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 (84.8%)

Results

2.6s	4383×	body	2048	valid
868.0ms	2052×	body	1024	valid
228.0ms	1059×	body	512	valid
87.0ms	762×	body	256	valid

Bogosity

preprocess16.0ms (0.4%)

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)

simplify12.0ms (0.3%)

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

32.8b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.8b	(-.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
✓	2.3b	(-.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))

rewrite48.0ms (1.1%)

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))))))))

simplify52.0ms (1.2%)

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 (0.2%)

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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.8b	(-.f64 1 (cos.f64 x))
▶	0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	0.4b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 19 to 14 computations (26.3% saved)

localize31.0ms (0.7%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	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))

rewrite49.0ms (1.1%)

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))))))))

simplify67.0ms (1.5%)

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%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

eval2.0ms (0.1%)

Compiler: Compiled 97 to 63 computations (35.1% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	13	4	17

Error

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.0b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
✓	32.8b	(-.f64 1 (cos.f64 x))
✓	0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	0.4b	(.f64 x (.f64 1/2 x))

Compiler

Compiled 29 to 22 computations (24.1% saved)

localize4.0ms (0.1%)

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

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 1/2 (.f64 x x))
✓	2.3b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite95.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1854×	`add-sqr-sqrt`
1830×	`*-un-lft-identity`
1722×	`add-cube-cbrt`
1712×	`add-cbrt-cube`
190×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	198	13
2	2635	13

Stop Event

1×	node limit

Counts

1 → 48

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 1/2 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 1/2 (*.f64 x x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (*.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 (*.f64 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 1/2 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (cbrt.f64 (*.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (*.f64 1/2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) (+.f64 (*.f64 1/2 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 1/2 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 1/2 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 1/2 x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) 1) (-.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/2 (*.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) (+.f64 (*.f64 1/2 (*.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1) (+.f64 (*.f64 1/2 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1) (-.f64 (fma.f64 1/2 (*.f64 x x) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) (+.f64 (*.f64 1/2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) (-.f64 1 (*.f64 (fma.f64 1/2 (*.f64 x x) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 1/2 (*.f64 x x) -1) (fma.f64 1/2 (*.f64 x x) -1))) (-.f64 1 (fma.f64 1/2 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 (*.f64 x x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 1/2 (*.f64 x x) -1) (fma.f64 1/2 (*.f64 x x) -1)) (fma.f64 1/2 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (*.f64 1/2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) (+.f64 (*.f64 1/2 (*.f64 x x)) 2))))))) (#(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 (*.f64 (pow.f64 (*.f64 x x) 3) 1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 1/8))))) (#(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 exp.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 1/2 (*.f64 x x) 1)) -1)))))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1332×	`associate-/l*`
952×	`associate-/r*`
898×	`associate-+r-`
882×	`associate-r`
878×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1656
1	299	1550
2	926	1538
3	3984	1538

Stop Event

1×	node limit

Counts

60 → 66

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 1 (fma.f64 1/2 (*.f64 x x) -1))
(+.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) -1) 1))
(+.f64 (.f64 1/2 (.f64 x x)) 0)
(+.f64 (fma.f64 1/2 (*.f64 x x) 1) -1)
(+.f64 (fma.f64 1/2 (*.f64 x x) -1) 1)
(+.f64 -1 (fma.f64 1/2 (*.f64 x x) 1))
(.f64 1 (.f64 1/2 (*.f64 x x)))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (.f64 x x) 1/2)
(.f64 (.f64 1/2 (*.f64 x x)) 1)
(.f64 (.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (*.f64 x x)) 1/2))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)))
(.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 1/2 (.f64 x x))))
(.f64 (.f64 1/2 x) x)
(.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (.f64 1/2 (.f64 x x)) 2)))
(.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (*.f64 x x)) 2))))
(.f64 (.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)))
(.f64 (.f64 (*.f64 1/2 x) 1) x)
(.f64 (.f64 (*.f64 1/2 x) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (.f64 1/2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))
(.f64 (+.f64 (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) 1) (-.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) 1))
(/.f64 1 (/.f64 (+.f64 (.f64 1/2 (.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (+.f64 (.f64 1/2 (*.f64 x x)) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (-.f64 (fma.f64 1/2 (.f64 x x) 1) -1))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (-.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) 1) -1))))
(/.f64 (-.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) -1) (fma.f64 1/2 (.f64 x x) -1))) (-.f64 1 (fma.f64 1/2 (.f64 x x) -1)))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 (.f64 x x) -1) 3)) (+.f64 1 (-.f64 (.f64 (fma.f64 1/2 (.f64 x x) -1) (fma.f64 1/2 (.f64 x x) -1)) (fma.f64 1/2 (*.f64 x x) -1))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (.f64 1/2 (*.f64 x x)) 2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2))))
(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 (.f64 (pow.f64 (.f64 x x) 3) 1/8) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 1/2 (.f64 x x)))))
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) 1/8))
(expm1.f64 (log1p.f64 (.f64 1/2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 1/2 (.f64 x x))))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (*.f64 x x))) 1))
(log1p.f64 (expm1.f64 (.f64 1/2 (.f64 x x))))
(fma.f64 1 (fma.f64 1/2 (*.f64 x x) 1) -1)
(fma.f64 (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 1/2 (.f64 x x) 1)) -1)

