Details

Time bar (total: 4.5s)

analyze361.0ms (8%)

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

Compiled 10 to 7 computations (30% saved)

sample3.0s (65.6%)

Results
1.5s2055×body2048valid
468.0ms1616×body512valid
457.0ms1105×body1024valid
301.0ms2524×body128valid
185.0ms852×body256valid
74.0ms104×body4096valid

preprocess25.0ms (0.5%)

Algorithm
2×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
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 9 to 6 computations (33.3% saved)

simplify18.0ms (0.4%)

Algorithm
1×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
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))

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
32.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶32.1b
(/.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
✓1.9b
(-.f64 1 (cos.f64 x))
✓13.9b
(/.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))

rewrite42.0ms (0.9%)

Algorithm
1×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
1×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 expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (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 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))))))

simplify23.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
555×distribute-lft-out_binary64
517×distribute-rgt-out_binary64
510×fma-def_binary64
425×associate-*l*_binary64
413×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037218
191216
2217214
3652212
42438212
Stop Event
1×node limit
Counts
82 → 83
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)
(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))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 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))
(/.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 x (*.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(*.f64 (*.f64 x 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 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (fma.f64 -1/24 (*.f64 x x) 1/2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/720) -1/24) (fma.f64 -1/40320 (pow.f64 x 6) 1/2)))

prune82.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New76783
Fresh000
Picked101
Done000
Total77784
Error
0.0b
Counts
84 → 7
Alt Table
StatusErrorProgram
15.3b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
31.9b
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))
32.2b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
▶14.6b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
32.3b
(/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (*.f64 x x))
31.9b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
31.2b
(fma.f64 x (*.f64 -1/24 x) 1/2)
Compiler

Compiled 1305 to 801 computations (38.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
✓0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.3b
(+.f64 1 (cos.f64 x))
✓13.9b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))

series7.0ms (0.1%)

Counts
4 → 44
Calls

12 calls:

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

rewrite63.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
482×prod-diff_binary64
212×log1p-udef_binary64
132×add-sqr-sqrt_binary64
127×*-un-lft-identity_binary64
127×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01146
125430
2387030
Stop Event
1×node limit
Counts
4 → 154
Calls
Call 1
Inputs
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.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 (+.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 x x) (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 (cos.f64 (+.f64 x x)) 1/2) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 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 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 2) (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) 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 (sin.f64 x) 1) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 (sin.f64 x) (+.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 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#<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 (/.f64 1 (+.f64 1 (cos.f64 x))) (cbrt.f64 (pow.f64 x 4))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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 (exp.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 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 (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 1 (+.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 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (+.f64 1 (cos.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(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 (+.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 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 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 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 +.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 (-.f64 (cos.f64 0) (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 1/8 (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 (*.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 /.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 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 (cbrt.f64 (pow.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 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 (log.f64 (pow.f64 (sin.f64 x) 2)))))) (#(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 (log.f64 (pow.f64 (sin.f64 x) 2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 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 (+.f64 1 (cos.f64 x)) (sin.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 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 4)) (/.f64 (+.f64 1 (cos.f64 x)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x))) 1) (*.f64 2 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x))) -1) (*.f64 2 (+.f64 -1 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x)))) (*.f64 (+.f64 -1 (neg.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) 1) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 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 (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x))) (/.f64 1 (+.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (pow.f64 (sin.f64 x) 2)) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) -1) (+.f64 -1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (-.f64 (cos.f64 0) (cos.f64 (+.f64 x x)))) 2)))) (#(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 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 cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 3) (pow.f64 (pow.f64 (sin.f64 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (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 (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))))))

simplify35.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
920×times-frac_binary64
571×distribute-lft-out_binary64
303×fma-def_binary64
199×*-commutative_binary64
195×unswap-sqr_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068576
1158572
2393520
31258520
42444520
Stop Event
1×node limit
Counts
198 → 191
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))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(+.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 (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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (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 (/.f64 (tan.f64 (/.f64 x 2)) 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 (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 (/.f64 (tan.f64 (/.f64 x 2)) 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 2 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 1/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 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 (*.f64 x 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 2 (fma.f64 x (*.f64 x -1/2) (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)))
(+.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 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 -1/315 (pow.f64 x 8)))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 -1/315 (pow.f64 x 8) (*.f64 (pow.f64 x 6) 2/45))))
(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)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 x (*.f64 1/2 x)))
(*.f64 (*.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(fma.f64 x (*.f64 1/2 x) (*.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))))
(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))))
(*.f64 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 1/720 (pow.f64 x 6) (fma.f64 x (*.f64 1/2 x) (*.f64 -1/24 (pow.f64 x 4))))
(+.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)))))
(/.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)))

