Details

analyze349.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample126.0ms (1.6%)

Algorithm

1×

intervals

Results

18.0ms	246×	body	128	valid
10.0ms	280×	pre	128	true
4.0ms	24×	body	128	nan
1.0ms	10×	body	256	valid

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify349.0ms (4.5%)

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 (0.1%)

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

28.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	28.5b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	28.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series147.0ms (1.9%)

Counts

4 → 76

Calls

4 calls:

82.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
52.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
11.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.f64 1/3 a)

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 123

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)
0.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify106.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
340×	`distribute-rgt-in_binary64`
235×	`cancel-sign-sub-inv_binary64`
185×	`fma-neg_binary64`
160×	`associate-r_binary64`

Counts

199 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	5008
1	661	4039
2	2464	3848
3	4911	3848

prune166.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	210	11	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	212	11	223

Error

0.1b

Counts

223 → 11

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (exp.f64 (-.f64 (log.f64 1/3) (log.f64 a))))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
	8.9b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
	31.1b	(.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (cbrt.f64 b) (.f64 (cbrt.f64 b) (cbrt.f64 b))))) (fma.f64 (neg.f64 (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))) (/.f64 1/3 a))
	6.9b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	28.9b	(.f64 (+.f64 (fma.f64 1 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (neg.f64 (.f64 (sqrt.f64 b) (sqrt.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) (*.f64 (sqrt.f64 b) (sqrt.f64 b)))) (/.f64 1/3 a))
	28.5b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a)))
	7.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
	28.6b	(/.f64 (.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)) 1/3) (.f64 (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))) a))
	28.6b	(.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)) (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 1/3 a))

Compiler

Compiled 6513 to 3781 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	0.3b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(fma.f64 a (*.f64 c -3) 0)
	0.3b	(/.f64 1/3 a)

series54.0ms (0.7%)

Counts

2 → 44

Calls

2 calls:

47.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
6.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`fma-def_binary64`
6×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
324×	`associate-r_binary64`
309×	`fma-neg_binary64`
278×	`associate-l_binary64`
275×	`fma-def_binary64`

Counts

74 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1209
1	269	1139
2	779	1115
3	4055	1094
4	4913	1094

prune154.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	123	14	137

Error

0.0b

Counts

137 → 14

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))
	1.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	0.8b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.6b	(/.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (sqrt.f64 (/.f64 1/3 a)) (sqrt.f64 (/.f64 1/3 a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	28.6b	(.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)) (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 1/3 a))
▶	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	6.9b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	7.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (exp.f64 (-.f64 (log.f64 1/3) (log.f64 a))))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) b))

Compiler

Compiled 4695 to 2921 computations (37.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.3b	(fma.f64 a (.f64 c -3) (.f64 b b))
	0.3b	(fma.f64 a (*.f64 c -3) 0)
	0.3b	(/.f64 1/3 a)

series9.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

7.0ms

(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

459×	`distribute-rgt-in_binary64`
454×	`associate-/l/_binary64`
348×	`associate-/r/_binary64`
344×	`associate-l_binary64`
259×	`distribute-lft-in_binary64`

Counts

58 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	756
1	167	633
2	585	579
3	2090	531
4	3537	528
5	4246	528
6	4764	528
7	4989	528
8	4815	528

prune274.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Error

0.0b

Counts

174 → 11

Alt Table

Status	Error	Program
	0.8b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))
	0.6b	(/.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	6.9b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	0.9b	(/.f64 (.f64 (.f64 (.f64 a (.f64 c -3)) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
▶	0.3b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	7.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (exp.f64 (-.f64 (log.f64 1/3) (log.f64 a))))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
	28.6b	(.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)) (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 1/3 a))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) b))

Compiler

Compiled 6951 to 4189 computations (39.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
✓	0.2b	(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b)
✓	0.2b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	0.3b	(fma.f64 a (.f64 c -3) (.f64 b b))

series394.0ms (5.1%)

Counts

3 → 92

Calls

3 calls:

236.0ms

(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))

113.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.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)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

3 → 84

Calls

3 calls:

5.0ms

(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))

1.0ms

(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))

0.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
515×	`associate-/l*_binary64`
216×	`fma-def_binary64`
159×	`*-commutative_binary64`
105×	`sub-neg_binary64`

Counts

176 → 266

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	552	8822
1	1743	8514
2	5147	8514

prune445.0ms (5.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	346	5	351
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	356	6	362

Error

Counts

362 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (exp.f64 (log.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))))) b))
	6.9b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	0.3b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3)))) b))
	0.6b	(.f64 (/.f64 -1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	0.5b	(/.f64 (sqrt.f64 c) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (neg.f64 (sqrt.f64 c))))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))

Compiler

Compiled 15659 to 9662 computations (38.3% saved)

regimes3.1s (40.6%)

Accuracy

Total 0.3b remaining (90.5%)

Threshold costs 0.3b (90.5%)

Counts

369 → 1

Compiler

Compiled 60229 to 39355 computations (34.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	28	43
2	32	43
3	35	43
4	36	43
5	36	43

end1.0ms (0%)

Compiler: Compiled 31 to 20 computations (35.5% saved)

sample1.6s (20.5%)

Algorithm

1×

intervals

Results

555.0ms	7701×	body	128	valid
363.0ms	9000×	pre	128	true
84.0ms	1000×	body	128	nan
42.0ms	299×	body	256	valid

Compiler

Compiled 255 to 171 computations (32.9% saved)

Details

analyze349.0ms (4.5%)

sample126.0ms (1.6%)

simplify349.0ms (4.5%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

series147.0ms (1.9%)

rewrite28.0ms (0.4%)

simplify106.0ms (1.4%)

prune166.0ms (2.2%)

localize12.0ms (0.2%)

series54.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify61.0ms (0.8%)

prune154.0ms (2%)

localize14.0ms (0.2%)

series9.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify100.0ms (1.3%)

prune274.0ms (3.6%)

localize12.0ms (0.2%)

series394.0ms (5.1%)

rewrite15.0ms (0.2%)

simplify138.0ms (1.8%)

prune445.0ms (5.8%)

regimes3.1s (40.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.6s (20.5%)

Profiling