Details

analyze1.8s (13.1%)

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)

sample82.0ms (0.6%)

Algorithm

1×

intervals

Results

57.0ms	256×	body	128	valid
4.0ms	21×	body	128	nan
1.0ms	5×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify191.0ms (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

prune10.0ms (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

19.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.9b	(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)))
	20.0b	(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

▶

19.9b

(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)))

20.0b

(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)

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series307.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

108.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
101.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
78.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite173.0ms (1.2%)

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:

16.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
13.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify408.0ms (2.9%)

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

prune738.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	316	11	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	317	12	329

Error

5.5b

Counts

329 → 12

Alt Table

Status	Error	Program
	30.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (-.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) 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)))
	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)))
	20.0b	(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)))
	20.0b	(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)))
▶	19.5b	(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 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	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) (.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 2 a)))
	21.3b	(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)))
	35.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 (.f64 c c) 16))) (fma.f64 4 (.f64 c a) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.9b	(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)))
	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) (.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 2 a)))
	26.8b	(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 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
	39.1b	(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) b) (*.f64 2 a)))

Compiler

Compiled 18943 to 10948 computations (42.2% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series15.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 34

Calls

1 calls:

12.0ms

(/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

930×	`div-sub_binary64`
882×	`fma-def_binary64`
606×	`times-frac_binary64`
347×	`fma-neg_binary64`
338×	`associate-/l*_binary64`

Counts

58 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	737
1	205	509
2	599	432
3	2746	432
4	5554	432

prune1.2s (8.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	256	8	264
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	262	14	276

Error

5.3b

Counts

276 → 14

Alt Table

Status	Error	Program
	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 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (.f64 -1 b)))))
	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)))
	20.0b	(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)))
	32.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (pow.f64 (neg.f64 (/.f64 b a)) 3)))
	26.8b	(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 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
▶	19.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 -1 (/.f64 b a)))
	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) (.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 2 a)))
	35.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 (.f64 c c) 16))) (fma.f64 4 (.f64 c a) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	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) (.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 2 a)))
	22.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.7b	(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 (cbrt.f64 (neg.f64 (/.f64 b a))) (cbrt.f64 (neg.f64 (/.f64 b a)))) (cbrt.f64 (neg.f64 (/.f64 b a)))))
	33.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	31.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (log.f64 (neg.f64 (/.f64 b a)))))
	20.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))

Compiler

Compiled 13893 to 8301 computations (40.3% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series644.0ms (4.7%)

Counts

1 → 20

Calls

1 calls:

643.0ms

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

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`associate-/r*_binary64`
7×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

21.0ms

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

simplify152.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
432×	`associate-/r*_binary64`
238×	`fma-neg_binary64`
221×	`associate-*l/_binary64`
220×	`fma-def_binary64`

Counts

53 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1740
1	388	1573
2	1316	1490
3	4772	1490
4	4988	1490
5	4912	1490

prune1.2s (8.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	277	13	290

Error

5.3b

Counts

290 → 13

Alt Table

Status	Error	Program
▶	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 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (.f64 -1 b)))))
	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)))
	20.0b	(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)))
	32.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (pow.f64 (neg.f64 (/.f64 b a)) 3)))
	26.8b	(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 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
	35.1b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 2 c) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 -1 (/.f64 b a)))
	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) (.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 2 a)))
	22.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.7b	(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 (cbrt.f64 (neg.f64 (/.f64 b a))) (cbrt.f64 (neg.f64 (/.f64 b a)))) (cbrt.f64 (neg.f64 (/.f64 b a)))))
	33.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	31.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (log.f64 (neg.f64 (/.f64 b a)))))
	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) (.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 2 a)))
	20.6b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (.f64 -1 (/.f64 b a)))

Compiler

Compiled 13351 to 7718 computations (42.2% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (.f64 -1 b)))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series14.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (*.f64 -1 b)))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 31

Calls

1 calls:

14.0ms

(/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (*.f64 -1 b)))

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

858×	`fma-def_binary64`
653×	`times-frac_binary64`
484×	`div-sub_binary64`
364×	`associate-/l*_binary64`
283×	`distribute-frac-neg_binary64`

Counts

55 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	712
1	190	496
2	588	433
3	2950	431
4	4926	431
5	5225	431

prune910.0ms (6.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	261	13	274

Error

5.3b

Counts

274 → 13

Alt Table

Status	Error	Program
✓	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 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (.f64 -1 b)))))
	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)))
	20.0b	(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)))
	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 1 (expm1.f64 (log1p.f64 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (.f64 -1 b)))))))
	32.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (pow.f64 (neg.f64 (/.f64 b a)) 3)))
	26.8b	(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 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
	35.1b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 2 c) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 -1 (/.f64 b a)))
	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) (.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 2 a)))
	22.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.7b	(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 (cbrt.f64 (neg.f64 (/.f64 b a))) (cbrt.f64 (neg.f64 (/.f64 b a)))) (cbrt.f64 (neg.f64 (/.f64 b a)))))
	33.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	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) (.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 2 a)))
	20.6b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (.f64 -1 (/.f64 b a)))

Compiler

Compiled 13713 to 8380 computations (38.9% saved)

regimes2.5s (17.8%)

Accuracy

Total 1.7b remaining (24.6%)

Threshold costs 0b (0%)

Counts

118 → 5

Compiler

Compiled 17266 to 11794 computations (31.7% saved)

bsearch14.0ms (0.1%)

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

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	476
1	75	462
2	101	462
3	121	462
4	135	462
5	141	462
6	142	462
7	140	462

end5.0ms (0%)

Compiler: Compiled 308 to 183 computations (40.6% saved)

sample3.1s (22.4%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
116.0ms	648×	body	128	nan
75.0ms	392×	body	128	invalid

Compiler

Compiled 923 to 580 computations (37.2% saved)

Details

analyze1.8s (13.1%)

sample82.0ms (0.6%)

simplify191.0ms (1.4%)

prune10.0ms (0.1%)

localize44.0ms (0.3%)

series307.0ms (2.2%)

rewrite173.0ms (1.2%)

simplify408.0ms (2.9%)

prune738.0ms (5.3%)

localize40.0ms (0.3%)

series15.0ms (0.1%)

rewrite15.0ms (0.1%)

simplify81.0ms (0.6%)

prune1.2s (8.4%)

localize43.0ms (0.3%)

series644.0ms (4.7%)

rewrite28.0ms (0.2%)

simplify152.0ms (1.1%)

prune1.2s (8.4%)

localize47.0ms (0.3%)

series14.0ms (0.1%)

rewrite17.0ms (0.1%)

simplify127.0ms (0.9%)

prune910.0ms (6.6%)

regimes2.5s (17.8%)

bsearch14.0ms (0.1%)

simplify25.0ms (0.2%)

end5.0ms (0%)

sample3.1s (22.4%)

Profiling