Details

analyze811.0ms (8.4%)

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)

sample51.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	38×	body	2048	valid
11.0ms	162×	body	128	valid
6.0ms	24×	body	1024	valid
4.0ms	11×	body	4096	valid
3.0ms	14×	body	512	valid
2.0ms	28×	body	128	nan
1.0ms	7×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify451.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

35.5b

Counts

2 → 2

Alt Table

Status	Error	Program
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 94 to 64 computations (31.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite150.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

35.3b

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2252 to 1118 computations (50.4% saved)

series147.0ms (1.5%)

Error

5.1b

Counts

4 → 62

Calls

4 calls:

46.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
28.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
27.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2535 to 1813 computations (28.5% saved)

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

814×	`times-frac_binary64`
613×	`fma-def_binary64`
572×	`fma-neg_binary64`
238×	`cancel-sign-sub-inv_binary64`
161×	`distribute-rgt-neg-in_binary64`

Counts

152 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2752
1	531	2406
2	1726	2353
3	4759	2353
4	5046	2353

prune69.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Error

5.1b

Counts

124 → 8

Alt Table

Status	Error	Program
	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	46.9b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	49.8b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (.f64 a 2)))
	44.6b	(/.f64 (neg.f64 b) a)
	38.6b	(neg.f64 (/.f64 c b))
	51.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 b b))) (.f64 2 a))
▶	34.0b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (*.f64 2 a))

Compiler

Compiled 1930 to 1010 computations (47.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))
3.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (*.f64 2 a))
11.0b	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))
24.5b	(sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))

rewrite199.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

75×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
60×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
45×	`add-cbrt-cube_binary64`

Counts

4 → 201

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (*.f64 2 a))
9.0ms	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))
8.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))

Compiler

Compiled 8232 to 3838 computations (53.4% saved)

series269.0ms (2.8%)

Error

5.1b

Counts

4 → 60

Calls

4 calls:

97.0ms	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (*.f64 2 a))
68.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))
57.0ms	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))
29.0ms	(sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))

Compiler

Compiled 3414 to 2323 computations (32% saved)

simplify388.0ms (4%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
343×	`fma-neg_binary64`
267×	`associate-/l*_binary64`
266×	`times-frac_binary64`
179×	`associate-/r*_binary64`

Counts

261 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	10061
1	837	7200
2	3236	5944
3	4618	5944
4	5000	5944
5	4900	5944

prune299.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	244	8	252

Error

5.1b

Counts

252 → 8

Alt Table

Status	Error	Program
	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	46.9b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
▶	32.6b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	38.4b	(expm1.f64 (log1p.f64 (.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))))))
	44.6b	(/.f64 (neg.f64 b) a)
	38.6b	(neg.f64 (/.f64 c b))
	37.4b	(/.f64 (.f64 2 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)

Compiler

Compiled 3406 to 1963 computations (42.4% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
0.5b	(-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
14.0b	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite235.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

57×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

3 → 118

Calls

3 calls:

14.0ms	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
12.0ms	(-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
6.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

Compiler

Compiled 4039 to 2651 computations (34.4% saved)

series295.0ms (3.1%)

Error

5.1b

Counts

3 → 32

Calls

3 calls:

148.0ms	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
108.0ms	(-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
20.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

Compiler

Compiled 2168 to 1685 computations (22.3% saved)

simplify270.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
585×	`associate-/r*_binary64`
427×	`fma-def_binary64`
391×	`fma-neg_binary64`
170×	`associate-/r/_binary64`

Counts

150 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	4592
1	528	3528
2	1617	3049
3	4994	3049
4	5101	3049

prune118.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Error

5.1b

Counts

143 → 8

Alt Table

Status	Error	Program
▶	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	46.9b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
✓	32.6b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	38.4b	(.f64 2 (.f64 1 (expm1.f64 (log1p.f64 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))))))))
	44.6b	(/.f64 (neg.f64 b) a)
	38.6b	(neg.f64 (/.f64 c b))
	37.4b	(/.f64 (.f64 2 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)

