Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
100%	49.6%	0%	50.4%	0%	0%	0%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample3.8s (68.6%)

Results

2.8s	4369×	body	2048	valid
626.0ms	2058×	body	1024	valid
219.0ms	1066×	body	512	valid
88.0ms	763×	body	256	valid

Bogosity

preprocess13.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

12×	`fma-def`
12×	`+-commutative`
10×	`associate-+l-`
8×	`sub-neg`
6×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	15	11
3	22	11
4	29	11
5	39	11
6	55	11
7	65	11
8	68	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(-.f64 1 (cos.f64 x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

12×	`fma-def`
12×	`+-commutative`
10×	`associate-+l-`
8×	`sub-neg`
6×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	15	11
3	22	11
4	29	11
5	39	11
6	55	11
7	65	11
8	68	11

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(-.f64 1 (cos.f64 x))

eval0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

47.75%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	47.75%	(-.f64 1 (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.1%	(-.f64 1 (cos.f64 x))

Compiler

Compiled 9 to 5 computations (44.4% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 1 (cos.f64 x))
0.0ms	x	@	inf	(-.f64 1 (cos.f64 x))
0.0ms	x	@	-inf	(-.f64 1 (cos.f64 x))

rewrite51.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1402×	`add-sqr-sqrt`
1386×	`*-un-lft-identity`
1288×	`add-cube-cbrt`
1276×	`add-cbrt-cube`
1266×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1686	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

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

Outputs

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

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

932×	`associate-/l*`
906×	`associate-r`
896×	`times-frac`
852×	`distribute-lft-in`
792×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	817
1	232	757
2	782	687
3	3180	687

Stop Event

1×	node limit

Counts

33 → 43

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 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)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))

Outputs
(*.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 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 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)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(-.f64 1 (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.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)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(-.f64 1 (cos.f64 x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(-.f64 1 (cos.f64 x))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(-.f64 1 (cos.f64 x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(-.f64 1 (cos.f64 x))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))

eval8.0ms (0.1%)

Compiler: Compiled 469 to 279 computations (40.5% saved)

prune6.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.03%	(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
✓	47.75%	(-.f64 1 (cos.f64 x))
▶	0.01%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	0.57%	(.f64 1/2 (.f64 x x))

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(.f64 1/2 (.f64 x x))

Compiler

Compiled 11 to 5 computations (54.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 1/2 (.f64 x x))
0.0ms	x	@	inf	(.f64 1/2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 1/2 (.f64 x x))

rewrite83.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1076×	`add-sqr-sqrt`
1058×	`*-un-lft-identity`
1006×	`pow1`
986×	`add-cube-cbrt`
978×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1408	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))

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

Outputs

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

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1470×	`distribute-rgt-in`
1446×	`distribute-lft-in`
1164×	`log-prod`
746×	`associate-r`
698×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	92	299
2	346	299
3	1898	299

Stop Event

1×	node limit

Counts

23 → 14

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
(pow.f64 (.f64 1/2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) 3)
(pow.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 1/2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 1/2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 1/2 (.f64 x x))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(pow.f64 (.f64 1/2 (.f64 x x)) 1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) 3)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(pow.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3) 1/3)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(log.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(expm1.f64 (log1p.f64 (.f64 1/2 (.f64 x x))))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(exp.f64 (log.f64 (.f64 1/2 (.f64 x x))))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(log1p.f64 (expm1.f64 (.f64 1/2 (.f64 x x))))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

rewrite69.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1792×	`add-sqr-sqrt`
1766×	`*-un-lft-identity`
1644×	`add-cube-cbrt`
1624×	`add-cbrt-cube`
182×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	187	21
2	2214	21

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Outputs

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

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1088×	`fma-def`
952×	`distribute-lft-in`
894×	`distribute-rgt-in`
874×	`*-commutative`
738×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	779
1	152	779
2	419	779
3	2320	779
4	6397	779

Stop Event

1×	node limit

Counts

27 → 33

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))))) 1)
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))
(pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 1)
(pow.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))) 3)
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 x 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))))))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 3))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))
(exp.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 1))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))

Outputs
(*.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)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 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 (.f64 x x) (fma.f64 x (.f64 x -1/24) 1/2) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (.f64 1/720 (pow.f64 x 6)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (.f64 1/720 (pow.f64 x 6))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))))) 1)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 1)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))) 2)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))) 3)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 3) 1/3)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(sqrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 2))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 x 1/2))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2))) 3))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 1))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x 1/2)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.03%	(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
✓	0.18%	(*.f64 -1/24 (pow.f64 x 4))

