Details

analyze650.0ms (5.8%)

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
34.7%	55.4%	9.9%	9
36.1%	51.1%	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)

sample2.5s (22.1%)

Results

759.0ms	5375×	body	128	valid
553.0ms	1150×	body	2048	valid
283.0ms	730×	body	1024	valid
245.0ms	414×	body	4096	valid
121.0ms	1012×	body	128	invalid
113.0ms	385×	body	512	valid
42.0ms	202×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify87.0ms (0.8%)

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 → 2

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

35.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	23.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series115.0ms (1%)

Counts

4 → 96

Calls

4 calls:

47.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
33.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
27.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite104.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
317×	`egg-rr`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Counts

4 → 317

Calls

4 calls:

84.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
84.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
84.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
84.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	234	55
2	3299	55
3	4945	55

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
493×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
361×	`fma-def_binary64`
191×	`associate-*l/_binary64`

Counts

413 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	388	2175
2	1292	2133
3	4966	2133

prune320.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	374	11	385
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	375	11	386

Error

5.5b

Counts

386 → 11

Alt Table

Status	Error	Program
	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	35.6b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
	46.0b	(/.f64 (*.f64 -2 b_2) a)
	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2) a)
	42.2b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	56.7b	(/.f64 (-.f64 b_2 b_2) a)
	35.8b	(.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
	46.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.2b	(*.f64 -1/2 (/.f64 c b_2))
	45.0b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
▶	35.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 9602 to 2904 computations (69.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	23.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series50.0ms (0.4%)

Counts

1 → 20

Calls

1 calls:

49.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

rewrite62.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`fma-def_binary64`
320×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`

Counts

1 → 43

Calls

1 calls:

61.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	267	18
2	3403	18
3	5037	18

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
217×	`associate-r_binary64`

Counts

63 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	204	642
2	668	624
3	3419	624
4	4941	624

prune301.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	380	1	381
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	380	12	392

Error

5.5b

Counts

392 → 12

Alt Table

Status	Error	Program
▶	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	35.6b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
	46.0b	(/.f64 (*.f64 -2 b_2) a)
	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2) a)
	42.2b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	56.7b	(/.f64 (-.f64 b_2 b_2) a)
	46.0b	(.f64 (.f64 b_2 -2) (/.f64 1 a))
	35.8b	(.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
	46.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.2b	(*.f64 -1/2 (/.f64 c b_2))
	45.0b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
✓	35.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 10131 to 3560 computations (64.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	23.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series720.0ms (6.4%)

Counts

1 → 20

Calls

1 calls:

720.0ms

(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) -1)

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`fma-def_binary64`
323×	`fma-neg_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`

Counts

1 → 46

Calls

1 calls:

59.0ms

(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) -1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	272	18
2	3530	18
3	5179	18

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
217×	`associate-r_binary64`

Counts

66 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	204	642
2	668	624
3	3419	624
4	4941	624

prune225.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	384	12	396

Error

5.5b

Counts

396 → 12

Alt Table

Status	Error	Program
✓	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	35.6b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
	46.0b	(/.f64 (*.f64 -2 b_2) a)
▶	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2) a)
	42.2b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	56.7b	(/.f64 (-.f64 b_2 b_2) a)
	46.0b	(.f64 (.f64 b_2 -2) (/.f64 1 a))
	35.8b	(.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
	46.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.2b	(*.f64 -1/2 (/.f64 c b_2))
	45.0b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
✓	35.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 10175 to 3526 computations (65.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 a c)) 2)
✓	0.6b	(-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2)
✓	11.9b	(cbrt.f64 (*.f64 a c))
✓	23.3b	(sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2)))

series2.1s (19.1%)

Counts

4 → 120

Calls

4 calls:

734.0ms	(sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2)))
732.0ms	(-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2)
342.0ms	(pow.f64 (cbrt.f64 (*.f64 a c)) 2)
326.0ms	(cbrt.f64 (*.f64 a c))

rewrite70.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`prod-diff_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
163×	`egg-rr`
132×	`add-sqr-sqrt_binary64`

Counts

4 → 163

Calls

4 calls:

66.0ms	(pow.f64 (cbrt.f64 (*.f64 a c)) 2)
66.0ms	(-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2)
66.0ms	(cbrt.f64 (*.f64 a c))
66.0ms	(sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	272	42
2	2845	42
3	5022	42

simplify116.0ms (1%)

Algorithm

1×	egg-herbie

Rules

409×	`times-frac_binary64`
323×	`associate-r_binary64`
278×	`associate-/l*_binary64`
273×	`associate-l_binary64`
259×	`fma-def_binary64`

Counts

283 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	2839
1	411	2743
2	1051	2587
3	4841	2363
4	4974	2363
5	4950	2363

prune170.0ms (1.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	288	12	300

Error

5.5b

Counts

300 → 12

Alt Table

Status	Error	Program
✓	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	35.6b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
	46.0b	(/.f64 (*.f64 -2 b_2) a)
✓	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 a c)) 2) (neg.f64 (cbrt.f64 (.f64 a c))) (*.f64 b_2 b_2))) b_2) a)
	42.2b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	56.7b	(/.f64 (-.f64 b_2 b_2) a)
	46.0b	(.f64 (.f64 b_2 -2) (/.f64 1 a))
	35.8b	(.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
	46.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.2b	(*.f64 -1/2 (/.f64 c b_2))
	45.0b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
✓	35.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 7227 to 2905 computations (59.8% saved)

regimes3.1s (28%)

Accuracy

Total 4.4b remaining (44.6%)

Threshold costs 0b (0%)

Counts

154 → 3

Compiler

Compiled 13016 to 7758 computations (40.4% saved)

bsearch59.0ms (0.5%)

Steps

Iters	Range		Point
7	5.19706392883188e-87	7.817895733659001e-85	6.8998787343294875e-87
6	-4.518577950027325e+154	-1.875287941105555e+150	-2.990742664210774e+150

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	54
1	35	54
2	50	54
3	60	54
4	67	54
5	69	54
6	69	54

end143.0ms (1.3%)

Compiler: Compiled 278 to 165 computations (40.6% saved)

Details

analyze650.0ms (5.8%)

sample2.5s (22.1%)

simplify87.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series115.0ms (1%)

rewrite104.0ms (0.9%)

simplify64.0ms (0.6%)

prune320.0ms (2.9%)

localize10.0ms (0.1%)

series50.0ms (0.4%)

rewrite62.0ms (0.6%)

simplify46.0ms (0.4%)

prune301.0ms (2.7%)

localize11.0ms (0.1%)

series720.0ms (6.4%)

rewrite61.0ms (0.5%)

simplify48.0ms (0.4%)

prune225.0ms (2%)

localize11.0ms (0.1%)

series2.1s (19.1%)

rewrite70.0ms (0.6%)

simplify116.0ms (1%)

prune170.0ms (1.5%)

regimes3.1s (28%)

bsearch59.0ms (0.5%)

simplify4.0ms (0%)

end143.0ms (1.3%)

Profiling