Compiler

Compiled 2133 to 1300 computations (39.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))
1.3b	(fma.f64 b b (.f64 c (.f64 a -4)))
24.5b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

rewrite133.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

4 → 82

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
11.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))
2.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))
1.0ms	(fma.f64 b b (.f64 c (.f64 a -4)))

Compiler

Compiled 1875 to 1108 computations (40.9% saved)

series273.0ms (2.8%)

Error

5.1b

Counts

4 → 62

Calls

4 calls:

153.0ms	(fma.f64 b b (.f64 c (.f64 a -4)))
45.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
34.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))
28.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))

Compiler

Compiled 2535 to 1813 computations (28.5% saved)

simplify784.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
520×	`fma-neg_binary64`
478×	`associate-/l*_binary64`
371×	`fma-def_binary64`
162×	`distribute-rgt-in_binary64`

Counts

144 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2510
1	455	2204
2	1329	2171
3	4748	2171
4	5050	2171

prune54.0ms (0.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	113	8	121

Error

5.1b

Counts

121 → 8

Alt Table

Status	Error	Program
	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	46.9b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
	32.6b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	38.4b	(.f64 2 (.f64 1 (expm1.f64 (log1p.f64 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))))))))
	44.6b	(/.f64 (neg.f64 b) a)
	38.6b	(neg.f64 (/.f64 c b))
	37.4b	(/.f64 (.f64 2 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)

Compiler

Compiled 1564 to 821 computations (47.5% saved)

regimes2.5s (25.9%)

Accuracy

Total 2.5b remaining (31.6%)

Threshold costs 0b (0%)

Compiler

Compiled 14723 to 9910 computations (32.7% saved)

bsearch114.0ms (1.2%)

Steps

Iters	Range	Point
9	5.925571812899276e-40	8.709619545227406e-35	5.718007789643402e-35
9	-4.262322796411399e-291	-2.4154537955971958e-296	-2.07694009677386e-291
8	-5.99400964558612e+157	-1.1397553837082806e+153	-1.3199871431635179e+153

Iters

Range

Point

5.925571812899276e-40

8.709619545227406e-35

5.718007789643402e-35

-4.262322796411399e-291

-2.4154537955971958e-296

-2.07694009677386e-291

-5.99400964558612e+157

-1.1397553837082806e+153

-1.3199871431635179e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	81
1	54	79
2	70	79
3	82	79
4	87	79
5	88	79
6	87	79

end1.0ms (0%)

Compiler: Compiled 56 to 35 computations (37.5% saved)

sample1.8s (19%)

Algorithm

1×

intervals

Results

397.0ms	1074×	body	2048	valid
341.0ms	5154×	body	128	valid
193.0ms	781×	body	1024	valid
185.0ms	419×	body	4096	valid
87.0ms	697×	body	128	nan
71.0ms	384×	body	512	valid
26.0ms	402×	body	128	invalid
24.0ms	188×	body	256	valid

Compiler

Compiled 211 to 146 computations (30.8% saved)

Details

analyze811.0ms (8.4%)

sample51.0ms (0.5%)

simplify451.0ms (4.7%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite150.0ms (1.6%)

series147.0ms (1.5%)

simplify119.0ms (1.2%)

prune69.0ms (0.7%)

localize13.0ms (0.1%)

rewrite199.0ms (2.1%)

series269.0ms (2.8%)

simplify388.0ms (4%)

prune299.0ms (3.1%)

localize22.0ms (0.2%)

rewrite235.0ms (2.4%)

series295.0ms (3.1%)

simplify270.0ms (2.8%)

prune118.0ms (1.2%)

localize23.0ms (0.2%)

rewrite133.0ms (1.4%)

series273.0ms (2.8%)

simplify784.0ms (8.1%)

prune54.0ms (0.6%)

regimes2.5s (25.9%)

bsearch114.0ms (1.2%)

simplify10.0ms (0.1%)

end1.0ms (0%)

sample1.8s (19%)

Profiling