Compiler

Compiled 26 to 17 computations (34.6% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(*.f64 -1/24 (pow.f64 x 4))
0.0ms	x	@	inf	(*.f64 -1/24 (pow.f64 x 4))
0.0ms	x	@	inf	(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
0.0ms	x	@	0	(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
0.0ms	x	@	-inf	(*.f64 -1/24 (pow.f64 x 4))

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1860×	`add-sqr-sqrt`
1828×	`*-un-lft-identity`
1712×	`add-cube-cbrt`
1700×	`add-cbrt-cube`
202×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	226	40
2	2447	40

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(*.f64 -1/24 (pow.f64 x 4))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 -1/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/2 (*.f64 x x)) 1) (*.f64 -1/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (*.f64 (pow.f64 x 8) 1/576)) (-.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3)) (+.f64 (*.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 1/2 (*.f64 x x))) (-.f64 (*.f64 (pow.f64 x 8) 1/576) (*.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))))))

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1176×	`associate-/l*`
764×	`associate-/r*`
642×	`unswap-sqr`
534×	`fma-def`
522×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	1204
1	229	1178
2	1113	1164
3	4379	1164

Stop Event

1×	node limit

Counts

48 → 51

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4)))) 1)
(pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)
(pow.f64 (.f64 (.f64 x x) (sqrt.f64 -1/24)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)
(pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))
(log.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4)))))
(cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))
(exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))
(exp.f64 (.f64 (log.f64 (.f64 -1/24 (pow.f64 x 4))) 1))
(log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (*.f64 x x)))
(+.f64 (.f64 1/2 (.f64 x x)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 (.f64 1/2 (.f64 x x)) 1) (.f64 -1/24 (pow.f64 x 4)))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))))) 1)
(.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 1)
(.f64 1 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4))))
(.f64 (sqrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))
(.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))))
(/.f64 (-.f64 (.f64 (.f64 1/2 (.f64 x x)) (.f64 1/2 (.f64 x x))) (.f64 (pow.f64 x 8) 1/576)) (-.f64 (.f64 1/2 (.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))
(/.f64 (+.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3) (pow.f64 (.f64 -1/24 (pow.f64 x 4)) 3)) (+.f64 (.f64 (.f64 1/2 (.f64 x x)) (.f64 1/2 (.f64 x x))) (-.f64 (.f64 (pow.f64 x 8) 1/576) (.f64 (.f64 1/2 (.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))))
(pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 1)
(pow.f64 (sqrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 2)
(pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 3)
(pow.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 2))
(log.f64 (exp.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))))))
(cbrt.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))))
(exp.f64 (log.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))))
(exp.f64 (.f64 (log.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 1))
(log1p.f64 (expm1.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))))

