Details

analyze959.0ms (10.5%)

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)

sample182.0ms (2%)

Algorithm

1×

intervals

Results

58.0ms	256×	body	128	valid
3.0ms	29×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify129.0ms (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

20.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	20.8b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	20.9b	(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

▶

20.8b

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

20.9b

(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)

localize24.0ms (0.3%)

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))))
✓	1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series175.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

61.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
54.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
48.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.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:

11.0ms	(-.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))

simplify207.0ms (2.3%)

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

prune656.0ms (7.2%)

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

6.2b

Counts

329 → 9

Alt Table

Status	Error	Program
	33.7b	(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)))
	24.7b	(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) (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 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 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
▶	20.9b	(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)))
	22.9b	(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) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.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)))
	29.6b	(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 (pow.f64 b 2))) (*.f64 2 a)))
	21.6b	(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 -1 b)) (.f64 2 a)))
	23.4b	(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)))

Compiler

Compiled 18455 to 10664 computations (42.2% 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))
✓	0.5b	(-.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))))
✓	23.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series259.0ms (2.8%)

Counts

4 → 80

Calls

4 calls:

91.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
62.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
59.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
46.0ms	(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:

12.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
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)))

simplify154.0ms (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

prune464.0ms (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	291	7	298
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	297	10	307

Error

6.1b

Counts

307 → 10

Alt Table

Status	Error	Program
	33.7b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	21.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (exp.f64 (log.f64 (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)))
	29.6b	(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 (pow.f64 b 2))) (*.f64 2 a)))
	21.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))))
	23.4b	(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)))
	20.9b	(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 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
▶	20.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	29.1b	(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 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 14328 to 8391 computations (41.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	10.5b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
	23.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series110.0ms (1.2%)

Counts

2 → 40

Calls

2 calls:

62.0ms

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

48.0ms

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
63×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
25×	`pow1_binary64`
16×	`rem-sqrt-square_binary64`

Counts

2 → 106

Calls

2 calls:

12.0ms

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

8.0ms

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

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
520×	`fma-neg_binary64`
492×	`associate-/l*_binary64`
466×	`associate-/r*_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

146 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3334
1	433	3107
2	1519	2864
3	4924	2864
4	5070	2864

prune770.0ms (8.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	336	10	346

Error

6.1b

Counts

346 → 10

Alt Table

Status	Error	Program
	33.7b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	21.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (exp.f64 (log.f64 (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)))
	29.6b	(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 (pow.f64 b 2))) (*.f64 2 a)))
	21.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))))
	23.4b	(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)))
▶	20.9b	(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 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
✓	20.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	29.1b	(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 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 18793 to 11199 computations (40.4% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	8.6b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
	23.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	24.4b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series155.0ms (1.7%)

Counts

2 → 72

Calls

2 calls:

96.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
58.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

2 → 33

Calls

2 calls:

6.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
1.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

404×	`associate-r_binary64`
351×	`times-frac_binary64`
305×	`associate-l_binary64`
267×	`associate-/r*_binary64`
259×	`fma-def_binary64`

Counts

105 → 149

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	407	6283
1	1307	5592
2	4937	5592
3	4949	5592

prune661.0ms (7.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	303	10	313

Error

6.1b

Counts

313 → 10

Alt Table

Status	Error	Program
	33.7b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	21.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (exp.f64 (log.f64 (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)))
	29.6b	(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 (pow.f64 b 2))) (*.f64 2 a)))
	21.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))))
	23.4b	(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)))
✓	20.9b	(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 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	21.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) (-.f64 (/.f64 c b) (/.f64 b a)))
✓	20.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a)))
	29.1b	(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 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 21293 to 13437 computations (36.9% saved)

regimes1.9s (20.4%)

Accuracy

Total 0.9b remaining (14%)

Threshold costs 0.9b (14%)

Counts

142 → 3

Compiler

Compiled 24398 to 16142 computations (33.8% saved)

bsearch47.0ms (0.5%)

Steps

Iters	Range		Point
8	8.262398165407483e+114	2.49066535905545e+117	1.3243813634661216e+116
2	-1.1442490457700476e+160	-1.5544390759223045e+151	-2.5932810897731523e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
14×	`+-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	41	148
1	62	144
2	88	144
3	107	144
4	119	144
5	123	144
6	122	144

end1.0ms (0%)

Compiler: Compiled 99 to 60 computations (39.4% saved)

sample1.9s (20.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
102.0ms	396×	body	128	invalid
85.0ms	672×	body	128	nan

Compiler

Compiled 569 to 362 computations (36.4% saved)

Details

analyze959.0ms (10.5%)

sample182.0ms (2%)

simplify129.0ms (1.4%)

prune5.0ms (0.1%)

localize24.0ms (0.3%)

series175.0ms (1.9%)

rewrite40.0ms (0.4%)

simplify207.0ms (2.3%)

prune656.0ms (7.2%)

localize19.0ms (0.2%)

series259.0ms (2.8%)

rewrite28.0ms (0.3%)

simplify154.0ms (1.7%)

prune464.0ms (5.1%)

localize21.0ms (0.2%)

series110.0ms (1.2%)

rewrite32.0ms (0.4%)

simplify114.0ms (1.2%)

prune770.0ms (8.4%)

localize25.0ms (0.3%)

series155.0ms (1.7%)

rewrite8.0ms (0.1%)

simplify136.0ms (1.5%)

prune661.0ms (7.2%)

regimes1.9s (20.4%)

bsearch47.0ms (0.5%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.9s (20.6%)

Profiling