Details

analyze893.0ms (11%)

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)

sample2.6s (32%)

Results

2.3s	8256×	body	128	valid
235.0ms	1122×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify125.0ms (1.5%)

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

21.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.2b	(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)))
▶	21.1b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Status

Error

Program

21.2b

(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)))

▶

21.1b

(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) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 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
✓	1.0b	(-.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))))
✓	1.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series163.0ms (2%)

Counts

4 → 96

Calls

4 calls:

56.0ms	(-.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))))
41.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite115.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 368

Calls

4 calls:

106.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
106.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
106.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify87.0ms (1.1%)

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

464 → 426

Iterations

Useful iterations: 2 (0.0ms)

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

prune859.0ms (10.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	653	4	657
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	654	5	659

Error

5.4b

Counts

659 → 5

Alt Table

Status	Error	Program
	34.1b	(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 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a)))
	21.8b	(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 -1 b)) (.f64 2 a)))
	21.2b	(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)))
	36.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (+.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
▶	17.7b	(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 34793 to 18964 computations (45.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series80.0ms (1%)

Counts

1 → 20

Calls

1 calls:

80.0ms

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

rewrite102.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

1 → 40

Calls

1 calls:

100.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	337	22
2	4158	22
3	4987	22
4	4850	22
0	0	0
1	0	0

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
351×	`unswap-sqr_binary64`
333×	`distribute-neg-frac_binary64`
328×	`times-frac_binary64`
221×	`associate-r_binary64`

Counts

60 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	612
1	210	609
2	666	585
3	3266	585
4	4979	585
5	5005	585

prune513.0ms (6.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	373	7	380

Error

5.4b

Counts

380 → 7

Alt Table

Status	Error	Program
	36.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (+.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	30.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) -1))
	21.2b	(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)))
	34.1b	(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 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a)))
	34.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (sqrt.f64 (.f64 a 2)))))
▶	18.3b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (-.f64 (/.f64 c b) (/.f64 b a)))
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 -1 (/.f64 b a)))

Compiler

Compiled 15824 to 8449 computations (46.6% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series11.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

11.0ms

(-.f64 (/.f64 c b) (/.f64 b a))

rewrite59.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

470×	`log-prod_binary64`
309×	`fma-def_binary64`
183×	`log-div_binary64`
174×	`fma-neg_binary64`
162×	`expm1-udef_binary64`

Counts

1 → 144

Calls

1 calls:

56.0ms

(-.f64 (/.f64 c b) (/.f64 b a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	164	10
2	2509	10
3	5033	10
0	0	0
1	0	0

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Counts

153 → 147

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	44
1	12	44
2	18	44
3	24	44
4	30	44
5	36	44
6	41	44
7	46	44
8	54	44
9	51	44
10	42	44

prune188.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Error

5.4b

Counts

154 → 8

Alt Table

Status	Error	Program
	21.2b	(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)))
	38.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))) (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))))))
	36.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (+.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	30.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) -1))
	34.4b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (pow.f64 (pow.f64 (-.f64 (/.f64 c b) (/.f64 b a)) 3) 1/3))
	34.1b	(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 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a)))
	34.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (sqrt.f64 (.f64 a 2)))))
▶	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 -1 (/.f64 b a)))

Compiler

Compiled 4994 to 1943 computations (61.1% saved)

localize13.0ms (0.2%)

Compiler: Compiled 1536 to 1280 computations (16.7% saved)

prune9.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

5.4b

Counts

8 → 8

Alt Table

Status	Error	Program
	21.2b	(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)))
	38.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))) (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (/.f64 c b) (/.f64 b a)))))))
	36.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (+.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	30.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) -1))
	34.4b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (pow.f64 (pow.f64 (-.f64 (/.f64 c b) (/.f64 b a)) 3) 1/3))
	34.1b	(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 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a)))
	34.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (sqrt.f64 (.f64 a 2)))))
✓	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 -1 (/.f64 b a)))

Compiler

Compiled 303 to 186 computations (38.6% saved)

regimes1.9s (23.4%)

Accuracy

Total 0.9b remaining (14.6%)

Threshold costs 0.9b (14.6%)

Counts

191 → 5

Compiler

Compiled 27282 to 17734 computations (35% saved)

bsearch10.0ms (0.1%)

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

simplify21.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	486
1	83	474
2	111	474
3	141	474
4	162	474
5	173	474
6	177	474
7	178	474
8	177	474

end244.0ms (3%)

Compiler: Compiled 933 to 554 computations (40.6% saved)

Iter	Nodes	Cost
0	61	486
1	83	474
2	111	474
3	141	474
4	162	474
5	173	474
6	177	474
7	178	474
8	177	474

Iter	Nodes	Cost
0	61	486
1	83	474
2	111	474
3	141	474
4	162	474
5	173	474
6	177	474
7	178	474
8	177	474

Details

analyze893.0ms (11%)

sample2.6s (32%)

simplify125.0ms (1.5%)

prune5.0ms (0.1%)

localize24.0ms (0.3%)

series163.0ms (2%)

rewrite115.0ms (1.4%)

simplify87.0ms (1.1%)

prune859.0ms (10.5%)

localize19.0ms (0.2%)

series80.0ms (1%)

rewrite102.0ms (1.2%)

simplify65.0ms (0.8%)

prune513.0ms (6.3%)

localize14.0ms (0.2%)

series11.0ms (0.1%)

rewrite59.0ms (0.7%)

simplify10.0ms (0.1%)

prune188.0ms (2.3%)

localize13.0ms (0.2%)

prune9.0ms (0.1%)

regimes1.9s (23.4%)

bsearch10.0ms (0.1%)

simplify21.0ms (0.3%)

end244.0ms (3%)

Profiling

Iter	Nodes	Cost
0	61	486
1	83	474
2	111	474
3	141	474
4	162	474
5	173	474
6	177	474
7	178	474
8	177	474