Details

analyze651.0ms (5.6%)

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 (20.4%)

Results

783.0ms	5418×	body	128	valid
629.0ms	1153×	body	2048	valid
304.0ms	724×	body	1024	valid
252.0ms	398×	body	4096	valid
144.0ms	1110×	body	128	invalid
117.0ms	366×	body	512	valid
46.0ms	197×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify348.0ms (3%)

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

33.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	33.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	33.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 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 b b) (.f64 (*.f64 3 a) c))
✓	0.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series191.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
56.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-neg_binary64`
319×	`cancel-sign-sub-inv_binary64`
242×	`distribute-rgt-neg-in_binary64`
156×	`associate-r_binary64`
151×	`distribute-rgt-neg-out_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	4256
1	716	3931
2	2528	3797
3	4700	3771
4	5026	3771

prune175.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	196	11	207
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	197	12	209

Error

8.0b

Counts

209 → 12

Alt Table

Status	Error	Program
▶	32.2b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) a)))
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	33.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	32.2b	(/.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))
	46.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
	51.5b	(exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (log.f64 (.f64 3 a))))
	37.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	33.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
	46.5b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	46.3b	(*.f64 -2/3 (/.f64 b a))
	42.4b	(*.f64 -1/2 (/.f64 c b))
	43.4b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))

Compiler

Compiled 5805 to 3430 computations (40.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 3 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) a))
✓	0.2b	(.f64 c (.f64 a -3))
✓	0.5b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
✓	15.4b	(sqrt.f64 (.f64 c (.f64 a -3)))

series666.0ms (5.7%)

Counts

4 → 48

Calls

4 calls:

476.0ms	(/.f64 3 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) a))
164.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
20.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))
5.0ms	(.f64 c (.f64 a -3))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64`
95×	`*-un-lft-identity_binary64`
95×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

4 → 160

Calls

4 calls:

6.0ms	(/.f64 3 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) a))
4.0ms	(.f64 c (.f64 a -3))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b)
3.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))

simplify188.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
269×	`cancel-sign-sub-inv_binary64`
248×	`fma-neg_binary64`
185×	`associate-r_binary64`
178×	`distribute-rgt-neg-in_binary64`

Counts

208 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	369	6123
1	853	5496
2	3042	5439
3	4708	5438
4	4967	5438
5	4889	5438

prune258.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	287	4	291
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	291	12	303

Error

4.6b

Counts

303 → 12

Alt Table

Status	Error	Program
	46.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
	42.4b	(/.f64 1 (fma.f64 6 (.f64 (/.f64 b (.f64 -3 c)) 1) (*.f64 3/2 (/.f64 a b))))
	51.5b	(exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (log.f64 (.f64 3 a))))
	37.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	33.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
▶	32.2b	(/.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)) (*.f64 a (cbrt.f64 3))))
	46.5b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	33.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	42.4b	(*.f64 -1/2 (/.f64 c b))
	44.6b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b) a)))
	43.4b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	46.3b	(/.f64 1 (*.f64 -3/2 (/.f64 a b)))

Compiler

Compiled 9323 to 6121 computations (34.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 a (cbrt.f64 3))
✓	0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)) (*.f64 a (cbrt.f64 3)))
✓	0.5b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)
✓	15.4b	(sqrt.f64 (.f64 -3 (.f64 c a)))

series649.0ms (5.6%)

Counts

4 → 24

Calls

4 calls:

465.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)) (*.f64 a (cbrt.f64 3)))
158.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)
22.0ms	(sqrt.f64 (.f64 -3 (.f64 c a)))
4.0ms	(*.f64 a (cbrt.f64 3))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cbrt-cube_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

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

simplify192.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
378×	`fma-neg_binary64`
263×	`cancel-sign-sub-inv_binary64`
225×	`associate-r_binary64`
200×	`associate-l_binary64`

Counts

129 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	3922
1	648	2672
2	2383	2586
3	4512	2584
4	4994	2584
5	4998	2584
6	4878	2584

prune300.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	172	12	184

Error

4.6b

Counts

184 → 12

Alt Table

Status	Error	Program
	46.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
	42.4b	(/.f64 1 (fma.f64 6 (.f64 (/.f64 b (.f64 -3 c)) 1) (*.f64 3/2 (/.f64 a b))))
	51.5b	(exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (log.f64 (.f64 3 a))))
	37.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
▶	33.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
✓	32.2b	(/.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)) (*.f64 a (cbrt.f64 3))))
	46.5b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	33.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	42.4b	(*.f64 -1/2 (/.f64 c b))
	44.6b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b) a)))
	43.4b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	46.3b	(/.f64 1 (*.f64 -3/2 (/.f64 a b)))

Compiler

Compiled 6362 to 4441 computations (30.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 a) c)
	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f64 (*.f64 3 a) c)

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 3 a) c)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-l_binary64`
477×	`unswap-sqr_binary64`
383×	`associate-r_binary64`
351×	`*-commutative_binary64`
334×	`log-div_binary64`

Counts

44 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	380
1	99	344
2	366	344
3	1031	344
4	1241	344
5	1501	344
6	1934	344
7	4036	344
8	4924	344
9	5048	344

prune150.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	168	12	180

Error

4.6b

Counts

180 → 12

Alt Table

Status	Error	Program
	43.4b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	46.3b	(/.f64 (/.f64 (*.f64 b -2) 3) a)
	46.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
	42.4b	(/.f64 1 (fma.f64 6 (.f64 (/.f64 b (.f64 -3 c)) 1) (*.f64 3/2 (/.f64 a b))))
	51.5b	(exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (log.f64 (.f64 3 a))))
	37.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
✓	33.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
✓	32.2b	(/.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) b) b)) (*.f64 a (cbrt.f64 3))))
	33.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	42.4b	(*.f64 -1/2 (/.f64 c b))
	44.6b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))) b) b) a)))
	46.3b	(/.f64 1 (*.f64 -3/2 (/.f64 a b)))

Compiler

Compiled 4372 to 2543 computations (41.8% saved)

regimes4.9s (41.8%)

Accuracy

Total 6.8b remaining (71.1%)

Threshold costs 0b (0%)

Counts

237 → 3

Compiler

Compiled 32157 to 23282 computations (27.6% saved)

bsearch75.0ms (0.6%)

Steps

Iters	Range		Point
10	4.4531898587707325e-46	2.4190282902010186e-35	4.458754763303836e-44
1	-1.8788982853712545e+155	-1.2803009199407046e+147	-1.540932896291113e+151

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	77
1	48	73
2	66	73
3	73	73
4	76	73
5	77	73
6	76	73

end228.0ms (2%)

Compiler: Compiled 338 to 235 computations (30.5% saved)

Details

analyze651.0ms (5.6%)

sample2.4s (20.4%)

simplify348.0ms (3%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series191.0ms (1.6%)

rewrite30.0ms (0.3%)

simplify126.0ms (1.1%)

prune175.0ms (1.5%)

localize10.0ms (0.1%)

series666.0ms (5.7%)

rewrite33.0ms (0.3%)

simplify188.0ms (1.6%)

prune258.0ms (2.2%)

localize13.0ms (0.1%)

series649.0ms (5.6%)

rewrite26.0ms (0.2%)

simplify192.0ms (1.6%)

prune300.0ms (2.6%)

localize13.0ms (0.1%)

series5.0ms (0%)

rewrite5.0ms (0%)

simplify75.0ms (0.6%)

prune150.0ms (1.3%)

regimes4.9s (41.8%)

bsearch75.0ms (0.6%)

simplify4.0ms (0%)

end228.0ms (2%)

Profiling