Details

analyze643.0ms (10.7%)

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)

sample2.3s (38.6%)

Results

701.0ms	5273×	body	128	valid
664.0ms	1228×	body	2048	valid
336.0ms	761×	body	1024	valid
265.0ms	430×	body	4096	valid
136.0ms	1064×	body	128	invalid
118.0ms	363×	body	512	valid
47.0ms	201×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
544×	`div-sub_binary64`
489×	`fma-neg_binary64`
405×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	100	24
3	259	22
4	460	22
5	840	22
6	1790	22
7	2999	22
8	3682	22
9	4742	22

Stop Event

1×	node limit

Counts

1 → 2

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

34.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
▶	34.8b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series130.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

51.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
41.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`
160×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	347	62

Stop Event

1×	node limit

Counts

4 → 160

Calls

4 calls:

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

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
469×	`associate-/l*_binary64`
432×	`fma-def_binary64`
425×	`associate-/r*_binary64`
158×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2060
1	415	1984
2	1475	1904

Stop Event

1×	node limit

Counts

256 → 236

prune175.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	230	6	236
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	230	8	238

Error

5.3b

Counts

238 → 8

Alt Table

Status	Error	Program
✓	34.8b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	48.7b	(/.f64 (neg.f64 b) a)
▶	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	42.4b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	36.9b	(/.f64 (neg.f64 c) b)
	49.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.6b	(pow.f64 (cbrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 3)
	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 4 (.f64 a c)))) (pow.f64 (cbrt.f64 (.f64 4 (.f64 a c))) 2) (.f64 4 (.f64 a c)))))) (*.f64 2 a))

Compiler

Compiled 6243 to 3641 computations (41.7% saved)

localize9.0ms (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 -1/2 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)))

series121.0ms (2%)

Counts

4 → 96

Calls

4 calls:

51.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
32.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
28.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
137×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`
130×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	279	62
2	3616	62

Stop Event

1×	node limit

Counts

4 → 130

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)))) (/.f64 -1/2 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)))

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
465×	`associate-/l*_binary64`
423×	`associate-/r*_binary64`
372×	`fma-def_binary64`
147×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2045
1	381	1971
2	1339	1891

Stop Event

1×	node limit

Counts

226 → 204

prune137.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	204	8	212

Error

5.3b

Counts

212 → 8

Alt Table

Status	Error	Program
✓	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	40.9b	(.f64 (.f64 2 (*.f64 (/.f64 c b) a)) (/.f64 -1/2 a))
▶	34.8b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
	42.4b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	36.9b	(/.f64 (neg.f64 c) b)
	49.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.7b	(/.f64 (neg.f64 b) a)
	42.4b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 -1/2 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

Compiler

Compiled 5081 to 2961 computations (41.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))
✓	0.1b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
	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)))

series173.0ms (2.9%)

Counts

2 → 40

Calls

2 calls:

123.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))
50.0ms	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
148×	`add-cbrt-cube_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	320	44
2	4211	44

Stop Event

1×	node limit

Counts

2 → 89

Calls

2 calls:

66.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))
66.0ms	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
498×	`associate-/l*_binary64`
432×	`associate-/r*_binary64`
306×	`fma-def_binary64`
116×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1185
1	360	1168
2	1268	1105

Stop Event

1×	node limit

Counts

129 → 135

prune161.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	235	3	238
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	236	10	246

Error

5.2b

Counts

246 → 10

Alt Table

Status	Error	Program
	48.8b	(/.f64 1 (/.f64 (neg.f64 a) b))
✓	34.8b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
✓	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	37.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 1/4) 2)) -1/2)))
	40.9b	(.f64 (.f64 2 (*.f64 (/.f64 c b) a)) (/.f64 -1/2 a))
	36.9b	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
	42.4b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
▶	36.9b	(/.f64 (neg.f64 c) b)
	49.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.7b	(/.f64 (neg.f64 b) a)

Compiler

Compiled 6138 to 3763 computations (38.7% saved)

localize3.0ms (0%)

prune6.0ms (0.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

5.2b

Counts

10 → 10

Alt Table

Status	Error	Program
	48.8b	(/.f64 1 (/.f64 (neg.f64 a) b))
✓	34.8b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
✓	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	37.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 1/4) 2)) -1/2)))
	40.9b	(.f64 (.f64 2 (*.f64 (/.f64 c b) a)) (/.f64 -1/2 a))
	36.9b	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
	42.4b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
✓	36.9b	(/.f64 (neg.f64 c) b)
	49.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.7b	(/.f64 (neg.f64 b) a)

Compiler

Compiled 152 to 103 computations (32.2% saved)

regimes1.5s (25.7%)

Accuracy

Total 4.2b remaining (43.1%)

Threshold costs 0b (0%)

Counts

119 → 3

Compiler

Compiled 10336 to 6994 computations (32.3% saved)

bsearch67.0ms (1.1%)

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)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	38	50
2	47	50
3	54	50
4	58	50
5	59	50

Stop Event

1×

saturated

end133.0ms (2.2%)

Compiler: Compiled 226 to 149 computations (34.1% saved)

Details

analyze643.0ms (10.7%)

sample2.3s (38.6%)

simplify38.0ms (0.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series130.0ms (2.2%)

rewrite46.0ms (0.8%)

simplify64.0ms (1.1%)

prune175.0ms (2.9%)

localize9.0ms (0.2%)

series121.0ms (2%)

rewrite68.0ms (1.1%)

simplify46.0ms (0.8%)

prune137.0ms (2.3%)

localize10.0ms (0.2%)

series173.0ms (2.9%)

rewrite68.0ms (1.1%)

simplify32.0ms (0.5%)

prune161.0ms (2.7%)

localize3.0ms (0%)

prune6.0ms (0.1%)

regimes1.5s (25.7%)

bsearch67.0ms (1.1%)

simplify4.0ms (0.1%)

end133.0ms (2.2%)

Profiling