Details

analyze662.0ms (4.9%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (17.7%)

Results

722.0ms	5328×	body	128	valid
640.0ms	1145×	body	2048	valid
347.0ms	786×	body	1024	valid
278.0ms	431×	body	4096	valid
137.0ms	377×	body	512	valid
133.0ms	1015×	body	128	invalid
43.0ms	189×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify348.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

33.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	34.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 a) c)
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	1.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series227.0ms (1.7%)

Counts

4 → 100

Calls

4 calls:

157.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
55.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
10×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(.f64 (.f64 3 a) c)
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
621×	`fma-neg_binary64`
305×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-neg-in_binary64`
197×	`distribute-lft-neg-in_binary64`

Counts

180 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2955
1	523	2836
2	1806	2732
3	4518	2728
4	4998	2728
5	4919	2728

prune168.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	155	13	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Error

11.1b

Counts

170 → 14

Alt Table

Status	Error	Program
	35.0b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	34.4b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (.f64 3 a))
	39.0b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
▶	33.3b	(/.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))) (.f64 3 a))
	57.5b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	34.8b	(/.f64 (+.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))))) (.f64 3 a))
	45.7b	(/.f64 (.f64 -2 b) (.f64 3 a))
	50.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 3 a) (sqrt.f64 c)) (sqrt.f64 c))))) (*.f64 3 a))
	45.9b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	53.9b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	37.5b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	49.5b	(/.f64 (fma.f64 (/.f64 (.f64 c a) b) -3/2 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))
	34.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 4810 to 2830 computations (41.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 c (.f64 a -3))
✓	0.3b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -3))) b) b)))
✓	0.8b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
✓	13.5b	(sqrt.f64 (.f64 c (.f64 a -3)))

series390.0ms (2.9%)

Counts

4 → 48

Calls

4 calls:

187.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
176.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -3))) b) b)))
22.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))
5.0ms	(.f64 c (.f64 a -3))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
31×	`sqrt-prod_binary64`
30×	`pow1_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 133

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -3))) b) b)))
4.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))
4.0ms	(.f64 c (.f64 a -3))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

764×	`associate-/l*_binary64`
560×	`associate-/r*_binary64`
362×	`fma-def_binary64`
208×	`fma-neg_binary64`
180×	`associate-l_binary64`

Counts

181 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4673
1	428	3633
2	1534	3454
3	4959	3454
4	4943	3454

prune347.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	292	15	307

Error

11.1b

Counts

307 → 15

Alt Table

Status	Error	Program
	53.9b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	50.4b	(/.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b))) (.f64 3 a))
	35.0b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	34.4b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (.f64 3 a))
	39.0b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	37.5b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
▶	33.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))))) (sqrt.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)))) (.f64 3 a))
	34.8b	(/.f64 (+.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))))) (.f64 3 a))
	45.7b	(/.f64 (.f64 -2 b) (.f64 3 a))
	50.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 3 a) (sqrt.f64 c)) (sqrt.f64 c))))) (*.f64 3 a))
	45.9b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	57.5b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	49.5b	(/.f64 (fma.f64 (/.f64 (.f64 c a) b) -3/2 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))
	34.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 11983 to 7812 computations (34.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -3))) b) b)))
✓	0.3b	(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))
	0.8b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
	13.5b	(sqrt.f64 (.f64 c (.f64 a -3)))

series2.2s (16.2%)

Counts

2 → 24

Calls

2 calls:

1.6s

(*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b)))

586.0ms

(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`cbrt-prod_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
14×	`cbrt-div_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 75

Calls

2 calls:

9.0ms

(*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b)))

2.0ms

(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) b) b))

simplify128.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

939×	`times-frac_binary64`
457×	`fma-def_binary64`
298×	`fma-neg_binary64`
157×	`cancel-sign-sub-inv_binary64`
136×	`associate-r_binary64`

Counts

99 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	5125
1	612	4766
2	1756	4224
3	4946	4220
4	5095	4220

prune949.0ms (7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	594	2	596
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	595	16	611

