (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 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 (pow.f64 (cos.f64 x) 2) (-.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 (pow.f64 (cos.f64 x) 2) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (cos.f64 x) 2) 1) (-.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (cos.f64 x))))))))
((#(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 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 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 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (cos.f64 0) 2) (/.f64 (cos.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x 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 (*.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (cos.f64 (+.f64 x x)) 1/2)) (*.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) 3)) (+.f64 1 (+.f64 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (*.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (cos.f64 (+.f64 x x)) 1/2))) (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (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 (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 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 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 expm1.f64 (log1p.f64 (pow.f64 (sin.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 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 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 (+.f64 1 (cos.f64 x)) (sin.f64 x))))))) (#(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) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (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))) (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 x))))))) (#(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)) 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 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 log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 1 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))))

simplify42.0ms (0.9%)

Algorithm
egg-herbie
Rules
920×times-frac_binary64
452×fma-neg_binary64
209×*-commutative_binary64
187×fma-def_binary64
167×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054564
1155556
2460496
31638496
44511496
Stop Event
node limit
Counts
185 → 179
Calls
Call 1
Inputs
1/2
(-.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (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 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 1 (cos.f64 x)) (pow.f64 x 2)))
2
(-.f64 2 (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 4)) 2) (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 4)) 2) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (*.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (*.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
(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 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.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 (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 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
Outputs
1/2
(-.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/24))
(fma.f64 (*.f64 x x) -1/24 1/2)
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(+.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (*.f64 -1/24 (*.f64 x x)))
(+.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (*.f64 (*.f64 x x) -1/24))
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (pow.f64 x 2))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/40320 (pow.f64 x 6) (*.f64 1/24 (*.f64 x x))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (*.f64 x x) (*.f64 1/40320 (pow.f64 x 6))))
(+.f64 (fma.f64 (*.f64 x x) -1/24 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 (pow.f64 x 6) -1/40320)))
(+.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 x (*.f64 x -1/24) (*.f64 (pow.f64 x 6) -1/40320)))
(/.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (/.f64 (sin.f64 x) (*.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 -1/2 (*.f64 x x)))
(+.f64 2 (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 2)
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 4)) 2) (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (fma.f64 1/24 (pow.f64 x 4) 2) (*.f64 -1/2 (*.f64 x x)))
(+.f64 (fma.f64 1/24 (pow.f64 x 4) 2) (*.f64 (*.f64 x x) -1/2))
(fma.f64 1/24 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/2 2))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 4)) 2) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(-.f64 (fma.f64 1/24 (pow.f64 x 4) 2) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))
(-.f64 (fma.f64 1/24 (pow.f64 x 4) 2) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 2 (fma.f64 1/24 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 6) -1/720))))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(+.f64 (*.f64 x x) (*.f64 -1/3 (pow.f64 x 4)))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (*.f64 1/3 (pow.f64 x 4)))
(+.f64 (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)) (*.f64 -1/3 (pow.f64 x 4)))
(fma.f64 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 (pow.f64 x 4) -1/3)))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (*.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
(-.f64 (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)) (fma.f64 1/3 (pow.f64 x 4) (*.f64 1/315 (pow.f64 x 8))))
(+.f64 (fma.f64 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))) (*.f64 -1/315 (pow.f64 x 8)))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 8) -1/315))))
(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 (*.f64 1/2 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/24 1/2))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
(+.f64 (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -1/24)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.f64 1/24 (pow.f64 x 4)) (*.f64 1/40320 (pow.f64 x 8))))
(-.f64 (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))) (fma.f64 1/24 (pow.f64 x 4) (*.f64 1/40320 (pow.f64 x 8))))
(-.f64 (fma.f64 1/2 (*.f64 x x) (*.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) (fma.f64 (pow.f64 x 4) -1/24 (*.f64 (pow.f64 x 8) -1/40320))))
(/.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 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)))

prune131.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1745179
Fresh347
Picked101
Done000
Total1789187
Error
0b
Counts
187 → 9
Alt Table
StatusErrorProgram
29.3b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
15.2b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))
33.7b
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
15.0b
(/.f64 (*.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))))) (*.f64 x x))
13.9b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
29.0b
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
14.5b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
13.6b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
28.9b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
Compiler

