Details

analyze1.3s (14.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample54.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	44×	body	2048	valid
11.0ms	165×	body	128	valid
5.0ms	21×	body	1024	valid
4.0ms	10×	body	4096	valid
2.0ms	35×	body	128	nan
2.0ms	10×	body	512	valid
1.0ms	10×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify116.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 45 to 27 computations (40% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite213.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

33.7b

Rules

52×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
19×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

53.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2616 to 463 computations (82.3% saved)

series244.0ms (2.7%)

Error

6.0b

Counts

4 → 73

Calls

4 calls:

124.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
39.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
35.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2718 to 1827 computations (32.8% saved)

simplify236.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
381×	`associate-*l/_binary64`
277×	`cancel-sign-sub-inv_binary64`
258×	`associate-/r/_binary64`
205×	`distribute-rgt-neg-in_binary64`

Counts

193 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	4549
1	565	3752
2	1913	3510
3	4853	3509
4	5073	3509

prune77.0ms (0.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	139	15	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	16	155

Error

7.9b

Counts

155 → 16

Alt Table

Status	Error	Program
▶	33.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	44.7b	(/.f64 (*.f64 b_2 -2) a)
	39.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	44.4b	(/.f64 (.f64 (/.f64 (.f64 c a) b_2) -1/2) a)
	48.7b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	49.6b	(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
✓	34.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	51.1b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b_2 5)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)))
	35.6b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a))))) b_2) a)
	46.9b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	34.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	36.6b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.6b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	33.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 a)))

Compiler

Compiled 2411 to 788 computations (67.3% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite103.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

20×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

4 → 84

Calls

4 calls:

7.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
6.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
4.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
3.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 3378 to 476 computations (85.9% saved)

series99.0ms (1.1%)

Error

7.9b

Counts

4 → 31

Calls

4 calls:

52.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
19.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
12.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
11.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 2879 to 1474 computations (48.8% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
691×	`associate-/l*_binary64`
575×	`associate-l_binary64`
434×	`associate-/r*_binary64`
237×	`fma-neg_binary64`

Counts

115 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1803
1	265	1425
2	945	1350
3	4534	1350
4	5146	1350

prune58.0ms (0.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	47	16	63

Error

7.9b

Counts

63 → 16

Alt Table

Status	Error	Program
✓	33.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	44.7b	(/.f64 (*.f64 b_2 -2) a)
	39.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	44.4b	(/.f64 (.f64 (/.f64 (.f64 c a) b_2) -1/2) a)
	48.7b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	49.6b	(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
✓	34.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	51.1b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b_2 5)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)))
	35.6b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a))))) b_2) a)
	46.9b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	34.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	36.6b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.6b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
▶	33.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 a)))

Compiler

Compiled 1639 to 533 computations (67.5% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
0.6b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite124.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
12×	`sqrt-prod_binary64`

Counts

4 → 96

Calls

4 calls:

7.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
7.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
5.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
4.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 3777 to 529 computations (86% saved)

series375.0ms (4.2%)

Error

7.9b

Counts

4 → 38

Calls

4 calls:

202.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
108.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
23.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
23.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 3467 to 2054 computations (40.8% saved)

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
691×	`associate-/l*_binary64`
575×	`associate-l_binary64`
434×	`associate-/r*_binary64`
237×	`fma-neg_binary64`

Counts

134 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2750
1	265	1994
2	945	1844
3	4534	1844
4	5146	1844

prune64.0ms (0.7%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	70	16	86

Error

7.9b

Counts

86 → 16

Alt Table

Status	Error	Program
✓	33.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	44.7b	(/.f64 (*.f64 b_2 -2) a)
	39.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	44.4b	(/.f64 (.f64 (/.f64 (.f64 c a) b_2) -1/2) a)
	48.7b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	49.6b	(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
✓	34.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	51.1b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b_2 5)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)))
	35.6b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a))))) b_2) a)
	46.9b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
▶	34.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	36.6b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.6b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
✓	33.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 a)))

Compiler

Compiled 1884 to 569 computations (69.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
7.9b	(-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2)
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))
12.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite152.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

35×	`add-sqr-sqrt_binary64`
30×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
10.0ms	(-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2)
4.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
4.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 2766 to 521 computations (81.2% saved)

series258.0ms (2.9%)

Error

7.9b

Counts

4 → 38

Calls

4 calls:

95.0ms	(-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2)
84.0ms	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
46.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
21.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

Compiler

Compiled 2167 to 1490 computations (31.2% saved)

simplify164.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
696×	`associate-/l*_binary64`
443×	`associate-/r*_binary64`
296×	`fma-neg_binary64`
259×	`*-commutative_binary64`

Counts

148 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2310
1	328	2137
2	1169	1972
3	4402	1972
4	5052	1972

prune71.0ms (0.8%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	11	12
Picked	1	0	1
Done	0	3	3
Total	95	16	111

Error

7.9b

Counts

111 → 16

Alt Table

Status	Error	Program
	33.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	44.7b	(/.f64 (*.f64 b_2 -2) a)
	35.7b	(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) b_2) a)
	36.0b	(/.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) 3)) b_2) a)
	39.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	44.4b	(/.f64 (.f64 (/.f64 (.f64 c a) b_2) -1/2) a)
	48.7b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	49.6b	(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
	34.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	51.1b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b_2 5)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)))
	35.6b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a))))) b_2) a)
	46.9b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	42.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.6b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	33.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 a)))

Compiler

Compiled 1387 to 466 computations (66.4% saved)

regimes2.7s (29.7%)

Accuracy

Total 2.6b remaining (25.8%)

Threshold costs 0b (0%)

Compiler

Compiled 16996 to 8498 computations (50% saved)

bsearch69.0ms (0.8%)

Steps

Iters	Range		Point
9	1.861635956926109e-51	1.7013829958205572e-45	4.6202567589438814e-51
9	-5.643543103535729e+73	-6.29576203068304e+64	-5.5612723658344555e+73

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	51
1	39	51
2	51	51
3	59	51
4	64	51
5	65	51
6	64	51

end2.0ms (0%)

Compiler: Compiled 38 to 23 computations (39.5% saved)

sample2.2s (24%)

Algorithm

1×

intervals

Results

466.0ms	5199×	body	128	valid
421.0ms	1082×	body	2048	valid
245.0ms	730×	body	1024	valid
220.0ms	433×	body	4096	valid
83.0ms	353×	body	512	valid
76.0ms	796×	body	128	nan
31.0ms	203×	body	256	valid
21.0ms	272×	body	128	invalid

Compiler

Compiled 400 to 224 computations (44% saved)

Details

analyze1.3s (14.5%)

sample54.0ms (0.6%)

simplify116.0ms (1.3%)

prune5.0ms (0.1%)

localize12.0ms (0.1%)

rewrite213.0ms (2.4%)

series244.0ms (2.7%)

simplify236.0ms (2.6%)

prune77.0ms (0.9%)

localize28.0ms (0.3%)

rewrite103.0ms (1.1%)

series99.0ms (1.1%)

simplify90.0ms (1%)

prune58.0ms (0.6%)

localize33.0ms (0.4%)

rewrite124.0ms (1.4%)

series375.0ms (4.2%)

simplify181.0ms (2%)

prune64.0ms (0.7%)

localize21.0ms (0.2%)

rewrite152.0ms (1.7%)

series258.0ms (2.9%)

simplify164.0ms (1.8%)

prune71.0ms (0.8%)

regimes2.7s (29.7%)

bsearch69.0ms (0.8%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample2.2s (24%)

Profiling