Details

analyze1.5s (12.6%)

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
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)

sample46.0ms (0.4%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
2.0ms	22×	body	128	nan
2.0ms	16×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify131.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1002×	`fma-def_binary64`
782×	`fma-neg_binary64`
748×	`distribute-rgt-in_binary64`
560×	`div-sub_binary64`
469×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	44	52
2	94	52
3	211	50
4	341	50
5	594	50
6	1082	50
7	1702	50
8	2066	50
9	2870	50
10	3495	50
11	3501	50
12	3503	50
13	4196	50
14	4249	50
15	4881	50

prune5.0ms (0%)

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

17.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.7b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	18.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))

Status

Error

Program

▶

17.7b

(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) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))

18.0b

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

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series234.0ms (2%)

Counts

4 → 96

Calls

4 calls:

113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
53.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`prod-diff_binary64`
59×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
37×	`sqrt-prod_binary64`

Counts

4 → 155

Calls

4 calls:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify224.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
235×	`exp-prod_binary64`
216×	`distribute-rgt-neg-in_binary64`
177×	`distribute-lft-neg-in_binary64`

Counts

251 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	7252
1	613	5514
2	2119	4942
3	4406	4869
4	4870	4869
5	4825	4869

prune604.0ms (5.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	320	7	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	321	8	329

Error

5.3b

Counts

329 → 8

Alt Table

Status	Error	Program
	18.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	19.3b	(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)))
	21.3b	(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)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
▶	17.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.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)))
	27.1b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.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 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (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)))

Compiler

Compiled 18407 to 10630 computations (42.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 b b (.f64 c (.f64 a -4)))
✓	7.2b	(-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))))
	20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	21.6b	(cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series127.0ms (1.1%)

Counts

3 → 92

Calls

3 calls:

59.0ms

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

58.0ms

(cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))

10.0ms

(fma.f64 b b (*.f64 c (*.f64 a -4)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`fma-neg_binary64`
10×	`prod-diff_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms

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

1.0ms

(cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))

0.0ms

(fma.f64 b b (*.f64 c (*.f64 a -4)))

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

520×	`cancel-sign-sub-inv_binary64`
279×	`unswap-sqr_binary64`
231×	`fma-neg_binary64`
187×	`associate-r_binary64`
186×	`sub-neg_binary64`

Counts

151 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	5617
1	888	4365
2	3208	4101
3	5229	4101

prune555.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	312	8	320

Error

5.3b

Counts

320 → 8

Alt Table

Status	Error	Program
	18.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	19.3b	(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)))
	21.3b	(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)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
✓	17.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.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)))
	27.1b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.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 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (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)))

Compiler

Compiled 20448 to 12609 computations (38.3% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	10.4b	(-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series121.0ms (1%)

Counts

2 → 56

Calls

2 calls:

63.0ms

(-.f64 (neg.f64 b) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

57.0ms

(cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`fma-neg_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`prod-diff_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

6.0ms

(cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

4.0ms

(-.f64 (neg.f64 b) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

309×	`associate-r_binary64`
255×	`fma-neg_binary64`
222×	`associate-l_binary64`
208×	`sub-neg_binary64`
186×	`times-frac_binary64`

Counts

110 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	4235
1	1031	3812
2	4014	3549
3	4925	3549

prune1.4s (12.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	654	0	654
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	654	8	662

Error

5.3b

Counts

662 → 8

Alt Table

Status	Error	Program
▶	18.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	19.3b	(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)))
	21.3b	(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)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
✓	17.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.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)))
	27.1b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.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 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (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)))

Compiler

Compiled 50575 to 30429 computations (39.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	20.9b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series161.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

54.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
50.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify123.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
487×	`associate-/l*_binary64`
478×	`associate-/r*_binary64`
345×	`cancel-sign-sub-inv_binary64`
150×	`distribute-rgt-in_binary64`

Counts

181 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	4403
1	460	3612
2	1571	3474
3	4821	3474
4	5063	3474

prune460.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	252	3	255
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	254	9	263

Error

5.3b

Counts

263 → 9

Alt Table

Status	Error	Program
	17.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a)))
✓	18.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (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)))
	21.3b	(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)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
✓	17.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.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)))
	22.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	27.1b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	19.3b	(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)))
	18.2b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a)))

Compiler

Compiled 11670 to 6819 computations (41.6% saved)

regimes2.2s (19.4%)

Accuracy

Total 0.9b remaining (14%)

Threshold costs 0.9b (14%)

Counts

149 → 3

Compiler

Compiled 26182 to 17170 computations (34.4% saved)

bsearch161.0ms (1.4%)

Steps

Iters	Range		Point
7	3.613082423739912e+91	3.7909222689785637e+93	1.1469712821991186e+92
10	-8.990827260058508e+155	-1.4305548729850936e+143	-3.977603578810567e+149

Compiler

Compiled 4 to 3 computations (25% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`*-commutative_binary64`
12×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	158
1	50	154
2	74	154
3	93	154
4	106	154
5	112	154
6	113	154
7	112	154

end3.0ms (0%)

Compiler: Compiled 105 to 63 computations (40% saved)

sample3.1s (26.6%)

Algorithm

1×

intervals

Results

1.8s	8000×	body	128	valid
139.0ms	656×	body	128	nan
76.0ms	363×	body	128	invalid

Compiler

Compiled 565 to 363 computations (35.8% saved)

Details

analyze1.5s (12.6%)

sample46.0ms (0.4%)

simplify131.0ms (1.1%)

prune5.0ms (0%)

localize19.0ms (0.2%)

series234.0ms (2%)

rewrite38.0ms (0.3%)

simplify224.0ms (1.9%)

prune604.0ms (5.2%)

localize28.0ms (0.2%)

series127.0ms (1.1%)

rewrite9.0ms (0.1%)

simplify106.0ms (0.9%)

prune555.0ms (4.8%)

localize27.0ms (0.2%)

series121.0ms (1%)

rewrite15.0ms (0.1%)

simplify105.0ms (0.9%)

prune1.4s (12.4%)

localize20.0ms (0.2%)

series161.0ms (1.4%)

rewrite13.0ms (0.1%)

simplify123.0ms (1.1%)

prune460.0ms (4%)

regimes2.2s (19.4%)

bsearch161.0ms (1.4%)

simplify14.0ms (0.1%)

end3.0ms (0%)

sample3.1s (26.6%)

Profiling