prune195.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1883191
Fresh156
Picked011
Done000
Total1899198
Error
0b
Counts
198 → 9
Alt Table
StatusErrorProgram
31.9b
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))
▶0.2b
(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
32.2b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
✓14.6b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
14.6b
(/.f64 (/.f64 (sin.f64 x) (/.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x))) (*.f64 x x))
32.3b
(/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (*.f64 x x))
31.9b
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
31.2b
(fma.f64 x (*.f64 -1/24 x) 1/2)
15.1b
(*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))
Compiler

Compiled 3567 to 2049 computations (42.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series7.0ms (0.2%)

Counts
3 → 36
Calls

9 calls:

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

rewrite53.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
532×log-prod_binary64
186×log-div_binary64
182×expm1-udef_binary64
182×log1p-udef_binary64
151×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
120138
2275338
Stop Event
1×node limit
Counts
3 → 107
Calls
Call 1
Inputs
(/.f64 (tan.f64 (/.f64 x 2)) x)
(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
(/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x)
Outputs
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simplify36.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
736×fma-def_binary64
548×associate-*l*_binary64
492×unswap-sqr_binary64
385×associate-*r*_binary64
343×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060653
1148647
2350641
3991637
43630637
Stop Event
1×node limit
Counts
143 → 133
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/24 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/240 (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))
1/2
(+.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 x)
(+.f64 (*.f64 1/24 x) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 17/40320 (pow.f64 x 5)) (*.f64 1/240 (pow.f64 x 3)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
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))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) 1/240 1/24) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 1/240) 1/24) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 17/40320 (pow.f64 x 6)) (*.f64 1/240 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 1/24 (*.f64 x x) (fma.f64 17/40320 (pow.f64 x 6) (*.f64 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 (*.f64 x x) (fma.f64 (*.f64 x x) 1/240 1/24) (fma.f64 17/40320 (pow.f64 x 6) 1/2))
(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)))
(/.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))))
1/2
(+.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 (fma.f64 (*.f64 x x) -1/24 1/2) (*.f64 (pow.f64 x 4) 1/720))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 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 1/2 (fma.f64 (*.f64 x x) -1/24 (fma.f64 (pow.f64 x 4) 1/720 (*.f64 (pow.f64 x 6) -1/40320))))
(+.f64 (fma.f64 x (*.f64 x -1/24) 1/2) (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)))
(/.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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 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 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(/.f64 1/2 x)
(+.f64 (*.f64 1/24 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 1/24 x (/.f64 1/2 x))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (fma.f64 1/24 x (/.f64 1/2 x)) (*.f64 1/240 (pow.f64 x 3)))
(fma.f64 1/24 x (fma.f64 1/240 (pow.f64 x 3) (/.f64 1/2 x)))
(fma.f64 x (fma.f64 (*.f64 x x) 1/240 1/24) (/.f64 1/2 x))
(fma.f64 x (fma.f64 x (*.f64 x 1/240) 1/24) (/.f64 1/2 x))
(+.f64 (*.f64 1/24 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 17/40320 (pow.f64 x 5)) (*.f64 1/240 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/24 x (/.f64 1/2 x)) (fma.f64 17/40320 (pow.f64 x 5) (*.f64 1/240 (pow.f64 x 3))))
(+.f64 (fma.f64 1/240 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 5))) (fma.f64 1/24 x (/.f64 1/2 x)))
(fma.f64 1/24 x (fma.f64 1/240 (pow.f64 x 3) (fma.f64 17/40320 (pow.f64 x 5) (/.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x)))))
(/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x)))

prune140.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1312133
Fresh437
Picked011
Done101
Total1366142
Error
0b
Counts
142 → 6
Alt Table
StatusErrorProgram
14.6b
(/.f64 (/.f64 (sin.f64 x) (/.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x))) (*.f64 x x))
▶0.4b
(/.f64 1 (/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))))
32.2b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
14.6b
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
15.1b
(*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))
Compiler