Outputs
(*.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 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 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 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 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 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 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 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 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 (exp.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4)))) 1)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (.f64 (.f64 x x) (sqrt.f64 -1/24)) 2)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)
(*.f64 -1/24 (pow.f64 x 4))
(sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))
(log.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4)))))
(*.f64 -1/24 (pow.f64 x 4))
(cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))
(*.f64 -1/24 (pow.f64 x 4))
(expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 -1/24 (pow.f64 x 4))
(exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 -1/24 (pow.f64 x 4))
(exp.f64 (.f64 (log.f64 (.f64 -1/24 (pow.f64 x 4))) 1))
(*.f64 -1/24 (pow.f64 x 4))
(log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (*.f64 x x)))
(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 1/2 (.f64 x x)) (*.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 (.f64 1/2 (.f64 x x)) 1) (.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 (exp.f64 (log1p.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))))) 1)
(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 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4))) 1)
(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 1 (fma.f64 1/2 (.f64 x x) (*.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 (sqrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 1/2 (.f64 x x) (*.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 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 2))
(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 (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 1/2 (.f64 x x) (*.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 (.f64 (.f64 1/2 (.f64 x x)) (.f64 1/2 (.f64 x x))) (.f64 (pow.f64 x 8) 1/576)) (-.f64 (.f64 1/2 (.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))
(/.f64 (-.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (pow.f64 x 8) 1/576)) (+.f64 (.f64 1/2 (.f64 x x)) (*.f64 1/24 (pow.f64 x 4))))
(/.f64 (fma.f64 1/4 (pow.f64 x 4) (.f64 (pow.f64 x 8) -1/576)) (fma.f64 1/2 (.f64 x x) (*.f64 (pow.f64 x 4) 1/24)))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (pow.f64 x 8) -1/576)) (fma.f64 (pow.f64 x 4) 1/24 (.f64 1/2 (*.f64 x x))))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (pow.f64 x 8) -1/576)) (fma.f64 (pow.f64 x 4) 1/24 (.f64 x (*.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3) (pow.f64 (.f64 -1/24 (pow.f64 x 4)) 3)) (+.f64 (.f64 (.f64 1/2 (.f64 x x)) (.f64 1/2 (.f64 x x))) (-.f64 (.f64 (pow.f64 x 8) 1/576) (.f64 (.f64 1/2 (.f64 x x)) (*.f64 -1/24 (pow.f64 x 4))))))
(/.f64 (+.f64 (.f64 -1/13824 (pow.f64 (pow.f64 x 4) 3)) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (-.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (pow.f64 x 8) 1/576)) (.f64 1/2 (.f64 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4))))))
(/.f64 (fma.f64 -1/13824 (pow.f64 (pow.f64 x 4) 3) (pow.f64 (.f64 1/2 (.f64 x x)) 3)) (fma.f64 1/4 (pow.f64 x 4) (fma.f64 (pow.f64 x 8) 1/576 (.f64 -1/2 (.f64 (pow.f64 (*.f64 x x) 3) -1/24)))))
(/.f64 (fma.f64 -1/13824 (pow.f64 (pow.f64 x 4) 3) (.f64 1/8 (pow.f64 x 6))) (fma.f64 (pow.f64 x 8) 1/576 (.f64 (pow.f64 x 4) (+.f64 (.f64 (.f64 x x) 1/48) 1/4))))
(/.f64 (fma.f64 -1/13824 (pow.f64 (pow.f64 x 4) 3) (.f64 1/8 (pow.f64 x 6))) (fma.f64 (pow.f64 x 8) 1/576 (.f64 (pow.f64 x 4) (+.f64 1/4 (.f64 (.f64 x x) 1/48)))))
(pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 1)
(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)))
(pow.f64 (sqrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 2)
(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)))
(pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))) 3)
(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)))
(pow.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 3) 1/3)
(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)))
(sqrt.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 2))
(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)))
(log.f64 (exp.f64 (fma.f64 1/2 (.f64 x x) (.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)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (.f64 x x) (.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)))
(cbrt.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))) 3))
(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)))
(expm1.f64 (log1p.f64 (fma.f64 1/2 (.f64 x x) (.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)))
(exp.f64 (log.f64 (fma.f64 1/2 (.f64 x x) (.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)))
(exp.f64 (.f64 (log.f64 (fma.f64 1/2 (.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))) 1))
(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)))
(log1p.f64 (expm1.f64 (fma.f64 1/2 (.f64 x x) (.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)))

eval39.0ms (0.7%)

Compiler: Compiled 1294 to 892 computations (31.1% saved)

prune14.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	98	4	102

Error

Counts

102 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	47.75%	(-.f64 1 (cos.f64 x))
▶	0.02%	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓	0.01%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	0.55%	(.f64 x (.f64 1/2 x))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.02%	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓	0.52%	(*.f64 x -1/24)

Compiler

Compiled 26 to 15 computations (42.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
0.0ms	x	@	-inf	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
0.0ms	x	@	0	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
0.0ms	x	@	0	(*.f64 x -1/24)
0.0ms	x	@	-inf	(*.f64 x -1/24)

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1866×	`add-sqr-sqrt`
1838×	`*-un-lft-identity`
1716×	`add-cube-cbrt`
1694×	`add-cbrt-cube`
192×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	203	34
2	2366	34

Stop Event

1×	node limit

Counts

2 → 28

Calls

Call 1

Inputs
(*.f64 x -1/24)
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x -1/24))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x -1/24) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x -1/24)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x -1/24)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x -1/24))) (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x x)) (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))))

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1454×	`fma-def`
1212×	`associate-+r+`
1174×	`associate-+l+`
632×	`log-prod`
600×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	862
1	200	862
2	745	862
3	2872	862

Stop Event

1×	node limit

Counts

52 → 38

Calls

Call 1

Inputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x -1/24))) 1)
(pow.f64 (*.f64 x -1/24) 1)
(pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)
(pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)
(pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)
(sqrt.f64 (.f64 (.f64 x x) 1/576))
(log.f64 (pow.f64 (exp.f64 x) -1/24))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x -1/24))))
(cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))
(expm1.f64 (log1p.f64 (*.f64 x -1/24)))
(exp.f64 (log.f64 (*.f64 x -1/24)))
(exp.f64 (.f64 (log.f64 (.f64 x -1/24)) 1))
(log1p.f64 (expm1.f64 (*.f64 x -1/24)))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x -1/24))) (.f64 (.f64 x x) 1/2))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))) 1)
(pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 1)
(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) 2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 (fma.f64 x (.f64 x -1/24) 1/2) 2) (pow.f64 x 4)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (fma.f64 x (*.f64 x -1/24) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(exp.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(exp.f64 (.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 1))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))

Outputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 1/2 (pow.f64 x 2))
(.f64 x (.f64 x 1/2))
(.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 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x -1/24))) 1)
(*.f64 -1/24 x)
(pow.f64 (*.f64 x -1/24) 1)
(*.f64 -1/24 x)
(pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)
(*.f64 -1/24 x)
(pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)
(*.f64 -1/24 x)
(pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)
(*.f64 -1/24 x)
(sqrt.f64 (.f64 (.f64 x x) 1/576))
(*.f64 -1/24 x)
(log.f64 (pow.f64 (exp.f64 x) -1/24))
(*.f64 -1/24 x)
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x -1/24))))
(*.f64 -1/24 x)
(cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))
(*.f64 -1/24 x)
(expm1.f64 (log1p.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)
(exp.f64 (log.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)
(exp.f64 (.f64 (log.f64 (.f64 x -1/24)) 1))
(*.f64 -1/24 x)
(log1p.f64 (expm1.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x -1/24))) (.f64 (.f64 x x) 1/2))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))) 1)
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 1)
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) 2)
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 3)
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(pow.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3) 1/3)
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(sqrt.f64 (.f64 (pow.f64 (fma.f64 x (.f64 x -1/24) 1/2) 2) (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (fma.f64 x (*.f64 x -1/24) 1/2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(exp.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 1))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(.f64 (.f64 x x) (fma.f64 -1/24 (*.f64 x x) 1/2))

eval16.0ms (0.3%)

Compiler: Compiled 446 to 280 computations (37.2% saved)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	0	0
Picked	1	0	1
Done	2	1	3
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.03%	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
▶	0%	(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
✓	0.55%	(.f64 x (.f64 1/2 x))

Compiler

Compiled 33 to 20 computations (39.4% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.52%	(*.f64 -1/24 x)

Compiler

Compiled 31 to 20 computations (35.5% saved)

series0.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 -1/24 x)
0.0ms	x	@	inf	(*.f64 -1/24 x)
0.0ms	x	@	-inf	(*.f64 -1/24 x)

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

922×	`associate-l`
904×	`add-sqr-sqrt`
884×	`*-un-lft-identity`
842×	`pow1`
828×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	100	7
2	1112	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 -1/24 x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 -1/24 x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 -1/24 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/576 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/24) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 x)))))))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

842×	`log-prod`
832×	`associate-+r-`
808×	`+-commutative`
696×	`fma-def`
670×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	143
1	83	77
2	260	77
3	1801	77
4	4047	77
5	6502	77

Stop Event

1×	node limit

Counts

11 → 13

Calls

Call 1

Inputs
(-.f64 (+.f64 (*.f64 -1/24 x) 1) 1)
(pow.f64 (*.f64 -1/24 x) 1)
(pow.f64 (sqrt.f64 (*.f64 -1/24 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 3)
(pow.f64 (pow.f64 (*.f64 -1/24 x) 3) 1/3)
(sqrt.f64 (.f64 1/576 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 -1/24) x))
(cbrt.f64 (pow.f64 (*.f64 -1/24 x) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/24 x)))
(exp.f64 (log.f64 (*.f64 -1/24 x)))
(log1p.f64 (expm1.f64 (*.f64 -1/24 x)))

Outputs
(-.f64 (+.f64 (*.f64 -1/24 x) 1) 1)
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(pow.f64 (*.f64 -1/24 x) 1)
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(pow.f64 (sqrt.f64 (*.f64 -1/24 x)) 2)
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 3)
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(pow.f64 (pow.f64 (*.f64 -1/24 x) 3) 1/3)
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(sqrt.f64 (.f64 1/576 (.f64 x x)))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(log.f64 (pow.f64 (exp.f64 -1/24) x))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(cbrt.f64 (pow.f64 (*.f64 -1/24 x) 3))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(expm1.f64 (log1p.f64 (*.f64 -1/24 x)))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(exp.f64 (log.f64 (*.f64 -1/24 x)))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)
(log1p.f64 (expm1.f64 (*.f64 -1/24 x)))
(+.f64 (*.f64 -1/24 x) 0)
(*.f64 -1/24 x)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.02%	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
✓	0.16%	(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))
✓	0.22%	(.f64 x (.f64 x -1/24))
	0.52%	(*.f64 x -1/24)

