Details

analyze689.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 41 to 24 computations (41.5% saved)

sample80.0ms (0.9%)

Algorithm

1×

intervals

Results

61.0ms	250×	body	256	valid
6.0ms	50×	body	128	nan
1.0ms	6×	body	128	valid

Compiler

Compiled 84 to 50 computations (40.5% saved)

simplify205.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-neg_binary64`
636×	`times-frac_binary64`
620×	`div-sub_binary64`
565×	`unsub-neg_binary64`
481×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	54	50
2	144	50
3	406	48
4	826	48
5	1523	48
6	1911	48
7	2632	48
8	2589	48
9	2971	48
10	3625	48
11	4193	48
12	4375	48
13	4485	48
14	4533	48
15	4557	48
16	4607	48
17	4882	48
18	4848	48

prune4.0ms (0.1%)

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

35.9b

Counts

2 → 2

Alt Table

Status	Error	Program
	36.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
▶	36.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))

Status

Error

Program

36.0b

(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))

▶

36.0b

(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))

Compiler

Compiled 182 to 100 computations (45.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.5b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
9.9b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite185.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

30.2b

Rules

10×	`cbrt-div_binary64`
8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 68

Calls

4 calls:

10.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
10.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 3217 to 1133 computations (64.8% saved)

series205.0ms (2.4%)

Error

30.7b

Counts

4 → 30

Calls

4 calls:

77.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
65.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
14.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
14.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 3661 to 2608 computations (28.8% saved)

simplify162.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-def_binary64`
610×	`fma-neg_binary64`
299×	`distribute-rgt-in_binary64`
240×	`times-frac_binary64`
139×	`distribute-rgt-neg-out_binary64`

Counts

98 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	3087
1	680	2957
2	1890	2851
3	4511	2839
4	4995	2839
5	4892	2839

prune115.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Error

30.0b

Counts

70 → 12

Alt Table

Status	Error	Program
	44.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))))))
	49.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	46.7b	(fma.f64 (cbrt.f64 -1/2) (cbrt.f64 (.f64 (/.f64 2 a) g)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	33.1b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	36.1b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a)))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	33.6b	(fma.f64 (cbrt.f64 -1/2) (.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
▶	33.1b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (.f64 2 a))))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	41.2b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	33.1b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	48.9b	(fma.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (/.f64 -1 g))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))

Compiler

Compiled 3393 to 1495 computations (55.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (.f64 g g) (.f64 h h))
6.5b	(cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a)))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite186.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

30.0b

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
11×	`cbrt-prod_binary64`
9×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 75

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(-.f64 (.f64 g g) (.f64 h h))

Compiler

Compiled 3073 to 1080 computations (64.9% saved)

series177.0ms (2.1%)

Error

29.7b

Counts

4 → 30

Calls

4 calls:

76.0ms	(cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a)))
19.0ms	(-.f64 (.f64 g g) (.f64 h h))
14.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
14.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 3043 to 2152 computations (29.3% saved)

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-neg_binary64`
378×	`times-frac_binary64`
286×	`fma-def_binary64`
274×	`div-sub_binary64`
236×	`associate-l_binary64`

Counts

105 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3172
1	482	3029
2	1092	2993
3	3488	2824
4	5034	2824

prune137.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	59	8	67
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	62	17	79

Error

30.0b

Counts

79 → 17

Alt Table

Status	Error	Program
	33.6b	(fma.f64 (cbrt.f64 -1/2) (.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	53.0b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a))))
	56.4b	(fma.f64 (pow.f64 a -1/3) (.f64 (cbrt.f64 1/2) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))) g))) (cbrt.f64 0))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	46.7b	(fma.f64 (cbrt.f64 -1/2) (cbrt.f64 (.f64 (/.f64 2 a) g)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	39.7b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (*.f64 2 a))))
▶	33.1b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	36.1b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a)))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	44.0b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (.f64 2 a))))
	37.2b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a))))
	50.4b	(.f64 (cbrt.f64 1/2) (fma.f64 (pow.f64 a -1/3) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a))))
	45.9b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (log.f64 (exp.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))))))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	55.2b	(fma.f64 (cbrt.f64 1/2) (.f64 (pow.f64 a -1/3) (cbrt.f64 (.f64 g -2))) (cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a))))
	33.1b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	48.9b	(fma.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (/.f64 -1 g))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))

Compiler

Compiled 3273 to 1548 computations (52.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (.f64 g g) (.f64 h h))
6.5b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite249.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

30.0b

Rules

8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

4 → 69

Calls

4 calls:

11.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(-.f64 (.f64 g g) (.f64 h h))

Compiler

Compiled 2987 to 1044 computations (65% saved)

series189.0ms (2.2%)

Error

29.7b

Counts

4 → 30

Calls

4 calls:

81.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
20.0ms	(-.f64 (.f64 g g) (.f64 h h))
17.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
15.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2989 to 2098 computations (29.8% saved)

simplify128.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-neg_binary64`
539×	`associate-l_binary64`
449×	`fma-def_binary64`
259×	`distribute-rgt-in_binary64`
255×	`distribute-lft-in_binary64`