Compiled 2330 to 1479 computations (36.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))))
✓0.2b
(/.f64 x (tan.f64 (*.f64 x 1/2)))
✓0.2b
(/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
✓0.4b
(/.f64 1 (/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))))

series7.0ms (0.2%)

Counts
4 → 48
Calls

12 calls:

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

rewrite67.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
228×log-div_binary64
212×expm1-udef_binary64
212×log1p-udef_binary64
180×log-pow_binary64
122×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01160
124357
2346657
Stop Event
1×node limit
Counts
4 → 170
Calls
Call 1
Inputs
(/.f64 1 (/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))))
(/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))
(/.f64 x (tan.f64 (*.f64 x 1/2)))
(/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))))
Outputs
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simplify41.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
436×associate-/l/_binary64
405×times-frac_binary64
310×associate-/l*_binary64
296×distribute-lft-out_binary64
295×associate-/r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
069924
1180918
2458910
31361910
42565910
Stop Event
1×node limit
Counts
218 → 205
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 x)
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 1/720 (pow.f64 x 5))))
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/40320 (pow.f64 x 7)) (*.f64 1/720 (pow.f64 x 5)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 -1/360 (pow.f64 x 4))))
(+.f64 (*.f64 -1/15120 (pow.f64 x 6)) (+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 -1/360 (pow.f64 x 4)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
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 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
Outputs
1/2
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/24 (*.f64 x x)))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/40320 (pow.f64 x 6)) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 -1/40320 (pow.f64 x 6) (*.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/24 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/24 (*.f64 x x) 1/2) (fma.f64 1/720 (pow.f64 x 4) (*.f64 -1/40320 (pow.f64 x 6))))
(/.f64 (*.f64 (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 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 x x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(fma.f64 -1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 -1/24 (pow.f64 x 3)))
(*.f64 x (fma.f64 -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 -1/24 (pow.f64 x 3) (fma.f64 1/720 (pow.f64 x 5) (*.f64 1/2 x)))
(fma.f64 1/2 x (fma.f64 1/720 (pow.f64 x 5) (*.f64 -1/24 (pow.f64 x 3))))
(+.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 -1/40320 (pow.f64 x 7) (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) x) (cos.f64 (*.f64 1/2 x))))
2
(+.f64 2 (*.f64 -1/6 (pow.f64 x 2)))
(+.f64 2 (*.f64 (*.f64 x x) -1/6))
(fma.f64 (*.f64 x x) -1/6 2)
(fma.f64 x (*.f64 x -1/6) 2)
(+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 -1/360 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/360)))
(+.f64 (fma.f64 (*.f64 x x) -1/6 2) (*.f64 (pow.f64 x 4) -1/360))
(fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) -1/360 2))
(fma.f64 (pow.f64 x 4) -1/360 (fma.f64 (*.f64 x x) -1/6 2))
(+.f64 (*.f64 -1/15120 (pow.f64 x 6)) (+.f64 2 (+.f64 (*.f64 -1/6 (pow.f64 x 2)) (*.f64 -1/360 (pow.f64 x 4)))))
(fma.f64 -1/15120 (pow.f64 x 6) (+.f64 2 (fma.f64 -1/6 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/360))))
(fma.f64 (pow.f64 x 6) -1/15120 (+.f64 (fma.f64 (*.f64 x x) -1/6 2) (*.f64 (pow.f64 x 4) -1/360)))
(fma.f64 (pow.f64 x 6) -1/15120 (fma.f64 x (*.f64 x -1/6) (fma.f64 (pow.f64 x 4) -1/360 2)))
(fma.f64 (pow.f64 x 6) -1/15120 (fma.f64 (pow.f64 x 4) -1/360 (fma.f64 (*.f64 x x) -1/6 2)))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 (*.f64 1/2 x)) x))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) x)
(*.f64 (/.f64 x (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (/.f64 x (sin.f64 (*.f64 1/2 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))))
(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 (pow.f64 x 4) 1/120 (fma.f64 x (*.f64 x 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 (pow.f64 x 6) 1/3024 (*.f64 (pow.f64 x 4) 1/120)) (fma.f64 (*.f64 x x) 1/6 2))
(fma.f64 x (*.f64 x 1/6) (fma.f64 (pow.f64 x 6) 1/3024 (fma.f64 (pow.f64 x 4) 1/120 2)))
(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 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))
(/.f64 (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (*.f64 x x) (cos.f64 (*.f64 1/2 x))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)) (/.f64 x (/.f64 (sin.f64 (*.f64 1/2 x)) x)))
(*.f64 (/.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (cos.f64 (*.f64 1/2 x)) (*.f64 (/.f64 x (sin.f64 x)) (/.f64 x (sin.f64 (*.f64 1/2 x)))))

