Details

analyze892.0ms (10.4%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample2.0s (22.7%)

Results

1.7s	8256×	body	128	valid
216.0ms	1070×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary64`
464×	`times-frac_binary64`
353×	`div-sub_binary64`
283×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	44	52
2	99	52
3	240	50
4	439	50
5	780	50
6	1493	50
7	2856	50
8	4302	50

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

14.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))

Status

Error

Program

▶

14.6b

(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))

14.6b

(if (>=.f64 b 0) (/.f64 (*.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))) (*.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))) (/.f64 -1/2 a)))

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.9b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	17.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series129.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

50.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
43.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
26.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite73.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
167×	`egg-rr`
147×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	301	56
2	4302	56

Stop Event

1×	node limit

Counts

4 → 167

Calls

4 calls:

69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
69.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
293×	`fma-def_binary64`
279×	`associate-r_binary64`
278×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2213
1	296	2123
2	973	2035

Stop Event

1×	node limit

Counts

263 → 226

prune584.0ms (6.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	326	8	334
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	327	9	336

Error

6.1b

Counts

336 → 9

Alt Table

Status	Error	Program
	20.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (*.f64 2 a)))
	20.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	14.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	27.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
	27.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a)))
▶	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))
	16.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 16671 to 9901 computations (40.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a))
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
✓	1.3b	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
✓	17.1b	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series154.0ms (1.8%)

Counts

4 → 80

Calls

4 calls:

54.0ms	(.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a))
39.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
33.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
27.0ms	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
237×	`fma-neg_binary64`
152×	`add-sqr-sqrt_binary64`
150×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	310	67
2	4105	67

Stop Event

1×	node limit

Counts

4 → 150

Calls

4 calls:

65.0ms	(.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a))
65.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
65.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
65.0ms	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

725×	`times-frac_binary64`
463×	`associate-/l*_binary64`
402×	`associate-/r*_binary64`
387×	`fma-def_binary64`
161×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2391
1	389	2360
2	1334	2254

Stop Event

1×	node limit

Counts

230 → 226

prune487.0ms (5.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	266	6	272
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	269	12	281

Error

6.1b

Counts

281 → 12

Alt Table

Status	Error	Program
	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	27.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -4) (.f64 b b))) (/.f64 -1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	15.1b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (/.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a)))
	14.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
▶	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 1 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2))))
	20.8b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (-.f64 (/.f64 (.f64 2 a) (/.f64 b c)) b)) (/.f64 -1/2 a)))
	20.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (*.f64 -1 (/.f64 b a)))
	27.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
✓	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))
	16.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (-.f64 (/.f64 c b) (/.f64 b a)))

Compiler

Compiled 12909 to 7551 computations (41.5% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
✓	1.3b	(-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
	17.1b	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))
✓	17.1b	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series60.0ms (0.7%)

Counts

2 → 40

Calls

2 calls:

35.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
25.0ms	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

rewrite57.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

783×	`prod-diff_binary64`
334×	`fma-def_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
156×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	211	29
2	2693	29

Stop Event

1×	node limit

Counts

2 → 121

Calls

2 calls:

53.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
53.0ms	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

441×	`times-frac_binary64`
417×	`fma-neg_binary64`
274×	`associate-/l*_binary64`
269×	`associate-r_binary64`
240×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	1210
1	250	1196
2	808	1140
3	4411	1140

Stop Event

1×	node limit

Counts

161 → 168

prune553.0ms (6.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	259	13	272

Error

6.1b

Counts

272 → 13

Alt Table

Status	Error	Program
▶	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	27.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -4) (.f64 b b))) (/.f64 -1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	15.1b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (/.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a)))
	14.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
✓	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 1 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2))))
	20.8b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (-.f64 (/.f64 (.f64 2 a) (/.f64 b c)) b)) (/.f64 -1/2 a)))
	20.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (*.f64 -1 (/.f64 b a)))
	20.8b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 1 (/.f64 a (.f64 (-.f64 b (.f64 -1 b)) -1/2))))
	27.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
✓	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))
	16.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (-.f64 (/.f64 c b) (/.f64 b a)))

Compiler

Compiled 14497 to 8395 computations (42.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	7.4b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
	17.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	17.6b	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series74.0ms (0.9%)

Counts

2 → 56

Calls

2 calls:

39.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)
34.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))

rewrite97.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`prod-diff_binary64`
196×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	307	29
2	3736	29

Stop Event

1×	node limit

Counts

2 → 196

Calls

2 calls:

88.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
88.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-def_binary64`
482×	`cancel-sign-sub-inv_binary64`
244×	`distribute-neg-frac_binary64`
177×	`sub-neg_binary64`
169×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2538
1	759	2480
2	2968	2444

Stop Event

1×	node limit

Counts

252 → 274

prune933.0ms (10.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	385	3	388
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	387	14	401

Error

3.3b

Counts

401 → 14

Alt Table

Status	Error	Program
✓	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	27.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -4) (.f64 b b))) (/.f64 -1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))
	32.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	15.1b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 (/.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a)))
	14.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
✓	14.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 1 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))) -1/2))))
	20.8b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (-.f64 (/.f64 (.f64 2 a) (/.f64 b c)) b)) (/.f64 -1/2 a)))
	20.7b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (*.f64 -1 (/.f64 b a)))
	20.8b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (/.f64 1 (/.f64 a (.f64 (-.f64 b (.f64 -1 b)) -1/2))))
	33.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	27.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
✓	14.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))
	20.6b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (-.f64 (/.f64 c b) (/.f64 b a)))

Compiler

Compiled 27218 to 17200 computations (36.8% saved)

regimes1.7s (19.4%)

Accuracy

Total 4.5b remaining (51.7%)

Threshold costs 0b (0%)

Counts

158 → 5

Compiler

Compiled 28562 to 18482 computations (35.3% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	71	486
1	108	474
2	149	474
3	176	474
4	189	474
5	192	474

Stop Event

1×

saturated

end475.0ms (5.5%)

Compiler: Compiled 1214 to 760 computations (37.4% saved)

Details

analyze892.0ms (10.4%)

sample2.0s (22.7%)

simplify31.0ms (0.4%)

prune5.0ms (0.1%)

localize20.0ms (0.2%)

series129.0ms (1.5%)

rewrite73.0ms (0.8%)

simplify44.0ms (0.5%)

prune584.0ms (6.8%)

localize18.0ms (0.2%)

series154.0ms (1.8%)

rewrite69.0ms (0.8%)

simplify46.0ms (0.5%)

prune487.0ms (5.7%)

localize23.0ms (0.3%)

series60.0ms (0.7%)

rewrite57.0ms (0.7%)

simplify47.0ms (0.5%)

prune553.0ms (6.4%)

localize27.0ms (0.3%)

series74.0ms (0.9%)

rewrite97.0ms (1.1%)

simplify59.0ms (0.7%)

prune933.0ms (10.8%)

regimes1.7s (19.4%)

bsearch10.0ms (0.1%)

simplify11.0ms (0.1%)

end475.0ms (5.5%)

Profiling