Details

analyze408.0ms (8.3%)

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 33 to 24 computations (27.3% saved)

sample45.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	138×	body	256	valid
8.0ms	287×	pre	128	true
5.0ms	38×	body	512	valid
4.0ms	80×	body	128	valid
1.0ms	31×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify342.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1261×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
772×	`distribute-rgt-in_binary64`
702×	`distribute-lft-in_binary64`
619×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	32	24
2	65	24
3	128	24
4	178	24
5	287	24
6	460	24
7	754	24
8	1120	24
9	1142	24
10	1799	24
11	2162	24
12	1953	24
13	2041	24
14	2105	24
15	2131	24
16	2843	24
17	2603	24
18	2841	24
19	2951	24
20	3071	24
21	3113	24
22	3183	24
23	3171	24
24	3171	24
25	2191	24
26	2141	24
27	2105	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune4.0ms (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

53.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	53.9b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite140.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

50.7b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `sqrt-prod_binary64` `times-frac_binary64` `associate-/l*_binary64`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1903 to 1105 computations (41.9% saved)

series212.0ms (4.3%)

Error

0.2b

Counts

4 → 72

Calls

4 calls:

59.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
49.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
41.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
37.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2658 to 1932 computations (27.3% saved)

simplify130.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64`
230×	`distribute-rgt-in_binary64`
199×	`distribute-lft-in_binary64`
182×	`cancel-sign-sub-inv_binary64`
181×	`div-sub_binary64`

Counts

146 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3603
1	550	3323
2	1858	3272
3	4753	3272
4	5209	3272

prune68.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Error

0.2b

Counts

123 → 7

Alt Table

Status	Error	Program
	54.1b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) a) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) (sqrt.f64 b)) 2))
	5.1b	(neg.f64 (/.f64 c b))
	1.5b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.9b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 3)) (.f64 a 2))
	53.5b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
▶	1.2b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	54.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b)) (.f64 a (.f64 c -4)))) (.f64 a 2))

Compiler

Compiled 2114 to 1183 computations (44% saved)

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 a (.f64 c c))
0.3b	(.f64 (.f64 a a) (pow.f64 c 3))
0.4b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
0.4b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))

rewrite306.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

105×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
39×	`div-exp_binary64`
33×	`pow-to-exp_binary64` `pow-exp_binary64`
28×	`add-cbrt-cube_binary64`

Counts

4 → 156

Calls

4 calls:

9.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
8.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
8.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
6.0ms	(.f64 a (.f64 c c))

Compiler

Compiled 5622 to 3337 computations (40.6% saved)

series183.0ms (3.7%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

70.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
54.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
29.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
24.0ms	(.f64 a (.f64 c c))

Compiler

Compiled 2766 to 1986 computations (28.2% saved)

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/r/_binary64`
515×	`unswap-sqr_binary64`
259×	`associate-l_binary64`
246×	`times-frac_binary64`
227×	`associate-/l*_binary64`

Counts

186 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	2953
1	500	2655
2	2493	2604
3	5136	2604

prune91.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

0.2b

Counts

141 → 7

Alt Table

Status	Error	Program
	54.1b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) a) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) (sqrt.f64 b)) 2))
	5.1b	(neg.f64 (/.f64 c b))
▶	1.5b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.9b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 3)) (.f64 a 2))
	53.5b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
✓	1.2b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	54.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b)) (.f64 a (.f64 c -4)))) (.f64 a 2))

Compiler

Compiled 2243 to 1346 computations (40% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
0.4b	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
0.5b	(.f64 (.f64 a c) (*.f64 a c))
0.7b	(pow.f64 (*.f64 a c) 3)

rewrite275.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

90×	`add-exp-log_binary64`
46×	`pow1_binary64`
45×	`prod-exp_binary64`
36×	`pow-exp_binary64`
35×	`pow-to-exp_binary64`

Counts

4 → 155

Calls

4 calls:

8.0ms	(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
7.0ms	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
6.0ms	(.f64 (.f64 a c) (*.f64 a c))
4.0ms	(pow.f64 (*.f64 a c) 3)

Compiler

Compiled 6321 to 3698 computations (41.5% saved)

series166.0ms (3.4%)

Error

0.2b

Counts

4 → 27

Calls

4 calls:

72.0ms	(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
32.0ms	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
30.0ms	(pow.f64 (*.f64 a c) 3)
27.0ms	(.f64 (.f64 a c) (*.f64 a c))

Compiler

Compiled 2984 to 2018 computations (32.4% saved)

simplify110.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
444×	`unswap-sqr_binary64`
382×	`log-prod_binary64`
379×	`associate-/l/_binary64`
249×	`associate-/r/_binary64`

Counts

182 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2373
1	363	1954
2	1601	1922
3	4401	1922
4	4967	1922

prune97.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	155	7	162

Error

0.2b

Counts

162 → 7

Alt Table

Status	Error	Program
	54.1b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) a) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) (sqrt.f64 b)) 2))
▶	5.1b	(neg.f64 (/.f64 c b))
✓	1.5b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.9b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 3)) (.f64 a 2))
	53.5b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
✓	1.2b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	54.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b)) (.f64 a (.f64 c -4)))) (.f64 a 2))

Compiler

Compiled 2760 to 1612 computations (41.6% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune8.0ms (0.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Error

0.2b

Counts

7 → 7

Alt Table

Status	Error	Program
	54.1b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) a) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) (sqrt.f64 b)) 2))
	5.1b	(neg.f64 (/.f64 c b))
	1.5b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.9b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 3)) (.f64 a 2))
	53.5b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	1.2b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	54.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b)) (.f64 a (.f64 c -4)))) (.f64 a 2))

Compiler

Compiled 240 to 155 computations (35.4% saved)

regimes488.0ms (9.9%)

Accuracy

Total 1.3b remaining (86.6%)

Threshold costs 0b (0%)

Compiler

Compiled 10008 to 6618 computations (33.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64`
10×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
6×	`unsub-neg_binary64` `distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	86	61
4	119	61
5	146	61
6	170	61
7	184	61
8	191	61
9	193	61
10	191	61

end1.0ms (0%)

Compiler: Compiled 44 to 33 computations (25% saved)

sample1.7s (33.6%)

Algorithm

1×

intervals

Results

372.0ms	3830×	body	256	valid
267.0ms	8816×	pre	128	true
203.0ms	1446×	body	512	valid
132.0ms	2724×	body	128	valid
39.0ms	816×	body	128	nan

Compiler

Compiled 320 to 215 computations (32.8% saved)

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	86	61
4	119	61
5	146	61
6	170	61
7	184	61
8	191	61
9	193	61
10	191	61

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	86	61
4	119	61
5	146	61
6	170	61
7	184	61
8	191	61
9	193	61
10	191	61

Details

analyze408.0ms (8.3%)

sample45.0ms (0.9%)

simplify342.0ms (7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite140.0ms (2.9%)

series212.0ms (4.3%)

simplify130.0ms (2.6%)

prune68.0ms (1.4%)

localize28.0ms (0.6%)

rewrite306.0ms (6.2%)

series183.0ms (3.7%)

simplify99.0ms (2%)

prune91.0ms (1.9%)

localize29.0ms (0.6%)

rewrite275.0ms (5.6%)

series166.0ms (3.4%)

simplify110.0ms (2.2%)

prune97.0ms (2%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune8.0ms (0.2%)

regimes488.0ms (9.9%)

simplify8.0ms (0.2%)

end1.0ms (0%)

sample1.7s (33.6%)

Profiling

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	86	61
4	119	61
5	146	61
6	170	61
7	184	61
8	191	61
9	193	61
10	191	61