Details

analyze1.1s (11.9%)

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)

sample156.0ms (1.7%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
2.0ms	21×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify127.0ms (1.4%)

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 (0.1%)

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

20.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	20.0b	(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)))
	20.1b	(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

▶

20.0b

(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)))

20.1b

(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)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series201.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

68.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite48.0ms (0.5%)

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:

12.0ms	(-.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))))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify222.0ms (2.5%)

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	8106
1	613	6063
2	2119	4942
3	4406	4869
4	4870	4869
5	4825	4869

prune606.0ms (6.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	319	8	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	320	9	329

Error

7.6b

Counts

329 → 9

Alt Table

Status	Error	Program
▶	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.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)))
	23.1b	(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 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	23.9b	(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)))
	22.3b	(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) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
	22.4b	(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)))
	30.5b	(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)))
	20.1b	(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)))
	22.4b	(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)))
	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.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 18453 to 10664 computations (42.2% saved)

localize24.0ms (0.3%)

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 (.f64 4 a) c)))) (.f64 2 a))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series92.0ms (1%)

Counts

1 → 20

Calls

1 calls:

92.0ms

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

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`associate-/l*_binary64`
5×	`times-frac_binary64`

Counts

1 → 30

Calls

1 calls:

15.0ms

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

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
700×	`div-sub_binary64`
470×	`associate-/l*_binary64`
317×	`fma-def_binary64`
278×	`fma-neg_binary64`

Counts

50 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1593
1	389	1379
2	1276	1319
3	4657	1319
4	6264	1319

prune459.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	270	9	279

Error

7.5b

Counts

279 → 9

Alt Table

Status	Error	Program
▶	20.1b	(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)))
	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a)))
	22.4b	(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)))
	27.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)) (/.f64 b a)))
	23.9b	(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)))
	23.1b	(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 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	22.4b	(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)))
	23.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.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 14377 to 7997 computations (44.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	1.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	22.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series257.0ms (2.9%)

Counts

4 → 80

Calls

4 calls:

88.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
63.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
60.0ms	(+.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)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 116

Calls

4 calls:

8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
8.0ms	(-.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)))

simplify155.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-neg_binary64`
376×	`cancel-sign-sub-inv_binary64`
373×	`distribute-rgt-in_binary64`
165×	`associate-r_binary64`
164×	`distribute-rgt-neg-in_binary64`

Counts

196 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	5766
1	733	4840
2	2707	4645
3	4911	4645
4	5121	4645

prune718.0ms (8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Error

7.5b

Counts

307 → 10

Alt Table

Status	Error	Program
✓	20.1b	(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)))
	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a)))
	22.4b	(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)))
	27.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)) (/.f64 b a)))
	24.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	23.9b	(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)))
	23.1b	(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 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	22.4b	(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)))
	23.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
▶	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.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 14275 to 8368 computations (41.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	10.8b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series62.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

62.0ms

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

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 37

Calls

1 calls:

4.0ms

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

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

753×	`times-frac_binary64`
598×	`fma-neg_binary64`
365×	`fma-def_binary64`
347×	`associate-l_binary64`
299×	`associate-/l*_binary64`

Counts

57 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1859
1	364	1481
2	1083	1264
3	5000	1262
4	5392	1262

prune763.0ms (8.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	364	0	364
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	364	10	374

Error

7.5b

Counts

374 → 10

Alt Table

Status	Error	Program
✓	20.1b	(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)))
	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a)))
	22.4b	(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)))
	27.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)) (/.f64 b a)))
	24.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	23.9b	(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)))
	23.1b	(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 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	22.4b	(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)))
	23.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
✓	20.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.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 21863 to 12772 computations (41.6% saved)

regimes1.6s (18.4%)

Accuracy

Total 1.0b remaining (16%)

Threshold costs 1.0b (16%)

Counts

136 → 3

Compiler

Compiled 24238 to 15950 computations (34.2% saved)

bsearch54.0ms (0.6%)

Steps

Iters	Range		Point
3	3.2206815536740836e+127	4.279754917139619e+132	9.79390074350916e+131
9	-1.6296719684562592e+159	-1.373014230936203e+153	-1.3895581000592264e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	152
1	64	148
2	92	148
3	111	148
4	123	148
5	127	148
6	126	148

end1.0ms (0%)

Compiler: Compiled 102 to 62 computations (39.2% saved)

sample2.0s (22.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
77.0ms	682×	body	128	nan
39.0ms	347×	body	128	invalid

Compiler

Compiled 564 to 364 computations (35.5% saved)

Details

analyze1.1s (11.9%)

sample156.0ms (1.7%)

simplify127.0ms (1.4%)

prune5.0ms (0.1%)

localize22.0ms (0.2%)

series201.0ms (2.2%)

rewrite48.0ms (0.5%)

simplify222.0ms (2.5%)

prune606.0ms (6.8%)

localize24.0ms (0.3%)

series92.0ms (1%)

rewrite18.0ms (0.2%)

simplify74.0ms (0.8%)

prune459.0ms (5.1%)

localize19.0ms (0.2%)

series257.0ms (2.9%)

rewrite28.0ms (0.3%)

simplify155.0ms (1.7%)

prune718.0ms (8%)

localize24.0ms (0.3%)

series62.0ms (0.7%)

rewrite7.0ms (0.1%)

simplify83.0ms (0.9%)

prune763.0ms (8.5%)

regimes1.6s (18.4%)

bsearch54.0ms (0.6%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.0s (22.4%)

Profiling