Compiler

Compiled 44 to 22 computations (50% saved)

series1.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
0.0ms	x	@	inf	(.f64 x (.f64 x -1/24))
0.0ms	x	@	0	(.f64 x (.f64 x -1/24))
0.0ms	x	@	-inf	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
0.0ms	x	@	-inf	(.f64 x (.f64 x -1/24))

rewrite92.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1122×	`unswap-sqr`
868×	`swap-sqr`
580×	`distribute-rgt-in`
538×	`distribute-lft-in`
446×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	69
1	243	53
2	3223	53

Stop Event

1×	node limit

Counts

3 → 143

Calls

Call 1

Inputs
(.f64 x (.f64 x -1/24))
(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x -1/24)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/24))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x -1/24)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 x -1/24) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x -1/24) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x -1/24))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x -1/24))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/24))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) -1/24) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x (sqrt.f64 -1/24))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -1/24)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/24)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24)))))))

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(*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/24 (pow.f64 x 3)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x x) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x (*.f64 x -1/24)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/2 (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (pow.f64 x 4) -1/24) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 x (sqrt.f64 -1/24))) (*.f64 x (*.f64 x (sqrt.f64 -1/24))) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)) (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -1/24)) 2) (cbrt.f64 (*.f64 (pow.f64 x 4) -1/24)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (*.f64 x (*.f64 x 1/2))) (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) x (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/24 (pow.f64 x 3)) x (*.f64 x (*.f64 x 1/2)))))))

simplify129.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1314×	`associate-/r/`
858×	`associate-r`
846×	`associate-l`
574×	`associate-/l*`
540×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	394	9087
1	1208	8219
2	5692	8213