Error

11.1b

Counts

611 → 16

Alt Table

Status	Error	Program
	53.9b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	50.4b	(/.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b))) (.f64 3 a))
	35.0b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	34.4b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (.f64 3 a))
	34.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))))))) (sqrt.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)))) (.f64 3 a))
	39.0b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	57.5b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	34.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))))) (sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)))))) (.f64 3 a))
	37.5b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
✓	33.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))))) (sqrt.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)))) (.f64 3 a))
	34.8b	(/.f64 (+.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (.f64 c a) -3 (.f64 b b)))))) (.f64 3 a))
	45.7b	(/.f64 (.f64 -2 b) (.f64 3 a))
	49.5b	(/.f64 (fma.f64 (/.f64 (.f64 c a) b) -3/2 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))
▶	34.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	45.9b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))

Compiler

Compiled 42109 to 28500 computations (32.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	1.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
✓	20.7b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series198.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

90.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
61.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
1.0ms	(/.f64 1/3 a)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 128

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
2.0ms	(/.f64 1/3 a)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
318×	`distribute-rgt-in_binary64`
276×	`cancel-sign-sub-inv_binary64`
271×	`neg-mul-1_binary64`
161×	`associate-r_binary64`

Counts

188 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	5224
1	709	4328
2	2581	4143
3	4488	4131
4	4864	4131

prune186.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	232	8	240
Fresh	10	4	14
Picked	0	1	1
Done	1	0	1
Total	243	13	256

Error

4.4b

Counts

256 → 13

Alt Table

Status	Error	Program
	38.9b	(*.f64 -1/2 (/.f64 c b))
	50.4b	(/.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b))) (.f64 3 a))
	33.2b	(/.f64 (.f64 1/3 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b)) a)
	35.0b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	34.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (sqrt.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))))))) (sqrt.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)))) (.f64 3 a))
	41.8b	(/.f64 (.f64 1/3 (+.f64 (.f64 a (.f64 c -3)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -3)))))))
	51.5b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 1/3 a)) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 1/3 a))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))))
	46.0b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	45.7b	(*.f64 -2/3 (/.f64 b a))
	45.7b	(/.f64 (.f64 -2 b) (.f64 3 a))
	43.6b	(.f64 1/3 (/.f64 (sqrt.f64 (neg.f64 (.f64 3 (*.f64 c a)))) a))
✓	34.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	42.6b	(fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))

Compiler

Compiled 6555 to 3843 computations (41.4% saved)

regimes4.5s (33.3%)

Accuracy

Total 3.5b remaining (38.7%)

Threshold costs 0b (0%)

Counts

245 → 4

Compiler

Compiled 36923 to 26023 computations (29.5% saved)

bsearch121.0ms (0.9%)

Steps

Iters	Range		Point
7	741614.038799508	18575342.685194008	1645583.6515607869
7	2.5008090626249936e-126	3.900927659939505e-124	2.543157513544152e-126
6	-3.999369888062522e+98	-4.985389729246998e+97	-3.9352038855422006e+98

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	94
1	64	92
2	81	92
3	97	92
4	107	92
5	112	92
6	113	92
7	110	92

end203.0ms (1.5%)

Compiler: Compiled 428 to 289 computations (32.5% saved)

Details

analyze662.0ms (4.9%)

sample2.4s (17.7%)

simplify348.0ms (2.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series227.0ms (1.7%)

rewrite22.0ms (0.2%)

simplify130.0ms (1%)

prune168.0ms (1.2%)

localize11.0ms (0.1%)

series390.0ms (2.9%)

rewrite32.0ms (0.2%)

simplify120.0ms (0.9%)

prune347.0ms (2.5%)

localize18.0ms (0.1%)

series2.2s (16.2%)

rewrite19.0ms (0.1%)

simplify128.0ms (0.9%)

prune949.0ms (7%)

localize10.0ms (0.1%)

series198.0ms (1.4%)

rewrite24.0ms (0.2%)

simplify135.0ms (1%)

prune186.0ms (1.4%)

regimes4.5s (33.3%)

bsearch121.0ms (0.9%)

simplify7.0ms (0%)

end203.0ms (1.5%)

Profiling