Compiled 3219 to 1793 computations (44.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
0.3b
(pow.f64 (sin.f64 x) 2)
0.5b
(+.f64 1 (cos.f64 x))
13.6b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

series4.0ms (0.1%)

Counts
3 → 12
Calls

9 calls:

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

rewrite54.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
519×log-prod_binary64
191×fma-def_binary64
184×expm1-udef_binary64
184×log1p-udef_binary64
159×prod-diff_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01138
123430
2295830
Stop Event
node limit
Counts
3 → 117
Calls
Call 1
Inputs
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(pow.f64 (sin.f64 x) 2)
(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
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 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) (cbrt.f64 (exp.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))))) (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 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 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)) (*.f64 x x)) 1)))) (#(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 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 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 (pow.f64 (sin.f64 x) 2)) (/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) (neg.f64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x))))) (pow.f64 (sin.f64 x) 2))))) (#(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 (sin.f64 x) 1) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (+.f64 1 (cos.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 x (*.f64 x (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (+.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 x x)))))) (#(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 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 x x)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x))))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x))))) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (*.f64 x (*.f64 x (+.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 x (*.f64 x (+.f64 1 (cos.f64 x))))) 2)) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x (hypot.f64 1 (sqrt.f64 (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (hypot.f64 1 (sqrt.f64 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (*.f64 x (hypot.f64 1 (sqrt.f64 (cos.f64 x))))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 x (hypot.f64 1 (sqrt.f64 (cos.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 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (neg.f64 (*.f64 x 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 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))) 3)))))) (#(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 exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) 1))))) (#(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 +.f64 1 (neg.f64 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 1/2 (cos.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (cbrt.f64 (pow.f64 (sin.f64 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 x) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 (-.f64 x x)) (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (cos.f64 x) 2) 3)) (+.f64 1 (fma.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 x) (*.f64 x x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (cos.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (cos.f64 x)))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (*.f64 x x)) (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) (*.f64 x x)) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (+.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 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (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 x (*.f64 x (+.f64 1 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (hypot.f64 1 (sqrt.f64 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) 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 (+.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(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 (fma.f64 2 (log.f64 x) (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 x) (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (cos.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (cos.f64 x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (*.f64 x x) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x (+.f64 1 (cos.f64 x))))))))))

simplify36.0ms (0.8%)