Stop Event

1×	node limit

Counts

179 → 218

Calls

Call 1

Inputs
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x -1/24)))) 1)
(pow.f64 (.f64 x (.f64 x -1/24)) 1)
(pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x -1/24))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 x -1/24)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/576))
(log.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 x -1/24)))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x -1/24)) 3))
(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 x -1/24) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 x -1/24) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x -1/24))))
(exp.f64 (log.f64 (.f64 x (.f64 x -1/24))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x -1/24))) 1))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x -1/24))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/24))) 1)
(pow.f64 (*.f64 (pow.f64 x 4) -1/24) 1)
(pow.f64 (.f64 x (.f64 x (sqrt.f64 -1/24))) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -1/24)) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2))
(log.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/24)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/24)))
(exp.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/24)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 4) -1/24)) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24)))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))) 1)
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x 1/2)))) (-.f64 1 (*.f64 (pow.f64 x 4) -1/24)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 x 4) -1/24))) (-.f64 1 (.f64 x (*.f64 x 1/2))))
(-.f64 (/.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 2) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (/.f64 (.f64 1/4 (pow.f64 x 4)) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(-.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (exp.f64 (log1p.f64 (.f64 x (*.f64 x 1/2))))) 1)
(-.f64 (+.f64 (.f64 x (.f64 x 1/2)) (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/24)))) 1)
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(.f64 x (+.f64 (.f64 -1/24 (pow.f64 x 3)) (.f64 (.f64 x 1/2) 1)))
(.f64 x (+.f64 (.f64 (.f64 -1/24 (pow.f64 x 3)) 1) (.f64 x 1/2)))
(.f64 x (+.f64 (.f64 (.f64 -1/24 (pow.f64 x 3)) 1) (.f64 (*.f64 x 1/2) 1)))
(.f64 x (+.f64 (.f64 x 1/2) (.f64 (.f64 -1/24 (pow.f64 x 3)) 1)))
(.f64 x (+.f64 (.f64 (.f64 x 1/2) 1) (.f64 -1/24 (pow.f64 x 3))))
(.f64 x (+.f64 (.f64 (.f64 x 1/2) 1) (.f64 (*.f64 -1/24 (pow.f64 x 3)) 1)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))) 1)
(.f64 1 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))
(.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) (.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))))
(.f64 (sqrt.f64 x) (+.f64 (.f64 (.f64 -1/24 (pow.f64 x 3)) (sqrt.f64 x)) (.f64 (*.f64 x 1/2) (sqrt.f64 x))))
(.f64 (sqrt.f64 x) (+.f64 (.f64 (.f64 x 1/2) (sqrt.f64 x)) (.f64 (*.f64 -1/24 (pow.f64 x 3)) (sqrt.f64 x))))
(.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(.f64 (cbrt.f64 x) (+.f64 (.f64 (.f64 -1/24 (pow.f64 x 3)) (cbrt.f64 (.f64 x x))) (.f64 (.f64 x 1/2) (cbrt.f64 (*.f64 x x)))))
(.f64 (cbrt.f64 x) (+.f64 (.f64 (.f64 x 1/2) (cbrt.f64 (.f64 x x))) (.f64 (.f64 -1/24 (pow.f64 x 3)) (cbrt.f64 (*.f64 x x)))))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 (.f64 (.f64 x (.f64 x -1/24)) (cbrt.f64 (pow.f64 x 4))) (.f64 1/2 (cbrt.f64 (pow.f64 x 4)))))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 (.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (.f64 (.f64 x (.f64 x -1/24)) (cbrt.f64 (pow.f64 x 4)))))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (.f64 x x)) (fma.f64 x (.f64 x -1/24) 1/2)))
(.f64 (fma.f64 x (.f64 x -1/24) 1/2) (*.f64 x x))
(.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))
(.f64 (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)))
(.f64 (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))) (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))
(.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))
(.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 -1/8 (pow.f64 (.f64 x x) 3)))) (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 x (.f64 x 1/2)))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (-.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (+.f64 (.f64 x (.f64 x 1/2)) (.f64 (pow.f64 x 4) 1/24)) (+.f64 (.f64 x (.f64 x 1/2)) (.f64 (pow.f64 x 4) 1/24)))))) (+.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 x (.f64 x 1/2)))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (+.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 2) 3) (pow.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) 3))) (+.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (-.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2)))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 2))))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 2))))
(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))))) (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2)) (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))))) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2)) (cbrt.f64 (.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))))))
(.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)) x) (.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)) x))
(/.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))
(/.f64 1 (/.f64 1 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))
(/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))
(/.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (sqrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))))
(/.f64 (sqrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)) (sqrt.f64 (.f64 (pow.f64 x 4) (-.f64 (*.f64 (pow.f64 x 4) 1/576) 1/4)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) (cbrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (cbrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))))
(/.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (cbrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)))) (/.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)) (cbrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)))))
(/.f64 (.f64 (pow.f64 x 4) (-.f64 1/4 (.f64 (pow.f64 x 4) 1/576))) (+.f64 (.f64 x (.f64 x 1/2)) (*.f64 (pow.f64 x 4) 1/24)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 (pow.f64 x 4) (.f64 (pow.f64 x 4) (pow.f64 x 4))) 1/64)) (.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 -1/8 (pow.f64 (.f64 x x) 3)))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 x 4)))) (.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)) (.f64 (pow.f64 x 4) (+.f64 (*.f64 (pow.f64 x 4) 1/576) 1/4))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) 3) (pow.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) 3)) (.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (+.f64 (.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) (-.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 2) 3) (pow.f64 (.f64 1/4 (pow.f64 x 4)) 3)) (.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)) (+.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (pow.f64 x 4) (+.f64 (*.f64 (pow.f64 x 4) 1/576) 1/4))))))
(/.f64 (neg.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (.f64 (.f64 x x) (neg.f64 (-.f64 (.f64 x (.f64 x -1/24)) 1/2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) (neg.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (-.f64 (.f64 x (*.f64 x -1/24)) 1/2))
(/.f64 (.f64 (.f64 x x) (+.f64 1/8 (pow.f64 (.f64 x (.f64 x -1/24)) 3))) (+.f64 (.f64 (pow.f64 x 4) 1/576) (-.f64 1/4 (.f64 (.f64 x (.f64 x -1/24)) 1/2))))
(/.f64 (.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) (sqrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))
(/.f64 (.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) (sqrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2) (cbrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2) (cbrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))
(/.f64 (.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) 1) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) 1) (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(/.f64 (.f64 (.f64 (pow.f64 x 4) (-.f64 1/4 (.f64 (pow.f64 x 4) 1/576))) 1) (+.f64 (.f64 x (.f64 x 1/2)) (.f64 (pow.f64 x 4) 1/24)))
(/.f64 (.f64 (neg.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) 1) (.f64 (.f64 x x) (neg.f64 (-.f64 (.f64 x (*.f64 x -1/24)) 1/2))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) 1) (neg.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3)))) (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2)) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))))
(/.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4))) (pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 2)) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4) (.f64 x x)) (-.f64 (.f64 x (*.f64 x -1/24)) 1/2))
(/.f64 (.f64 (+.f64 1/8 (pow.f64 (.f64 x (.f64 x -1/24)) 3)) (.f64 x x)) (+.f64 (.f64 (pow.f64 x 4) 1/576) (-.f64 1/4 (.f64 (.f64 x (.f64 x -1/24)) 1/2))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 x 4)))) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))) (.f64 (pow.f64 x 4) (+.f64 (*.f64 (pow.f64 x 4) 1/576) 1/4)))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 2) 3) (pow.f64 (.f64 1/4 (pow.f64 x 4)) 3)) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))) (+.f64 (.f64 (.f64 (pow.f64 x 4) -1/24) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 (pow.f64 x 4) (+.f64 (*.f64 (pow.f64 x 4) 1/576) 1/4)))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 (pow.f64 x 4) (.f64 (pow.f64 x 4) (pow.f64 x 4))) 1/64)) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))) (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 -1/8 (pow.f64 (.f64 x x) 3))))
(/.f64 (.f64 (+.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) 3) (pow.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) 3)) (/.f64 1 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))) (+.f64 (.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3)) (.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) (-.f64 (.f64 1/8 (pow.f64 (.f64 x x) 3)) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3)))))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) x) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (.f64 x -1/2)))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 x x)) (-.f64 (.f64 x (*.f64 x -1/24)) 1/2))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) 1) (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))
(/.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 x (+.f64 (.f64 x (sqrt.f64 -1/24)) (sqrt.f64 1/2)))) (.f64 x (-.f64 (.f64 x (sqrt.f64 -1/24)) (sqrt.f64 1/2))))
(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) 1) (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))
(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2))))) (sqrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2)))))
(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (.f64 x x) -1/2)))))
(pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 1)
(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -1/24) 1/2))) 2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3) 1/3)
(neg.f64 (/.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 x x) (neg.f64 (-.f64 (.f64 x (.f64 x -1/24)) 1/2)))))
(neg.f64 (/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -1/24) 3) (.f64 1/8 (pow.f64 (.f64 x x) 3))) (neg.f64 (+.f64 (.f64 (pow.f64 x 4) (+.f64 (.f64 (pow.f64 x 4) 1/576) 1/4)) (.f64 (.f64 (pow.f64 x 4) -1/24) (.f64 (*.f64 x x) -1/2))))))
(sqrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (fma.f64 x (*.f64 x -1/24) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2))) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(exp.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(exp.f64 (.f64 (log.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x -1/24) 1/2)))) 1))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))
(fma.f64 x (.f64 -1/24 (pow.f64 x 3)) (.f64 x (*.f64 x 1/2)))
(fma.f64 (.f64 x (.f64 x -1/24)) (.f64 x x) (.f64 x (*.f64 x 1/2)))
(fma.f64 (.f64 x x) (.f64 x (.f64 x -1/24)) (.f64 x (*.f64 x 1/2)))
(fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 4) -1/24))
(fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 4) -1/24))
(fma.f64 1 (.f64 (pow.f64 x 4) -1/24) (.f64 x (*.f64 x 1/2)))
(fma.f64 1 (.f64 x (.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 -1/24))) (.f64 x (.f64 x (sqrt.f64 -1/24))) (.f64 x (.f64 x 1/2)))
(fma.f64 (.f64 x (sqrt.f64 1/2)) (.f64 x (sqrt.f64 1/2)) (*.f64 (pow.f64 x 4) -1/24))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) -1/24)) 2) (cbrt.f64 (.f64 (pow.f64 x 4) -1/24)) (.f64 x (.f64 x 1/2)))
(fma.f64 (cbrt.f64 (.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (.f64 x (.f64 x 1/2))) (.f64 (pow.f64 x 4) -1/24))
(fma.f64 (.f64 x 1/2) x (.f64 (pow.f64 x 4) -1/24))
(fma.f64 (.f64 -1/24 (pow.f64 x 3)) x (.f64 x (*.f64 x 1/2)))