Counts

99 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	2816
1	503	2676
2	1432	2612
3	4883	2612
4	5311	2612

prune154.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	64	17	81

Error

29.7b

Counts

81 → 17

Alt Table

Status	Error	Program
	33.6b	(fma.f64 (cbrt.f64 -1/2) (.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	53.0b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a))))
	37.2b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a))))
	46.4b	(+.f64 (cbrt.f64 0) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (*.f64 2 a))))
▶	30.9b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (.f64 2 a))))
	45.9b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (log.f64 (exp.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))))))
	56.4b	(fma.f64 (pow.f64 a -1/3) (.f64 (cbrt.f64 1/2) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))) g))) (cbrt.f64 0))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	46.7b	(fma.f64 (cbrt.f64 -1/2) (cbrt.f64 (.f64 (/.f64 2 a) g)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	39.7b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (*.f64 2 a))))
	36.1b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a)))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	44.0b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (.f64 2 a))))
	50.4b	(.f64 (cbrt.f64 1/2) (fma.f64 (pow.f64 a -1/3) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a))))
	43.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 g -2)) (cbrt.f64 (*.f64 2 a))))
	33.1b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	48.9b	(fma.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (/.f64 -1 g))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))

Compiler

Compiled 3243 to 1536 computations (52.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (.f64 g g) (.f64 h h))
2.2b	(-.f64 (.f64 g g) (.f64 h h))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite251.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

29.7b

Rules

8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
3.0ms	(-.f64 (.f64 g g) (.f64 h h))
3.0ms	(-.f64 (.f64 g g) (.f64 h h))

Compiler

Compiled 2821 to 904 computations (68% saved)

series103.0ms (1.2%)

Error

29.7b

Counts

4 → 30

Calls

4 calls:

18.0ms	(-.f64 (.f64 g g) (.f64 h h))
18.0ms	(-.f64 (.f64 g g) (.f64 h h))
14.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
13.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2453 to 1676 computations (31.7% saved)

simplify145.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1045×	`fma-neg_binary64`
338×	`neg-mul-1_binary64`
332×	`*-commutative_binary64`
281×	`distribute-rgt-neg-out_binary64`
253×	`distribute-lft-neg-out_binary64`

Counts

100 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2573
1	245	2396
2	560	2380
3	1789	2380
4	3584	2380
5	4954	2380
6	5007	2380

prune117.0ms (1.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	59	16	75

Error

29.7b

Counts

75 → 16

Alt Table

Status	Error	Program
	50.4b	(.f64 (cbrt.f64 1/2) (fma.f64 (pow.f64 a -1/3) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a))))
	50.9b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g)) (cbrt.f64 (.f64 2 a))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	46.3b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (.f64 2 a))) (/.f64 (cbrt.f64 0) (cbrt.f64 (.f64 2 a))))
	45.9b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (log.f64 (exp.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))))))
	56.4b	(fma.f64 (pow.f64 a -1/3) (.f64 (cbrt.f64 1/2) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))) g))) (cbrt.f64 0))
	33.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	46.7b	(fma.f64 (cbrt.f64 -1/2) (cbrt.f64 (.f64 (/.f64 2 a) g)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	39.7b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (*.f64 2 a))))
	36.1b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a)))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	44.0b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (.f64 2 a))))
	33.6b	(fma.f64 (cbrt.f64 -1/2) (.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))
	37.2b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g)) (cbrt.f64 (/.f64 1 a))) (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (*.f64 2 a))))
	43.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 g -2)) (cbrt.f64 (*.f64 2 a))))
	33.1b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	48.9b	(fma.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (/.f64 -1 g))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))))

Compiler

Compiled 2024 to 939 computations (53.6% saved)

regimes2.0s (24%)

Accuracy

Total 1.9b remaining (5.8%)

Threshold costs 0b (0%)

Compiler

Compiled 59977 to 35159 computations (41.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	37	54
2	50	54
3	61	54
4	66	54
5	67	54
6	67	54

end1.0ms (0%)

Compiler: Compiled 37 to 21 computations (43.2% saved)

sample2.7s (32.2%)

Algorithm

1×

intervals

Results

1.8s	7576×	body	256	valid
152.0ms	1259×	body	128	nan
54.0ms	424×	body	128	valid

Compiler

Compiled 702 to 415 computations (40.9% saved)

Details

analyze689.0ms (8.2%)

sample80.0ms (0.9%)

simplify205.0ms (2.4%)

prune4.0ms (0.1%)

localize24.0ms (0.3%)

rewrite185.0ms (2.2%)

series205.0ms (2.4%)

simplify162.0ms (1.9%)

prune115.0ms (1.4%)

localize25.0ms (0.3%)

rewrite186.0ms (2.2%)

series177.0ms (2.1%)

simplify116.0ms (1.4%)

prune137.0ms (1.6%)

localize22.0ms (0.3%)

rewrite249.0ms (3%)

series189.0ms (2.2%)

simplify128.0ms (1.5%)

prune154.0ms (1.8%)

localize21.0ms (0.2%)

rewrite251.0ms (3%)

series103.0ms (1.2%)

simplify145.0ms (1.7%)

prune117.0ms (1.4%)

regimes2.0s (24%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.7s (32.2%)

Profiling