Algorithm
egg-herbie
Rules
779×fma-def_binary64
649×cancel-sign-sub-inv_binary64
390×fma-neg_binary64
204×*-commutative_binary64
145×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042192
1121184
2355176
31271174
44840174
Stop Event
node limit
Counts
129 → 140
Calls
Call 1
Inputs
1/2
(-.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (pow.f64 x 2))))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (*.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (*.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
(*.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 1/2 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))) (*.f64 1/2 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (*.f64 1/720 (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)))
(+.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 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (*.f64 1/24 (*.f64 x x)))
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 1/40320 (pow.f64 x 6)) (*.f64 1/24 (pow.f64 x 2))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/40320 (pow.f64 x 6) (*.f64 1/24 (*.f64 x x))))
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (*.f64 x x) (*.f64 1/40320 (pow.f64 x 6))))
(+.f64 1/2 (fma.f64 1/720 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/24 (*.f64 (pow.f64 x 6) -1/40320))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 6) -1/40320 (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(+.f64 (*.f64 x x) (*.f64 -1/3 (pow.f64 x 4)))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (*.f64 1/3 (pow.f64 x 4)))
(+.f64 (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)) (*.f64 -1/3 (pow.f64 x 4)))
(fma.f64 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 (pow.f64 x 4) -1/3)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 6) 2/45)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (*.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
(-.f64 (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)) (fma.f64 1/3 (pow.f64 x 4) (*.f64 1/315 (pow.f64 x 8))))
(-.f64 (fma.f64 (pow.f64 x 6) 2/45 (*.f64 x x)) (fma.f64 (pow.f64 x 4) 1/3 (*.f64 1/315 (pow.f64 x 8))))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 8) -1/315))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 (pow.f64 x 8) -1/315))))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 x (*.f64 x 2))
(-.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 1/2 (pow.f64 x 4)))
(+.f64 (*.f64 2 (*.f64 x x)) (*.f64 -1/2 (pow.f64 x 4)))
(fma.f64 2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/2))
(fma.f64 x (*.f64 x 2) (*.f64 (pow.f64 x 4) -1/2))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/2 2))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))) (*.f64 1/2 (pow.f64 x 4)))
(+.f64 (fma.f64 1/24 (pow.f64 x 6) (*.f64 2 (*.f64 x x))) (*.f64 -1/2 (pow.f64 x 4)))
(fma.f64 1/24 (pow.f64 x 6) (fma.f64 2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/2)))
(fma.f64 1/24 (pow.f64 x 6) (fma.f64 x (*.f64 x 2) (*.f64 (pow.f64 x 4) -1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/2 2) (*.f64 1/24 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 1/24 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 8))))
(-.f64 (fma.f64 1/24 (pow.f64 x 6) (*.f64 2 (*.f64 x x))) (fma.f64 1/2 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 8))))
(+.f64 (fma.f64 1/24 (pow.f64 x 6) (fma.f64 2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/2))) (*.f64 -1/720 (pow.f64 x 8)))
(fma.f64 1/24 (pow.f64 x 6) (fma.f64 x (*.f64 x 2) (fma.f64 (pow.f64 x 4) -1/2 (*.f64 (pow.f64 x 8) -1/720))))
(fma.f64 x (*.f64 x 2) (fma.f64 1/24 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1/720 (*.f64 (pow.f64 x 4) -1/2))))

prune152.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1772179
Fresh268
Picked101
Done000
Total1808188
Error
0b
Counts
188 → 8
Alt Table
StatusErrorProgram
29.3b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
15.2b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))
33.7b
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
15.0b
(/.f64 (*.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))))) (*.f64 x x))
14.4b
(*.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x)))
13.9b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
14.5b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
29.6b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (cos.f64 x))) (pow.f64 x 2)))
Compiler

Compiled 3381 to 2011 computations (40.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x)
0.3b
(pow.f64 (sin.f64 x) 2)
0.5b
(+.f64 1 (cos.f64 x))
13.3b
(/.f64 (pow.f64 (sin.f64 x) 2) x)

series4.0ms (0.1%)

Counts
2 → 16
Calls

6 calls:

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

rewrite51.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
535×log-prod_binary64
197×expm1-udef_binary64
197×log1p-udef_binary64
175×fma-def_binary64
168×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01121
124221
2316719
Stop Event
node limit
Counts
2 → 72
Calls
Call 1
Inputs
(/.f64 (pow.f64 (sin.f64 x) 2) x)
(/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (sin.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (sin.f64 x) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) 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) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)) (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 4) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 4) (*.f64 x x))) (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (sqrt.f64 x)) (/.f64 (sin.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) 1) (/.f64 (sin.f64 x) 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) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sin.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (sqrt.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (pow.f64 (sin.f64 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (sin.f64 x) 4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 x (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)))) (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 x (cos.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))) (pow.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))) 2) (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)) (*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (cos.f64 x) x))) (/.f64 1 (sqrt.f64 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (*.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (+.f64 1 (cos.f64 x))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)) 1) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) 1) (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) -2)) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (cos.f64 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (cos.f64 x) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (exp.f64 (*.f64 3 (neg.f64 (log1p.f64 (cos.f64 x))))) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 x (cos.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x (cos.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x (cos.f64 x) x))))))))

simplify30.0ms (0.7%)