Outputs
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 2))
(.f64 -1/24 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))
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(fma.f64 (.f64 x x) (.f64 x (.f64 x -1/24)) (.f64 x (*.f64 x 1/2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 4) -1/24))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 4) -1/24))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 1 (.f64 (pow.f64 x 4) -1/24) (.f64 x (*.f64 x 1/2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 1 (.f64 x (.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 -1/24))) (.f64 x (.f64 x (sqrt.f64 -1/24))) (.f64 x (.f64 x 1/2)))
(+.f64 (pow.f64 (.f64 x (.f64 x (sqrt.f64 -1/24))) 2) (.f64 x (.f64 x 1/2)))
(.f64 (.f64 x x) (+.f64 (pow.f64 (*.f64 x (sqrt.f64 -1/24)) 2) 1/2))
(fma.f64 (.f64 x (sqrt.f64 1/2)) (.f64 x (sqrt.f64 1/2)) (*.f64 (pow.f64 x 4) -1/24))
(fma.f64 (.f64 x (sqrt.f64 1/2)) (.f64 x (sqrt.f64 1/2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) -1/24)) 2) (cbrt.f64 (.f64 (pow.f64 x 4) -1/24)) (.f64 x (.f64 x 1/2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 (cbrt.f64 (.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (.f64 x (.f64 x 1/2))) (.f64 (pow.f64 x 4) -1/24))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 x (.f64 x 1/2))) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 (.f64 x 1/2) x (.f64 (pow.f64 x 4) -1/24))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))
(fma.f64 (.f64 -1/24 (pow.f64 x 3)) x (.f64 x (*.f64 x 1/2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (fma.f64 x (.f64 -1/24 x) 1/2) (*.f64 x x))

