Details

analyze684.0ms (6.8%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (24%)

Results

750.0ms	5366×	body	128	valid
606.0ms	1162×	body	2048	valid
317.0ms	759×	body	1024	valid
276.0ms	417×	body	4096	valid
133.0ms	1074×	body	128	invalid
119.0ms	383×	body	512	valid
38.0ms	169×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

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

34.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	20.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series173.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

70.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
50.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
42.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite68.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

963×	`prod-diff_binary64`
209×	`log1p-udef_binary64`
119×	`egg-rr`
118×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`

Counts

4 → 119

Calls

4 calls:

65.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
65.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
65.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
65.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	235	59
2	2944	59
3	5021	59
0	0	0
1	0	0

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
480×	`associate-/l*_binary64`
434×	`associate-/r*_binary64`
344×	`fma-def_binary64`
209×	`fma-neg_binary64`

Counts

215 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	2081
1	351	1997
2	1169	1913
3	4896	1913
4	4993	1913

prune143.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	181	10	191

Error

4.5b

Counts

191 → 10

Alt Table

Status	Error	Program
	34.4b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.2b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) a))
✓	34.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
▶	34.3b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	58.3b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
	34.5b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1 a))))
	34.8b	(.f64 -1/2 (.f64 (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) 2)))
	43.8b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	43.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 4917 to 2954 computations (39.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.1b	(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) -1)
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	20.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series1.5s (15.4%)

Counts

2 → 40

Calls

2 calls:

1.3s	(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) -1)
226.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

rewrite62.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

963×	`prod-diff_binary64`
136×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
127×	`add-cbrt-cube_binary64`

Counts

2 → 80

Calls

2 calls:

60.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
60.0ms	(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	276	38
2	3305	38
3	4981	38
0	0	0
1	0	0

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
520×	`associate-/l*_binary64`
485×	`associate-/r*_binary64`
256×	`fma-def_binary64`
233×	`fma-neg_binary64`

Counts

120 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1240
1	318	1192
2	1113	1138
3	4905	1138
4	5047	1138

prune180.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	227	8	235

Error

4.5b

Counts

235 → 8

Alt Table

Status	Error	Program
✓	34.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	49.2b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
▶	34.3b	(.f64 -1/2 (pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) -1))
	43.8b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	34.4b	(.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	38.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
	38.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 6110 to 3783 computations (38.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) -1)
✓	0.2b	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	20.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series1.5s (15.3%)

Counts

2 → 40

Calls

2 calls:

1.3s	(pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) -1)
202.0ms	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))

rewrite64.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

62.0ms	(pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) -1)
62.0ms	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	314	38
2	3562	38
3	5198	38
0	0	0
1	0	0

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
520×	`associate-/l*_binary64`
485×	`associate-/r*_binary64`
256×	`fma-def_binary64`
233×	`fma-neg_binary64`

Counts

91 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1240
1	318	1192
2	1113	1138
3	4905	1138
4	5047	1138

prune143.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	196	8	204

Error

4.5b

Counts

204 → 8

Alt Table

Status	Error	Program
✓	34.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	49.2b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
✓	34.3b	(.f64 -1/2 (pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) -1))
	43.8b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
▶	34.4b	(.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	38.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
	38.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 5442 to 3492 computations (35.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	20.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series249.0ms (2.5%)

Counts

2 → 40

Calls

2 calls:

183.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
67.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

rewrite74.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

977×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
138×	`add-cbrt-cube_binary64`

Counts

2 → 65

Calls

2 calls:

72.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
72.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	302	38
2	3619	38
3	5327	38
0	0	0
1	0	0

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

642×	`times-frac_binary64`
414×	`associate-/r*_binary64`
398×	`associate-/l*_binary64`
341×	`associate-r_binary64`
283×	`associate-l_binary64`

Counts

105 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1163
1	297	1130
2	1007	1088
3	5121	1088

prune151.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	210	9	219

Error

4.5b

Counts

219 → 9

Alt Table

Status	Error	Program
✓	34.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	49.2b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
✓	34.3b	(.f64 -1/2 (pow.f64 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) -1))
	43.8b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
✓	34.4b	(.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	38.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
	45.3b	(.f64 -1/2 (/.f64 (/.f64 1 a) (fma.f64 1/2 (/.f64 b (.f64 a c)) (/.f64 -1/2 b))))
	38.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 5845 to 3771 computations (35.5% saved)

regimes1.9s (19%)

Accuracy

Total 4.3b remaining (43.1%)

Threshold costs 0b (0%)

Counts

128 → 3

Compiler

Compiled 10924 to 7782 computations (28.8% saved)

bsearch65.0ms (0.6%)

Steps

Iters	Range		Point
3	1.1930040529625274e+118	3.063545414621053e+119	2.112249961483768e+119
10	-3.3175280852393708e-115	-4.5028412856082614e-128	-8.184097496269323e-116

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	60
1	37	60
2	44	60
3	48	60
4	51	60
5	52	60
6	52	60

end137.0ms (1.4%)

Compiler: Compiled 250 to 170 computations (32% saved)

Details

analyze684.0ms (6.8%)

sample2.4s (24%)

simplify140.0ms (1.4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series173.0ms (1.7%)

rewrite68.0ms (0.7%)

simplify74.0ms (0.7%)

prune143.0ms (1.4%)

localize10.0ms (0.1%)

series1.5s (15.4%)

rewrite62.0ms (0.6%)

simplify81.0ms (0.8%)

prune180.0ms (1.8%)

localize11.0ms (0.1%)

series1.5s (15.3%)

rewrite64.0ms (0.6%)

simplify58.0ms (0.6%)

prune143.0ms (1.4%)

localize12.0ms (0.1%)

series249.0ms (2.5%)

rewrite74.0ms (0.7%)

simplify41.0ms (0.4%)

prune151.0ms (1.5%)

regimes1.9s (19%)

bsearch65.0ms (0.6%)

simplify4.0ms (0%)

end137.0ms (1.4%)

Profiling