prune218.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2041205
Fresh134
Picked011
Done011
Total2056211
Error
0b
Counts
211 → 6
Alt Table
StatusErrorProgram
14.6b
(/.f64 (/.f64 (sin.f64 x) (/.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x))) (*.f64 x x))
✓0.4b
(/.f64 1 (/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))))
0.1b
(*.f64 (pow.f64 (/.f64 x (sin.f64 x)) -1) (/.f64 (tan.f64 (*.f64 x 1/2)) x))
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
14.6b
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
15.1b
(*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))
Compiler

Compiled 3751 to 2461 computations (34.4% saved)

regimes75.0ms (1.7%)

Accuracy

Total -63.2b remaining (-56272.2%)

Threshold costs -63.2b (-56272.2%)

Counts
66 → 1
Calls
Call 1
Inputs
(log.f64 (exp.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))))
(sqrt.f64 (pow.f64 (*.f64 x (/.f64 x (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))) -2))
(pow.f64 (*.f64 x (/.f64 x (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))) -1)
(*.f64 (pow.f64 (/.f64 x (sin.f64 x)) -1) (/.f64 (tan.f64 (*.f64 x 1/2)) x))
(*.f64 1 (/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x))))
(/.f64 1 (fma.f64 x (*.f64 x 1/6) 2))
(/.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) 2))
(fma.f64 -1/24 (*.f64 x x) 1/2)
(/.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))) x)
(/.f64 1 (/.f64 x (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2))))))
(/.f64 (sin.f64 x) (*.f64 x (/.f64 x (tan.f64 (*.f64 x 1/2)))))
(+.f64 0 (/.f64 (sin.f64 x) (*.f64 x (/.f64 x (tan.f64 (*.f64 x 1/2))))))
(*.f64 (sin.f64 x) (/.f64 (pow.f64 (/.f64 x (tan.f64 (*.f64 x 1/2))) -1) x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 (*.f64 1/2 x))))))
(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 4) 1/720 1/2))
(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 x) (/.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x))) (*.f64 x x))
(/.f64 (+.f64 1 (neg.f64 (cos.f64 x))) (*.f64 x x))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x (neg.f64 x))))
(pow.f64 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)) -1)
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
(*.f64 (pow.f64 x -2) (-.f64 1 (cos.f64 x)))
(*.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)
(*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 x -2)))
(*.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))
(*.f64 (sin.f64 x) (*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (pow.f64 x -2)))
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
(/.f64 (expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
(/.f64 (pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 x x))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.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))
(/.f64 (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (*.f64 x x))
(exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)
(pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)
(*.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)))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 x x)))
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))
(*.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))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 x -2)))
(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
(*.f64 1 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)))
(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
(+.f64 (pow.f64 x -2) (neg.f64 (*.f64 (cos.f64 x) (pow.f64 x -2))))
(fma.f64 1/720 (pow.f64 x 4) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/24 (pow.f64 x 2)) (*.f64 1/720 (pow.f64 x 4))))
(fma.f64 x (*.f64 -1/24 x) 1/2)
(+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2)))
1/2
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Outputs
(/.f64 (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))) x)
Results
32.0ms0.1bx
10.0ms0.1b(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
11.0ms0.1b(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 824 to 494 computations (40% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))) x)
Outputs
(/.f64 (/.f64 (sin.f64 x) (/.f64 x (tan.f64 (*.f64 x 1/2)))) x)

end16.0ms (0.4%)

Stop Event
1×fuel
Compiler

Compiled 24 to 16 computations (33.3% saved)

Profiling

Loading profile data...