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 1 (fma.f64 1/2 (*.f64 x x) -1))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) -1) 1))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 (.f64 1/2 (.f64 x x)) 0)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 (fma.f64 1/2 (*.f64 x x) 1) -1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 (fma.f64 1/2 (*.f64 x x) -1) 1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(+.f64 -1 (fma.f64 1/2 (*.f64 x x) 1))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 1 (.f64 1/2 (*.f64 x x)))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 x (.f64 1/2 x))
(.f64 1/2 (.f64 x x))
(.f64 (.f64 x x) 1/2)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (.f64 1/2 (*.f64 x x)) 1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (*.f64 x x)) 1/2))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 1/2 (cbrt.f64 (*.f64 x x))))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 1/2 (cbrt.f64 (pow.f64 x 4))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)))
(.f64 (cbrt.f64 (.f64 x (.f64 1/2 x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)))
(.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 1/2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)))
(.f64 (cbrt.f64 (.f64 x (.f64 1/2 x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)))
(.f64 (.f64 1/2 x) x)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (.f64 1/2 (.f64 x x)) 2)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (/.f64 1 (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (fma.f64 1/2 (.f64 x x) 2))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 2)) (fma.f64 x (.f64 1/2 x) 2))
(.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (*.f64 x x)) 2))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (.f64 x x) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 3)) (+.f64 2 (fma.f64 1/2 (.f64 x x) (pow.f64 (fma.f64 x (*.f64 1/2 x) 1) 2))))
(.f64 (.f64 1/2 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 1/2 (cbrt.f64 (*.f64 x x))))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 1/2 (cbrt.f64 (pow.f64 x 4))))
(.f64 (.f64 (*.f64 1/2 x) 1) x)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (.f64 (*.f64 1/2 x) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(.f64 (.f64 (.f64 1/2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))
(.f64 x (.f64 1/2 (.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 x))))
(.f64 (.f64 1/2 x) (.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 x)))
(.f64 (+.f64 (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) 1) (-.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) 1))
(.f64 (+.f64 1 (hypot.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) -1))
(fma.f64 (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) -1)
(/.f64 1 (/.f64 (+.f64 (.f64 1/2 (.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 1/2 (*.f64 x x) 1) 2) -1)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (/.f64 1 (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (fma.f64 1/2 (.f64 x x) 2))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 2)) (fma.f64 x (.f64 1/2 x) 2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (.f64 x x) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 3)) (+.f64 2 (fma.f64 1/2 (.f64 x x) (pow.f64 (fma.f64 x (*.f64 1/2 x) 1) 2))))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (+.f64 (.f64 1/2 (*.f64 x x)) 2))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (/.f64 1 (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (fma.f64 1/2 (.f64 x x) 2))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 2)) (fma.f64 x (.f64 1/2 x) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1) (-.f64 (fma.f64 1/2 (.f64 x x) 1) -1))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (/.f64 1 (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (fma.f64 1/2 (.f64 x x) 2))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 2)) (fma.f64 x (.f64 1/2 x) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (.f64 x x) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 3)) (+.f64 2 (fma.f64 1/2 (.f64 x x) (pow.f64 (fma.f64 x (*.f64 1/2 x) 1) 2))))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (-.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) 1) -1))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (.f64 x x) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 3)) (+.f64 2 (fma.f64 1/2 (.f64 x x) (pow.f64 (fma.f64 x (*.f64 1/2 x) 1) 2))))
(/.f64 (-.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) -1) (fma.f64 1/2 (.f64 x x) -1))) (-.f64 1 (fma.f64 1/2 (.f64 x x) -1)))
(/.f64 (fma.f64 (fma.f64 x (.f64 1/2 x) -1) (fma.f64 x (.f64 x -1/2) 1) 1) (+.f64 (.f64 x (.f64 x -1/2)) 2))
(/.f64 (fma.f64 (fma.f64 x (.f64 1/2 x) -1) (fma.f64 x (.f64 x -1/2) 1) 1) (+.f64 2 (.f64 x (.f64 x -1/2))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 (.f64 x x) -1) 3)) (+.f64 1 (-.f64 (.f64 (fma.f64 1/2 (.f64 x x) -1) (fma.f64 1/2 (.f64 x x) -1)) (fma.f64 1/2 (*.f64 x x) -1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 (.f64 x x) -1) 3)) (+.f64 1 (.f64 (fma.f64 1/2 (.f64 x x) -1) (-.f64 (fma.f64 1/2 (.f64 x x) -1) 1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 x (.f64 1/2 x) -1) 3)) (fma.f64 (fma.f64 x (.f64 1/2 x) -1) (+.f64 (.f64 x (.f64 1/2 x)) -2) 1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (.f64 1/2 (*.f64 x x)) 2)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (/.f64 1 (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2)) (fma.f64 1/2 (.f64 x x) 2))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 2)) (fma.f64 x (.f64 1/2 x) 2))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (+.f64 (.f64 1/2 (.f64 x x)) 2))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (.f64 x x) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 (.f64 x x) 1) 2) (fma.f64 1/2 (*.f64 x x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (.f64 1/2 x) 1) 3)) (+.f64 2 (fma.f64 1/2 (.f64 x x) (pow.f64 (fma.f64 x (*.f64 1/2 x) 1) 2))))
(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 (.f64 (pow.f64 (.f64 x x) 3) 1/8) 1/3)
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) 1/8))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(log.f64 (+.f64 1 (expm1.f64 (.f64 1/2 (.f64 x x)))))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) 1/8))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(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))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (*.f64 x x))) 1))
(.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))
(fma.f64 1 (fma.f64 1/2 (*.f64 x x) 1) -1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(fma.f64 (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) (hypot.f64 1 (.f64 x (sqrt.f64 1/2))) -1)
(.f64 (+.f64 1 (hypot.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/2))) -1))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 1/2 (.f64 x x) 1)) -1)
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))

