Details

analyze716.0ms (8.7%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample150.0ms (1.8%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
2.0ms	19×	body	128	invalid
2.0ms	15×	body	128	nan

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify156.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1753×	`fma-neg_binary64`
1288×	`fma-def_binary64`
631×	`div-sub_binary64`
512×	`times-frac_binary64`
430×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	118	52
3	269	50
4	429	50
5	743	50
6	1315	50
7	1738	50
8	2176	50
9	2853	50
10	4066	50
11	3523	50
12	3575	50
13	3543	50
14	3557	50
15	4510	50
16	4622	50
17	4761	50

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

20.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 149 to 91 computations (38.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series456.0ms (5.6%)

Counts

4 → 80

Calls

4 calls:

297.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
60.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
54.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
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)))

simplify143.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-neg-in_binary64`
159×	`distribute-rgt-in_binary64`
157×	`distribute-lft-neg-in_binary64`

Counts

186 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	5384
1	686	4516
2	2546	4321
3	4500	4319
4	4865	4319

prune428.0ms (5.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	267	11	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	11	279

Error

3.9b

Counts

279 → 11

Alt Table

Status	Error	Program
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 c (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	30.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	34.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	20.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (.f64 2 c))))
	24.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (.f64 2 b) (.f64 2 (/.f64 (.f64 c a) b))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.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)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))

Compiler

Compiled 13523 to 7947 computations (41.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series88.0ms (1.1%)

Counts

2 → 56

Calls

2 calls:

76.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
12.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

2 → 45

Calls

2 calls:

5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-neg_binary64`
411×	`times-frac_binary64`
332×	`associate-r_binary64`
308×	`associate-l_binary64`
293×	`associate-/l*_binary64`

Counts

101 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	2198
1	339	2031
2	996	1956
3	4397	1956
4	4966	1956

prune327.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	194	10	204

Error

3.8b

Counts

204 → 10

Alt Table

Status	Error	Program
	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.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)))))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	30.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 c (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
▶	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	34.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	20.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (.f64 2 c))))
	21.2b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))

Compiler

Compiled 8111 to 5144 computations (36.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series76.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

76.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 43

Calls

1 calls:

8.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

460×	`times-frac_binary64`
408×	`associate-l_binary64`
317×	`unswap-sqr_binary64`
311×	`associate-/l*_binary64`
305×	`fma-def_binary64`

Counts

63 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1718
1	370	1571
2	1178	1497
3	4445	1497
4	5276	1497

prune328.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	206	10	216

Error

3.8b

Counts

216 → 10

Alt Table

Status	Error	Program
▶	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.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)))))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	30.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 c (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
✓	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	34.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	20.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (.f64 2 c))))
	21.2b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))

Compiler

Compiled 8830 to 5735 computations (35.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	0.3b	(.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)))))
✓	10.7b	(+.f64 b (.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))))))
✓	24.8b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series333.0ms (4.1%)

Counts

4 → 144

Calls

4 calls:

105.0ms	(.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)))))
97.0ms	(+.f64 b (.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))))))
69.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
62.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
22×	`sqrt-prod_binary64`
15×	`unswap-sqr_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 100

Calls

4 calls:

8.0ms	(.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)))))
2.0ms	(+.f64 b (.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))))))
1.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify258.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

446×	`times-frac_binary64`
355×	`associate-/r*_binary64`
335×	`fma-def_binary64`
315×	`associate-/l*_binary64`
204×	`cancel-sign-sub-inv_binary64`

Counts

244 → 346

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	568	14040
1	1835	12883
2	4951	12883
3	4948	12883

prune1.1s (13.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	409	10	419

Error

3.8b

Counts

419 → 10

Alt Table

Status	Error	Program
✓	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.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)))))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	30.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 c (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
✓	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	34.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	20.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (.f64 2 c))))
	21.2b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))

Compiler

Compiled 28010 to 18688 computations (33.3% saved)

regimes1.5s (17.8%)

Accuracy

Total 1.6b remaining (22.8%)

Threshold costs 0b (0%)

Counts

109 → 5

Compiler

Compiled 17482 to 11818 computations (32.4% saved)

bsearch6.0ms (0.1%)

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

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	499
1	87	487
2	120	487
3	145	487
4	161	487
5	167	487
6	168	487
7	167	487

end4.0ms (0%)

Compiler: Compiled 326 to 191 computations (41.4% saved)

sample1.8s (22.3%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
125.0ms	622×	body	128	nan
43.0ms	391×	body	128	invalid

Compiler

Compiled 764 to 488 computations (36.1% saved)

Details

analyze716.0ms (8.7%)

sample150.0ms (1.8%)

simplify156.0ms (1.9%)

prune4.0ms (0.1%)

localize19.0ms (0.2%)

series456.0ms (5.6%)

rewrite24.0ms (0.3%)

simplify143.0ms (1.7%)

prune428.0ms (5.2%)

localize22.0ms (0.3%)

series88.0ms (1.1%)

rewrite8.0ms (0.1%)

simplify82.0ms (1%)

prune327.0ms (4%)

localize22.0ms (0.3%)

series76.0ms (0.9%)

rewrite12.0ms (0.1%)

simplify79.0ms (1%)

prune328.0ms (4%)

localize23.0ms (0.3%)

series333.0ms (4.1%)

rewrite22.0ms (0.3%)

simplify258.0ms (3.2%)

prune1.1s (13.4%)

regimes1.5s (17.8%)

bsearch6.0ms (0.1%)

simplify20.0ms (0.2%)

end4.0ms (0%)

sample1.8s (22.3%)

Profiling