Details

analyze633.0ms (7.5%)

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 (28.3%)

Results

705.0ms	5364×	body	128	valid
624.0ms	1169×	body	2048	valid
320.0ms	775×	body	1024	valid
278.0ms	414×	body	4096	valid
129.0ms	1010×	body	128	invalid
106.0ms	341×	body	512	valid
43.0ms	193×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify140.0ms (1.7%)

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

32.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.9b	(.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)
✓	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series167.0ms (2%)

Counts

4 → 96

Calls

4 calls:

68.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
48.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite71.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

119× egg-rr

Counts

4 → 119

Calls

2 calls:

68.0ms

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

0.0ms

()

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

simplify80.0ms (0.9%)

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

prune139.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	11	191

Error

4.5b

Counts

191 → 11

Alt Table

Status	Error	Program
	42.8b	(.f64 -1/2 (/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))))) a))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) 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))))
	41.5b	(.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 3/2))) a))
▶	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	33.0b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
	36.1b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	33.4b	(.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)))
	46.8b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 4991 to 3004 computations (39.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series71.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

71.0ms

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

rewrite58.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

42× egg-rr

Counts

1 → 42

Calls

2 calls:

57.0ms	((.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify49.0ms (0.6%)

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`

Counts

62 → 65

Iterations

Useful iterations: 2 (0.0ms)

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

prune140.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	197	3	200
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Error

4.5b

Counts

211 → 9

Alt Table

Status	Error	Program
▶	32.9b	(.f64 -1/2 (/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (neg.f64 a)))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	44.9b	(.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)))))))
	33.0b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) -1))
✓	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	36.1b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 5406 to 3323 computations (38.5% saved)

localize11.0ms (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 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (neg.f64 a))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series73.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

73.0ms

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

rewrite61.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

43× egg-rr

Counts

1 → 43

Calls

2 calls:

60.0ms	((/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (neg.f64 a)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	284	19
2	3102	18
3	5671	18
0	0	0
1	0	0

simplify45.0ms (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`

Counts

63 → 66

Iterations

Useful iterations: 2 (0.0ms)

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

prune144.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	200	10	210

Error

4.5b

Counts

210 → 10

Alt Table

Status	Error	Program
✓	32.9b	(.f64 -1/2 (/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (neg.f64 a)))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
✓	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	44.9b	(.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)))))))
	36.1b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))))
▶	32.9b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) -1))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 5351 to 3280 computations (38.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) -1)
✓	0.9b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	13.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

series1.6s (19.6%)

Counts

4 → 42

Calls

4 calls:

1.2s	(pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) -1)
332.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
136.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
17.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite79.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

142× egg-rr

Counts

4 → 142

Calls

2 calls:

76.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	63
1	280	60
2	3401	60
3	5130	60
0	0	0
1	0	0

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
620×	`associate-/l*_binary64`
609×	`associate-/r*_binary64`
336×	`fma-neg_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

184 → 209

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1563
1	408	1413
2	1359	1379
3	4726	1377
4	5211	1377

prune158.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	208	11	219

Error

2.4b

Counts

219 → 11

Alt Table

Status	Error	Program
✓	32.9b	(.f64 -1/2 (/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (neg.f64 a)))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
✓	32.9b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) -1))
	45.5b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 a (.f64 c -4)))) (.f64 a (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.8b	(.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))))) -1))
	44.2b	(.f64 -1/2 (pow.f64 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 a (/.f64 (.f64 -4 (.f64 c a)) b)) -2)) -1))
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 5694 to 3833 computations (32.7% saved)

regimes2.0s (23.5%)

Accuracy

Total 7.9b remaining (73.8%)

Threshold costs 0b (0%)

Counts

127 → 3

Compiler

Compiled 10760 to 7622 computations (29.2% saved)

bsearch44.0ms (0.5%)

Steps

Iters	Range		Point
6	3.8657611513446867e+90	2.928767619032365e+91	2.818024375880192e+91
5	-1.1401732337828577e-138	-2.8577058786826562e-139	-1.1192253259106201e-138

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	56
1	37	56
2	37	56

end144.0ms (1.7%)

Compiler: Compiled 294 to 207 computations (29.6% saved)

Details

analyze633.0ms (7.5%)

sample2.4s (28.3%)

simplify140.0ms (1.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series167.0ms (2%)

rewrite71.0ms (0.8%)

simplify80.0ms (0.9%)

prune139.0ms (1.7%)

localize10.0ms (0.1%)

series71.0ms (0.8%)

rewrite58.0ms (0.7%)

simplify49.0ms (0.6%)

prune140.0ms (1.7%)

localize11.0ms (0.1%)

series73.0ms (0.9%)

rewrite61.0ms (0.7%)

simplify45.0ms (0.5%)

prune144.0ms (1.7%)

localize10.0ms (0.1%)

series1.6s (19.6%)

rewrite79.0ms (0.9%)

simplify62.0ms (0.7%)

prune158.0ms (1.9%)

regimes2.0s (23.5%)

bsearch44.0ms (0.5%)

simplify2.0ms (0%)

end144.0ms (1.7%)

Profiling