eval21.0ms (0.5%)

Compiler: Compiled 1082 to 742 computations (31.4% saved)

prune9.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.0b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
✓	32.8b	(-.f64 1 (cos.f64 x))
✓	0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	0.4b	(.f64 x (.f64 1/2 x))

Compiler

Compiled 29 to 22 computations (24.1% saved)

regimes12.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 1/2 x))
(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

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

Calls

3 calls:

5.0ms	(-.f64 1 (cos.f64 x))
4.0ms	x
2.0ms	(cos.f64 x)

Results

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

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes8.0ms (0.2%)

Accuracy

Total -32.6b remaining (-7983.3%)

Threshold costs -32.6b (-7983.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(-.f64 1 (cos.f64 x))`
0.4b	1	`(cos.f64 x)`

Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	18	47

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(.f64 x (.f64 1/2 x))
(.f64 1/2 (.f64 x x))

Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(.f64 x (.f64 1/2 x))
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))

Compiler

Compiled 20 to 14 computations (30% saved)

soundness119.0ms (2.6%)

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

Compiler

Compiled 52 to 25 computations (51.9% saved)

end20.0ms (0.4%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

Details

analyze0.0ms (0%)

sample3.8s (84.8%)

preprocess16.0ms (0.4%)

simplify12.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite48.0ms (1.1%)

simplify52.0ms (1.2%)

eval8.0ms (0.2%)

prune5.0ms (0.1%)

localize31.0ms (0.7%)

series1.0ms (0%)

rewrite49.0ms (1.1%)

simplify67.0ms (1.5%)

localize8.0ms (0.2%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

localize9.0ms (0.2%)

series1.0ms (0%)

rewrite95.0ms (2.1%)

simplify74.0ms (1.6%)

eval21.0ms (0.5%)

prune9.0ms (0.2%)

regimes12.0ms (0.3%)

regimes8.0ms (0.2%)

simplify4.0ms (0.1%)

soundness119.0ms (2.6%)

end20.0ms (0.4%)

Profiling