Details

analyze406.0ms (5.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample387.0ms (5.6%)

Algorithm

1×

intervals

Results

16.0ms	121×	body	256	valid
10.0ms	290×	pre	128	true
7.0ms	36×	body	512	valid
6.0ms	99×	body	128	valid
3.0ms	34×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify262.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	22

prune4.0ms (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

50.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	50.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	50.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	27.3b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series201.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

90.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
56.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.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)
2.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify198.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune150.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	219	7	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	221	7	228

Error

0.0b

Counts

228 → 7

Alt Table

Status	Error	Program
	2.4b	(.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
	51.3b	(.f64 (+.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 b)) (.f64 (-.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 b)) (/.f64 1/2 a)))
	50.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
▶	0.3b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	50.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (/.f64 (cbrt.f64 1/2) a))
	3.8b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	2.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))

Compiler

Compiled 6347 to 3718 computations (41.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.1b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series333.0ms (4.8%)

Counts

3 → 64

Calls

3 calls:

277.0ms

(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

52.0ms

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

3.0ms

(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
15×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

12.0ms

(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

9.0ms

(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

3.0ms

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

simplify167.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
248×	`associate-l_binary64`
225×	`associate-/l*_binary64`
220×	`associate-r_binary64`
176×	`div-sub_binary64`

Counts

156 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3787
1	708	3244
2	3132	3157
3	4613	3157
4	4932	3157

prune230.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	218	6	224

Error

Counts

224 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
	0.6b	(/.f64 (.f64 (/.f64 c (/.f64 (sqrt.f64 a) (.f64 a -4))) (/.f64 1/2 (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
▶	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.5b	(.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.7b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (.f64 c (.f64 a -4)) 0)) (/.f64 (.f64 (.f64 1/2 1/2) 1/2) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	2.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))

Compiler

Compiled 7256 to 4578 computations (36.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))

series273.0ms (3.9%)

Counts

1 → 20

Calls

1 calls:

272.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

7.0ms

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

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
615×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
352×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

47 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1488
1	366	1333
2	1180	1254
3	4844	1254
4	5078	1254

prune185.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	183	5	188

Error

Counts

188 → 5

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	0.5b	(.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
	2.0b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.7b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (.f64 c (.f64 a -4)) 0)) (/.f64 (.f64 (.f64 1/2 1/2) 1/2) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 4790 to 2900 computations (39.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c)
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))

series358.0ms (5.2%)

Counts

2 → 40

Calls

2 calls:

279.0ms	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
79.0ms	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 119

Calls

2 calls:

7.0ms	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
6.0ms	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c)

simplify143.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-/l*_binary64`
483×	`associate-/r/_binary64`
395×	`fma-def_binary64`
293×	`associate-/l/_binary64`
145×	`cancel-sign-sub-inv_binary64`

Counts

159 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	5605
1	689	5339
2	2145	5104
3	5012	5104

prune256.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	303	5	308

Error

Counts

308 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	0.5b	(.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
	2.0b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.7b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (.f64 c (.f64 a -4)) 0)) (/.f64 (.f64 (.f64 1/2 1/2) 1/2) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 8570 to 5159 computations (39.8% saved)

regimes1.4s (20.3%)

Accuracy

Total 0.1b remaining (80.9%)

Threshold costs 0.1b (80.9%)

Counts

239 → 1

Compiler

Compiled 28332 to 18726 computations (33.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	16	22
2	16	22

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.8s (25.4%)

Algorithm

1×

intervals

Results

493.0ms	3789×	body	256	valid
290.0ms	8787×	pre	128	true
266.0ms	1420×	body	512	valid
182.0ms	2791×	body	128	valid
49.0ms	787×	body	128	nan

Compiler

Compiled 245 to 174 computations (29% saved)

Details

analyze406.0ms (5.9%)

sample387.0ms (5.6%)

simplify262.0ms (3.8%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series201.0ms (2.9%)

rewrite23.0ms (0.3%)

simplify198.0ms (2.9%)

prune150.0ms (2.2%)

localize15.0ms (0.2%)

series333.0ms (4.8%)

rewrite32.0ms (0.5%)

simplify167.0ms (2.4%)

prune230.0ms (3.3%)

localize11.0ms (0.2%)

series273.0ms (3.9%)

rewrite8.0ms (0.1%)

simplify64.0ms (0.9%)

prune185.0ms (2.7%)

localize11.0ms (0.2%)

series358.0ms (5.2%)

rewrite27.0ms (0.4%)

simplify143.0ms (2.1%)

prune256.0ms (3.7%)

regimes1.4s (20.3%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.8s (25.4%)

Profiling