Details

analyze375.0ms (4.3%)

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)

sample136.0ms (1.6%)

Algorithm

1×

intervals

Results

17.0ms	120×	body	256	valid
11.0ms	270×	pre	128	true
9.0ms	46×	body	512	valid
6.0ms	90×	body	128	valid
1.0ms	14×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify259.0ms (3%)

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%)

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

54.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	54.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
▶	54.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

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))
✓	27.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series498.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

383.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
57.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
47.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite22.0ms (0.2%)

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)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify195.0ms (2.2%)

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

prune176.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	223	5	228

Error

0.0b

Counts

228 → 5

Alt Table

Status	Error	Program
	54.1b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) 1/2) a)
▶	0.4b	(/.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))
	1.3b	(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))))))
	1.7b	(.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (/.f64 1/2 a))
	53.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 b) (sqrt.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) (.f64 (sqrt.f64 b) (sqrt.f64 b)))) (/.f64 1/2 a))

Compiler

Compiled 6273 to 3638 computations (42% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series344.0ms (3.9%)

Counts

3 → 64

Calls

3 calls:

286.0ms

(/.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))

54.0ms

(+.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))

rewrite31.0ms (0.4%)

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:

11.0ms

(/.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)

simplify144.0ms (1.6%)

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 → 196

Iterations

Useful iterations: 2 (0.0ms)

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

prune205.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	209	6	215
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	212	8	220

Error

Counts

220 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f64 (/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	54.1b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) 1/2) a)
	0.7b	(/.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))
	0.6b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	1.3b	(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))))))
▶	0.5b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	0.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (-.f64 (.f64 c (*.f64 a -4)) 0) a)))
	1.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 c (.f64 a -4)) 0)) (cbrt.f64 (+.f64 (.f64 c (.f64 a -4)) 0))) (.f64 (/.f64 1/2 a) (cbrt.f64 (.f64 c (.f64 a -4))))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 7342 to 4632 computations (36.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.3b	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))
✓	0.4b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))

series384.0ms (4.4%)

Counts

2 → 40

Calls

2 calls:

293.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
91.0ms	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))

rewrite95.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

620×	`times-frac_binary64`
409×	`*-un-lft-identity_binary64`
277×	`add-sqr-sqrt_binary64`
277×	`add-cube-cbrt_binary64`
70×	`associate-/r*_binary64`

Counts

2 → 340

Calls

2 calls:

18.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
7.0ms	(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))

simplify404.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-/r/_binary64`
461×	`associate-/l*_binary64`
403×	`associate-*l/_binary64`
403×	`associate-/l/_binary64`
355×	`fma-neg_binary64`

Counts

380 → 558

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	573	19325
1	1413	18727
2	4970	18727
3	5314	18727

prune729.0ms (8.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	625	2	627
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	629	6	635

Error

Counts

635 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	1.3b	(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))))))
▶	0.3b	(.f64 (/.f64 1/2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 c (/.f64 a (.f64 a -4))))
	0.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (-.f64 (.f64 c (*.f64 a -4)) 0) a)))
✓	0.5b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	0.6b	(.f64 (/.f64 1/2 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (/.f64 (*.f64 a -4) a)))

Compiler

Compiled 27149 to 16911 computations (37.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series565.0ms (6.5%)

Counts

3 → 60

Calls

3 calls:

291.0ms

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

218.0ms

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

55.0ms

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

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
37×	`add-cbrt-cube_binary64`
37×	`add-exp-log_binary64`

Counts

3 → 130

Calls

3 calls:

18.0ms

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

4.0ms

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

3.0ms

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

simplify184.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
268×	`associate-/l*_binary64`
251×	`associate-*r/_binary64`
230×	`associate-r_binary64`
218×	`*-commutative_binary64`

Counts

190 → 278

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	6493
1	1030	5244
2	3852	5056
3	4685	5056
4	4960	5056
5	4868	5056

prune262.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	297	6	303

Error

Counts

303 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 c (/.f64 a (.f64 a -4))))
	0.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (-.f64 (.f64 c (*.f64 a -4)) 0) a)))
✓	0.5b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	0.6b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	1.3b	(-.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))) (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))))
	0.6b	(.f64 (/.f64 1/2 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (/.f64 (*.f64 a -4) a)))

Compiler

Compiled 9560 to 5858 computations (38.7% saved)

regimes1.7s (19.4%)

Accuracy

Total 0.1b remaining (88.1%)

Threshold costs 0.1b (88.1%)

Counts

323 → 1

Compiler

Compiled 41160 to 28438 computations (30.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	15	22
2	15	22

end1.0ms (0%)

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

sample1.9s (22.2%)

Algorithm

1×

intervals

Results

503.0ms	3758×	body	256	valid
356.0ms	8847×	pre	128	true
295.0ms	1515×	body	512	valid
206.0ms	2727×	body	128	valid
54.0ms	847×	body	128	nan

Compiler

Compiled 266 to 184 computations (30.8% saved)

Details

analyze375.0ms (4.3%)

sample136.0ms (1.6%)

simplify259.0ms (3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series498.0ms (5.7%)

rewrite22.0ms (0.2%)

simplify195.0ms (2.2%)

prune176.0ms (2%)

localize16.0ms (0.2%)

series344.0ms (3.9%)

rewrite31.0ms (0.4%)

simplify144.0ms (1.6%)

prune205.0ms (2.3%)

localize14.0ms (0.2%)

series384.0ms (4.4%)

rewrite95.0ms (1.1%)

simplify404.0ms (4.6%)

prune729.0ms (8.3%)

localize14.0ms (0.2%)

series565.0ms (6.5%)

rewrite40.0ms (0.5%)

simplify184.0ms (2.1%)

prune262.0ms (3%)

regimes1.7s (19.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.9s (22.2%)

Profiling