Details

analyze668.0ms (8.6%)

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
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 (31.4%)

Results

691.0ms	5273×	body	128	valid
658.0ms	1228×	body	2048	valid
330.0ms	761×	body	1024	valid
283.0ms	430×	body	4096	valid
143.0ms	1064×	body	128	invalid
120.0ms	363×	body	512	valid
44.0ms	201×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify125.0ms (1.6%)

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`

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

Stop Event

1×	node limit

Counts

1 → 2

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

34.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.8b	(.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)
✓	0.3b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series109.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

42.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
30.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
27.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite63.0ms (0.8%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 119

Calls

4 calls:

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

simplify74.0ms (1%)

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`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

215 → 190

prune143.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

5.3b

Counts

191 → 9

Alt Table

Status	Error	Program
	42.4b	(.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	36.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
▶	34.8b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	49.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	34.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	48.7b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	35.0b	(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 1) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) a)))
	49.3b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a))))

Compiler

Compiled 4877 to 2932 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)
	0.3b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series1.0s (13.5%)

Counts

2 → 40

Calls

2 calls:

898.0ms	(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) -1)
143.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

rewrite107.0ms (1.4%)

Algorithm

1×	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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 80

Calls

2 calls:

105.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
105.0ms	(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) -1)

simplify84.0ms (1.1%)

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`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

120 → 124

prune246.0ms (3.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	224	10	234

Error

5.2b

Counts

234 → 10

Alt Table

Status	Error	Program
	42.4b	(.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	36.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	34.8b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	49.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	37.3b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 1/4) 2))) -1))
▶	34.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	48.8b	(.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 a b)) -1))
	48.7b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	36.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))

Compiler

Compiled 6158 to 3823 computations (37.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	0.3b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series46.0ms (0.6%)

Counts

1 → 20

Calls

1 calls:

46.0ms

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

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
227×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	271	19
2	3181	19
3	5232	19

Stop Event

1×	node limit

Counts

1 → 42

Calls

1 calls:

49.0ms

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

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

751×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
285×	`fma-neg_binary64`
236×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	567
1	195	555
2	629	529
3	3169	529
4	5154	529

Stop Event

1×	node limit

Counts

62 → 65

prune141.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	200	10	210

Error

5.2b

Counts

210 → 10

Alt Table

Status	Error	Program
	42.4b	(.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
▶	36.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	34.8b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	49.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	37.3b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 1/4) 2))) -1))
✓	34.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	48.8b	(.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 a b)) -1))
	48.7b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	36.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))

Compiler

Compiled 5378 to 3317 computations (38.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	0.0b	(*.f64 2 (/.f64 c b))

series14.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(.f64 -1/2 (.f64 2 (/.f64 c b)))
6.0ms	(*.f64 2 (/.f64 c b))

rewrite39.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`log1p-expm1-u_binary64`
699×	`expm1-log1p-u_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`
111×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	171	11
2	1839	11
3	4906	11

Stop Event

1×	node limit

Counts

2 → 57

Calls

2 calls:

38.0ms	(.f64 -1/2 (.f64 2 (/.f64 c b)))
38.0ms	(*.f64 2 (/.f64 c b))

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	144
1	10	144
2	16	144
3	22	144
4	28	144
5	34	144
6	39	144
7	44	144
8	52	144
9	49	144
10	40	144

Stop Event

1×

saturated

Counts

81 → 58

prune38.0ms (0.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	56	12	68

Error

5.2b

Counts

68 → 12

Alt Table

Status	Error	Program
	42.4b	(.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
✓	36.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	34.8b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	49.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	37.3b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 1/4) 2))) -1))
✓	34.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	55.6b	(pow.f64 (pow.f64 (/.f64 c b) 3) 1/3)
	48.8b	(.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 a b)) -1))
	48.7b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	36.9b	(.f64 -1/2 (pow.f64 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
	51.5b	(.f64 -1/2 (pow.f64 (pow.f64 (.f64 2 (/.f64 c b)) 3) 1/3))

Compiler

Compiled 627 to 393 computations (37.3% saved)

regimes2.0s (25.8%)

Accuracy

Total 4.1b remaining (42.9%)

Threshold costs 0b (0%)

Counts

133 → 3

Compiler

Compiled 10832 to 7454 computations (31.2% saved)

bsearch70.0ms (0.9%)

Steps

Iters	Range		Point
9	9.01997338348866e+138	6.498360735467026e+146	1.543614676518798e+140
6	-1.3789039591403066e-57	-2.5130832043425794e-58	-5.518100183308216e-58

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	30	56
1	42	56
2	47	56
3	50	56
4	51	56
5	50	56

Stop Event

1×

saturated

end154.0ms (2%)

Compiler: Compiled 274 to 193 computations (29.6% saved)

Iter	Nodes	Cost
0	6	144
1	10	144
2	16	144
3	22	144
4	28	144
5	34	144
6	39	144
7	44	144
8	52	144
9	49	144
10	40	144

Iter	Nodes	Cost
0	6	144
1	10	144
2	16	144
3	22	144
4	28	144
5	34	144
6	39	144
7	44	144
8	52	144
9	49	144
10	40	144

Details

analyze668.0ms (8.6%)

sample2.4s (31.4%)

simplify125.0ms (1.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series109.0ms (1.4%)

rewrite63.0ms (0.8%)

simplify74.0ms (1%)

prune143.0ms (1.8%)

localize10.0ms (0.1%)

series1.0s (13.5%)

rewrite107.0ms (1.4%)

simplify84.0ms (1.1%)

prune246.0ms (3.2%)

localize12.0ms (0.2%)

series46.0ms (0.6%)

rewrite50.0ms (0.6%)

simplify42.0ms (0.5%)

prune141.0ms (1.8%)

localize4.0ms (0.1%)

series14.0ms (0.2%)

rewrite39.0ms (0.5%)

simplify13.0ms (0.2%)

prune38.0ms (0.5%)

regimes2.0s (25.8%)

bsearch70.0ms (0.9%)

simplify3.0ms (0%)

end154.0ms (2%)

Profiling

Iter	Nodes	Cost
0	6	144
1	10	144
2	16	144
3	22	144
4	28	144
5	34	144
6	39	144
7	44	144
8	52	144
9	49	144
10	40	144