Algorithm
egg-herbie
Rules
550×fma-neg_binary64
452×fma-def_binary64
391×distribute-rgt-neg-in_binary64
370×cancel-sign-sub-inv_binary64
289×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
038203
198201
2250177
3744175
42031175
53777175
Stop Event
node limit
Counts
88 → 88
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 5)) x) (+.f64 (*.f64 1/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(/.f64 1/2 x)
(+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 x) (*.f64 1/48 (pow.f64 x 3))))
(+.f64 (*.f64 17/5760 (pow.f64 x 5)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 x) (*.f64 1/48 (pow.f64 x 3)))))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
Outputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (fma.f64 2/45 (pow.f64 x 5) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/45 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/45 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/45 (pow.f64 x 5)) x) (+.f64 (*.f64 1/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/45 (pow.f64 x 5) x) (fma.f64 1/315 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/45 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/315 (pow.f64 x 7))))
(+.f64 (fma.f64 2/45 (pow.f64 x 5) x) (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -1/315)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 7) -1/315 (fma.f64 2/45 (pow.f64 x 5) x)))
(/.f64 1/2 x)
(+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 x))
(+.f64 (/.f64 1/2 x) (*.f64 x 1/8))
(fma.f64 x 1/8 (/.f64 1/2 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 x) (*.f64 1/48 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (fma.f64 1/8 x (*.f64 (pow.f64 x 3) 1/48)))
(+.f64 (/.f64 1/2 x) (fma.f64 (pow.f64 x 3) 1/48 (*.f64 x 1/8)))
(fma.f64 x 1/8 (fma.f64 (pow.f64 x 3) 1/48 (/.f64 1/2 x)))
(+.f64 (*.f64 17/5760 (pow.f64 x 5)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 x) (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 17/5760 (pow.f64 x 5) (+.f64 (/.f64 1/2 x) (fma.f64 1/8 x (*.f64 (pow.f64 x 3) 1/48))))
(+.f64 (fma.f64 (pow.f64 x 3) 1/48 (*.f64 x 1/8)) (fma.f64 (pow.f64 x 5) 17/5760 (/.f64 1/2 x)))
(fma.f64 (pow.f64 x 5) 17/5760 (fma.f64 x 1/8 (fma.f64 (pow.f64 x 3) 1/48 (/.f64 1/2 x))))
(fma.f64 x 1/8 (fma.f64 (pow.f64 x 3) 1/48 (fma.f64 (pow.f64 x 5) 17/5760 (/.f64 1/2 x))))
(fma.f64 x (fma.f64 x (*.f64 x 1/48) 1/8) (fma.f64 (pow.f64 x 5) 17/5760 (/.f64 1/2 x)))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))
(/.f64 1 (*.f64 (+.f64 1 (cos.f64 x)) x))
(/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 1 (fma.f64 x (cos.f64 x) x))

prune153.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1621163
Fresh167
Picked011
Done000
Total1638171
Error
0b
Counts
171 → 8
Alt Table
StatusErrorProgram
29.3b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
15.2b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 x x)))
33.7b
(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
14.4b
(*.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x)))
13.9b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
14.5b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
29.6b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (cos.f64 x))) (pow.f64 x 2)))
14.1b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (cos.f64 x))))) x))
Compiler

Compiled 3451 to 2164 computations (37.3% saved)

regimes255.0ms (5.5%)

Accuracy

Total 0.4b remaining (95.7%)

Threshold costs 0.4b (95.7%)

Counts
118 → 3
Compiler

Compiled 1594 to 893 computations (44% saved)

bsearch12.0ms (0.3%)

Algorithm
binary-search
Calls

2 calls:

6.0ms
x
4.0ms
x
Steps
ItersPointRange
1e-90
∈ [
1.7464718943020767e-97
,
4.380360787086247e-88
]
-0.0025
∈ [
-0.002745054295041108
,
-0.0016321500042475042
]
Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03368
13868
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 x -5764607523034235/2305843009213693952) (*.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x))) (if (<=.f64 x 4586997231980143/4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220251373109248) (fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (exp.f64 (log1p.f64 (cos.f64 x)))) x))))
Outputs
(if (<=.f64 x -5764607523034235/2305843009213693952) (*.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x))) (if (<=.f64 x 4586997231980143/4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220251373109248) (fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 (/.f64 1 (exp.f64 (log1p.f64 (cos.f64 x)))) x))))

end180.0ms (3.9%)

Stop Event
fuel
Compiler

Compiled 210 to 151 computations (28.1% saved)

Profiling

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