Details

analyze1.0s (11.4%)

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)

sample150.0ms (1.6%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
2.0ms	20×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify125.0ms (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

19.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.8b	(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

▶

19.5b

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

19.8b

(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
✓	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.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))))
✓	22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series202.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

82.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite40.0ms (0.4%)

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:

10.0ms	(-.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))

simplify225.0ms (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

prune696.0ms (7.6%)

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

5.0b

Counts

329 → 12

Alt Table

Status	Error	Program
	35.6b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.4b	(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)))
	28.8b	(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 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	20.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.8b	(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)))
	19.8b	(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)))
	25.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (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)))
	26.1b	(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)))
	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 (+.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)))
▶	19.6b	(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 18851 to 10910 computations (42.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	9.7b	(-.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))))))
	22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series65.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

64.0ms

(-.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))))))

rewrite9.0ms (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))))))

simplify87.0ms (1%)

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

prune725.0ms (7.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	363	1	364
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	364	12	376

Error

5.0b

Counts

376 → 12

Alt Table

Status	Error	Program
	25.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3))) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.6b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.4b	(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)))
	28.8b	(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 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	20.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.8b	(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)))
	19.8b	(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)))
	26.1b	(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)))
▶	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 (+.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)))
✓	19.6b	(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 22496 to 13182 computations (41.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	11.0b	(+.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)))))))
	22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	23.5b	(cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series116.0ms (1.3%)

Counts

2 → 56

Calls

2 calls:

59.0ms	(cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))
57.0ms	(+.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)))))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`fma-def_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 38

Calls

2 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))))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

543×	`cancel-sign-sub-inv_binary64`
230×	`unswap-sqr_binary64`
217×	`fma-neg_binary64`
185×	`associate-r_binary64`
176×	`sub-neg_binary64`

Counts

94 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	3695
1	839	3276
2	3099	3224
3	5002	3224

prune1.0s (11.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	371	12	383

Error

5.0b

Counts

383 → 12

Alt Table

Status	Error	Program
	25.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3))) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.6b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.4b	(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)))
	22.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	19.8b	(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)))
	19.8b	(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)))
	26.1b	(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)))
✓	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 (+.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)))
	28.8b	(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 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.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 0 (-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))) 3))) (*.f64 2 a)))
✓	19.6b	(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 26694 to 16329 computations (38.8% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	16.6b	(-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))) 3))
	22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	23.5b	(cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series118.0ms (1.3%)

Counts

2 → 56

Calls

2 calls:

61.0ms	(-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))) 3))
57.0ms	(cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
52×	`sqrt-prod_binary64`

Counts

2 → 134

Calls

2 calls:

12.0ms	(-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))) 3))
1.0ms	(cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))

simplify211.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-neg_binary64`
411×	`unswap-sqr_binary64`
272×	`associate-r_binary64`
205×	`associate-l_binary64`
191×	`sub-neg_binary64`

Counts

190 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	9903
1	967	7460
2	3556	5850
3	4770	5850
4	4825	5850

prune814.0ms (8.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	345	2	347
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	346	13	359

Error

3.0b

Counts

359 → 13

Alt Table

Status	Error	Program
	25.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3))) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.6b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.4b	(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)))
	19.8b	(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)))
	19.8b	(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)))
	26.1b	(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)))
	32.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (-.f64 0 (-.f64 b (pow.f64 (sqrt.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a)))))) 3))) (*.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 (+.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)))
	28.8b	(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 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.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 0 (-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 -4 (.f64 c a))))) 3))) (*.f64 2 a)))
	20.1b	(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)))
	32.3b	(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 0 (-.f64 b (pow.f64 (sqrt.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c)))))) 3))) (*.f64 2 a)))
✓	19.6b	(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 24803 to 15483 computations (37.6% saved)

regimes1.1s (12.5%)

Accuracy

Total 3.4b remaining (50.3%)

Threshold costs 0b (0%)

Counts

79 → 3

Compiler

Compiled 15614 to 10358 computations (33.7% saved)

bsearch71.0ms (0.8%)

Steps

Iters	Range		Point
7	1.0709906923331112e+128	3.773110330540282e+133	2.1551913558757867e+128
10	-3.773369676859572e+160	-4.104825089895383e+149	-6.183544261957572e+150

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (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

end1.0ms (0%)

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

sample2.0s (22.3%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
71.0ms	667×	body	128	nan
47.0ms	390×	body	128	invalid

Compiler

Compiled 757 to 498 computations (34.2% saved)

Details

analyze1.0s (11.4%)

sample150.0ms (1.6%)

simplify125.0ms (1.4%)

prune5.0ms (0.1%)

localize22.0ms (0.2%)

series202.0ms (2.2%)

rewrite40.0ms (0.4%)

simplify225.0ms (2.5%)

prune696.0ms (7.6%)

localize23.0ms (0.3%)

series65.0ms (0.7%)

rewrite9.0ms (0.1%)

simplify87.0ms (1%)

prune725.0ms (7.9%)

localize26.0ms (0.3%)

series116.0ms (1.3%)

rewrite7.0ms (0.1%)

simplify87.0ms (0.9%)

prune1.0s (11.3%)

localize33.0ms (0.4%)

series118.0ms (1.3%)

rewrite33.0ms (0.4%)

simplify211.0ms (2.3%)

prune814.0ms (8.9%)

regimes1.1s (12.5%)

bsearch71.0ms (0.8%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.0s (22.3%)

Profiling