Details

analyze347.0ms (5.9%)

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)

sample1.8s (30.7%)

Results

790.0ms	5267×	body	128	valid
790.0ms	2988×	body	256	valid
131.0ms	924×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify263.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	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

44.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	44.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	44.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	39.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series189.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

84.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
53.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite122.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

156× egg-rr

Counts

4 → 156

Calls

2 calls:

117.0ms

((+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	337	62
2	4158	62
3	4987	62
4	4850	62
0	0	0
1	0	0

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
436×	`fma-def_binary64`
432×	`fma-neg_binary64`
426×	`associate-/r*_binary64`

Counts

252 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	398	2164
2	1327	2078
3	4954	2078
4	5218	2078

prune149.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	223	5	228
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	224	6	230

Error

0.3b

Counts

230 → 6

Alt Table

Status	Error	Program
	1.9b	(/.f64 (-.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (.f64 2 a))
	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	44.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
▶	1.9b	(-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	44.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (.f64 (.f64 4 a) c))) (-.f64 b (sqrt.f64 (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	44.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 6140 to 3637 computations (40.8% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
✓	0.4b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
✓	0.4b	(/.f64 (*.f64 c c) (pow.f64 b 3))
✓	0.4b	(.f64 (.f64 a a) (pow.f64 c 3))

series174.0ms (3%)

Counts

4 → 108

Calls

4 calls:

105.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
35.0ms	(/.f64 (*.f64 c c) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
15.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite76.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

111× egg-rr

Counts

4 → 111

Calls

2 calls:

73.0ms	((.f64 (.f64 a a) (pow.f64 c 3)) (/.f64 (.f64 c c) (pow.f64 b 3)) (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (*.f64 (pow.f64 a 3) (pow.f64 c 4)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	389	46
2	4337	46
3	4913	46
0	0	0
1	0	0

simplify124.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

711×	`associate-/l*_binary64`
614×	`associate-l_binary64`
518×	`associate-r_binary64`
406×	`sqr-pow_binary64`
367×	`associate-/r*_binary64`

Counts

219 → 117

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1296
1	52	1296
2	156	1296
3	660	1296
4	3816	1296
5	3872	1296
6	4063	1296
7	4392	1296
8	4734	1296
9	4998	1296

prune191.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	117	6	123

Error

0.3b

Counts

123 → 6

Alt Table

Status	Error	Program
▶	1.9b	(/.f64 (-.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (.f64 2 a))
	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	44.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	1.9b	(-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	44.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (.f64 (.f64 4 a) c))) (-.f64 b (sqrt.f64 (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	44.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 5389 to 3346 computations (37.9% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))

series285.0ms (4.8%)

Counts

4 → 24

Calls

4 calls:

154.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
99.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
21.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite276.0ms (4.7%)

Algorithm

2×	batch-egg-rewrite

Rules

107× egg-rr

Counts

4 → 107

Calls

2 calls:

274.0ms	((.f64 (.f64 c a) (.f64 c a)) (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 (pow.f64 c 4) (pow.f64 a 4)) (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	445	40
2	4502	40
3	5134	40
0	0	0
1	0	0

simplify169.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1022×	`sqr-pow_binary64`
785×	`associate-l_binary64`
636×	`*-commutative_binary64`
598×	`fabs-mul_binary64`
578×	`cube-prod_binary64`

Counts

131 → 109

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	240
1	16	240
2	35	240
3	88	240
4	295	240
5	1349	240
6	1413	240
7	1542	240
8	1721	240
9	1930	240
10	2180	240
11	2322	240
12	2724	240
13	3047	240
14	3626	240
15	3983	240
16	4262	240
17	4371	240
18	4402	240
19	4414	240
20	4876	240

prune262.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	109	6	115

Error

0.3b

Counts

115 → 6

Alt Table

Status	Error	Program
✓	1.9b	(/.f64 (-.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (.f64 2 a))
▶	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	44.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	1.9b	(-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	44.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (.f64 (.f64 4 a) c))) (-.f64 b (sqrt.f64 (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	44.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 5928 to 3681 computations (37.9% saved)

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))

series85.0ms (1.4%)

Counts

1 → 0

Calls

1 calls:

85.0ms

(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))

rewrite57.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

53× egg-rr

Counts

1 → 53

Calls

2 calls:

55.0ms	((/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	235	13
2	2592	13
3	5041	13
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune257.0ms (4.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	144	6	150

Error

0.3b

Counts

150 → 6

Alt Table

Status	Error	Program
✓	1.9b	(/.f64 (-.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (.f64 2 a))
✓	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	44.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	1.9b	(-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	44.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (.f64 (.f64 4 a) c))) (-.f64 b (sqrt.f64 (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	44.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 8365 to 5816 computations (30.5% saved)

regimes679.0ms (11.5%)

Accuracy

Total 2.5b remaining (86.3%)

Threshold costs 0b (0%)

Counts

89 → 1

Compiler

Compiled 13228 to 9422 computations (28.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	57
1	32	57
2	37	57
3	39	57
4	40	57
5	40	57

end182.0ms (3.1%)

Compiler: Compiled 312 to 217 computations (30.4% saved)

Details

analyze347.0ms (5.9%)

sample1.8s (30.7%)

simplify263.0ms (4.5%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series189.0ms (3.2%)

rewrite122.0ms (2.1%)

simplify81.0ms (1.4%)

prune149.0ms (2.5%)

localize23.0ms (0.4%)

series174.0ms (3%)

rewrite76.0ms (1.3%)

simplify124.0ms (2.1%)

prune191.0ms (3.2%)

localize28.0ms (0.5%)

series285.0ms (4.8%)

rewrite276.0ms (4.7%)

simplify169.0ms (2.9%)

prune262.0ms (4.4%)

localize44.0ms (0.7%)

series85.0ms (1.4%)

rewrite57.0ms (1%)

simplify7.0ms (0.1%)

prune257.0ms (4.4%)

regimes679.0ms (11.5%)

simplify4.0ms (0.1%)

end182.0ms (3.1%)

Profiling