Details

analyze765.0ms (7.7%)

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
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)

sample2.3s (23.5%)

Results

2.0s	8256×	body	128	valid
177.0ms	1055×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify129.0ms (1.3%)

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

18.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	18.7b	(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

▶

18.4b

(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))

18.7b

(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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.4b	(-.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))))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series111.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite119.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`fma-def_binary64`
416×	`fma-neg_binary64`
371×	`egg-rr`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`

Counts

4 → 371

Calls

4 calls:

103.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
103.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
103.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
103.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	296	56
2	3584	56
3	5331	56

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
447×	`unswap-sqr_binary64`
295×	`fma-def_binary64`
283×	`associate-r_binary64`
278×	`associate-/l*_binary64`

Counts

467 → 429

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2213
1	293	2123
2	918	2035
3	4407	2035
4	5258	2035

prune1.1s (11.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	654	7	661
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	655	8	663

Error

5.4b

Counts

663 → 8

Alt Table

Status	Error	Program
	18.7b	(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)))
▶	18.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.3b	(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 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 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)))
	21.9b	(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)))
	22.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.1b	(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) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2))) (*.f64 2 a)))
	18.5b	(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) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2)) (*.f64 2 a)))

Compiler

Compiled 35149 to 19190 computations (45.4% 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))))
✓	7.2b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))
	23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	23.8b	(pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series88.0ms (0.9%)

Counts

2 → 56

Calls

2 calls:

45.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))
43.0ms	(pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4)

rewrite111.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`prod-diff_binary64`
229×	`log1p-udef_binary64`
210×	`egg-rr`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`

Counts

2 → 210

Calls

2 calls:

101.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))
101.0ms	(pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	305	30
2	3063	30
3	4906	30

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
482×	`cancel-sign-sub-inv_binary64`
244×	`distribute-neg-frac_binary64`
177×	`sub-neg_binary64`
169×	`times-frac_binary64`

Counts

266 → 287

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2538
1	755	2480
2	2827	2444
3	5123	2444

prune787.0ms (7.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	415	10	425

Error

2.2b

Counts

425 → 10

Alt Table

Status	Error	Program
	37.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 a))) (log.f64 (/.f64 1 c))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.3b	(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 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)))
	18.7b	(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)))
✓	18.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	37.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2))) (/.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 (.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)))
	21.9b	(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)))
	22.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.1b	(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) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2))) (*.f64 2 a)))
▶	18.5b	(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) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2)) (*.f64 2 a)))

Compiler

Compiled 29651 to 16171 computations (45.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	12.5b	(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))
	23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
	23.8b	(pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series37.0ms (0.4%)

Counts

1 → 20

Calls

1 calls:

37.0ms

(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
297×	`fma-def_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
201×	`log-pow_binary64`

Counts

1 → 69

Calls

1 calls:

58.0ms

(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	304	16
2	3042	15
3	5330	15

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-neg_binary64`
411×	`unswap-sqr_binary64`
408×	`times-frac_binary64`
250×	`associate-/l*_binary64`
246×	`associate-r_binary64`

Counts

89 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	684
1	213	668
2	694	638
3	3573	638
4	5061	638

prune856.0ms (8.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	326	3	329
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	327	12	339

Error

0.7b

Counts

339 → 12

Alt Table

Status	Error	Program
	37.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 a))) (log.f64 (/.f64 1 c))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.3b	(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 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)))
	32.0b	(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) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 a 4)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a)))
	22.1b	(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) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2))) (*.f64 2 a)))
▶	18.7b	(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)))
✓	18.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	37.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	21.9b	(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)))
	22.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
✓	18.5b	(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) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2)) (*.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) (pow.f64 (sqrt.f64 (neg.f64 b)) 2)) (*.f64 2 a)))
	29.1b	(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) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 c 4)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a)))

Compiler

Compiled 18486 to 10642 computations (42.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	1.4b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series120.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

40.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
35.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
33.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
12.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite83.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`fma-def_binary64`
267×	`fma-neg_binary64`
213×	`egg-rr`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`

Counts

4 → 213

Calls

4 calls:

77.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
77.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
77.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
77.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	237	56
2	2959	53
3	4953	53

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
447×	`unswap-sqr_binary64`
299×	`fma-def_binary64`
283×	`associate-r_binary64`
278×	`associate-/l*_binary64`

Counts

309 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2198
1	294	2110
2	903	2022
3	4393	2022
4	5244	2022

prune673.0ms (6.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	368	3	371
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	371	12	383

Error

0.4b

Counts

383 → 12

Alt Table

Status	Error	Program
	37.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 a))) (log.f64 (/.f64 1 c))))) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.3b	(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 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)))
	33.4b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	29.1b	(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) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 c 4)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a)))
	21.9b	(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)))
	22.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.1b	(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) (cbrt.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 3/2))) (*.f64 2 a)))
✓	18.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
✓	18.5b	(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) (pow.f64 (pow.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)) 1/4) 2)) (*.f64 2 a)))
	19.3b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (/.f64 1/2 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) (pow.f64 (sqrt.f64 (neg.f64 b)) 2)) (*.f64 2 a)))
	28.5b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))) b) (/.f64 1/2 a)))

Compiler

Compiled 16496 to 9867 computations (40.2% saved)

regimes1.7s (17.3%)

Accuracy

Total 5.9b remaining (92.1%)

Threshold costs 0b (0%)

Counts

115 → 3

Compiler

Compiled 19894 to 13586 computations (31.7% saved)

bsearch61.0ms (0.6%)

Steps

Iters	Range		Point
10	8.352653001455336e+102	3.7642961010636734e+115	4.778234809810149e+105
3	-6.237999209161542e+154	-3.497256798768183e+152	-6.729379008114002e+152

Compiler

Compiled 4 to 3 computations (25% saved)

simplify40.0ms (0.4%)

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

end325.0ms (3.3%)

Compiler: Compiled 690 to 451 computations (34.6% saved)

Details

analyze765.0ms (7.7%)

sample2.3s (23.5%)

simplify129.0ms (1.3%)

prune5.0ms (0.1%)

localize20.0ms (0.2%)

series111.0ms (1.1%)

rewrite119.0ms (1.2%)

simplify92.0ms (0.9%)

prune1.1s (11.3%)

localize26.0ms (0.3%)

series88.0ms (0.9%)

rewrite111.0ms (1.1%)

simplify81.0ms (0.8%)

prune787.0ms (7.9%)

localize26.0ms (0.3%)

series37.0ms (0.4%)

rewrite60.0ms (0.6%)

simplify49.0ms (0.5%)

prune856.0ms (8.6%)

localize23.0ms (0.2%)

series120.0ms (1.2%)

rewrite83.0ms (0.8%)

simplify85.0ms (0.9%)

prune673.0ms (6.8%)

regimes1.7s (17.3%)

bsearch61.0ms (0.6%)

simplify40.0ms (0.4%)

end325.0ms (3.3%)

Profiling