eval124.0ms (2.3%)

Compiler: Compiled 6886 to 4999 computations (27.4% saved)

prune65.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.03%	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
✓	0%	(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
✓	0.55%	(.f64 x (.f64 1/2 x))

Compiler

Compiled 33 to 20 computations (39.4% saved)

regimes12.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 1 (cos.f64 x))
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))

Outputs
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))

Calls

3 calls:

6.0ms	x
2.0ms	(cos.f64 x)
2.0ms	(-.f64 1 (cos.f64 x))

Results

Error	Segments	Branch
0%	1	`x`
0%	1	`(-.f64 1 (cos.f64 x))`
0%	1	`(cos.f64 x)`

Compiler

Compiled 77 to 46 computations (40.3% saved)

regimes8.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 1 (cos.f64 x))

Outputs
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))

Calls

3 calls:

3.0ms	x
2.0ms	(cos.f64 x)
2.0ms	(-.f64 1 (cos.f64 x))

Results

Error	Segments	Branch
0.03%	1	`x`
0.03%	1	`(-.f64 1 (cos.f64 x))`
0.03%	1	`(cos.f64 x)`

Compiler

Compiled 40 to 24 computations (40% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-2.2%)

Threshold costs -0b (-2.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))

Outputs
(.f64 x (.f64 1/2 x))

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
0.55%	1	`x`

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	96
1	27	96

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(.f64 x (.f64 1/2 x))
(.f64 1/2 (.f64 x x))

Outputs
(.f64 x (.f64 x (fma.f64 x (*.f64 -1/24 x) 1/2)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(.f64 x (.f64 1/2 x))
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))

Compiler

Compiled 39 to 24 computations (38.5% saved)

soundness275.0ms (5%)

Algorithm

3×	egg-herbie

Rules

1454×	`fma-def`
1212×	`associate-+r+`
1174×	`associate-+l+`
1088×	`fma-def`
952×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	817
1	232	757
2	782	687
3	3180	687
0	69	779
1	152	779
2	419	779
3	2320	779
4	6397	779
0	83	862
1	200	862
2	745	862
3	2872	862

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 383 to 242 computations (36.8% saved)

end51.0ms (0.9%)

Compiler: Compiled 36 to 20 computations (44.4% saved)

Details

analyze0.0ms (0%)

sample3.8s (68.6%)

preprocess13.0ms (0.2%)

simplify53.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite51.0ms (0.9%)

simplify76.0ms (1.4%)

eval8.0ms (0.1%)

prune6.0ms (0.1%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite83.0ms (1.5%)

simplify38.0ms (0.7%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite69.0ms (1.3%)

simplify60.0ms (1.1%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite68.0ms (1.2%)

simplify60.0ms (1.1%)

eval39.0ms (0.7%)

prune14.0ms (0.2%)

localize4.0ms (0.1%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite61.0ms (1.1%)

simplify50.0ms (0.9%)

eval16.0ms (0.3%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series0.0ms (0%)

rewrite46.0ms (0.8%)

simplify64.0ms (1.2%)

localize14.0ms (0.2%)

series1.0ms (0%)

rewrite92.0ms (1.7%)

simplify129.0ms (2.4%)

eval124.0ms (2.3%)

prune65.0ms (1.2%)

regimes12.0ms (0.2%)

regimes8.0ms (0.1%)

regimes3.0ms (0.1%)

simplify6.0ms (0.1%)

soundness275.0ms (5%)

end51.0ms (0.9%)

Profiling