Details

analyze355.0ms (5.4%)

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)

sample365.0ms (5.5%)

Algorithm

1×

intervals

Results

64.0ms	130×	body	256	valid
10.0ms	48×	body	512	valid
10.0ms	278×	pre	128	true
5.0ms	78×	body	128	valid
1.0ms	22×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify259.0ms (3.9%)

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

53.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
▶	53.6b	(.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)

localize10.0ms (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))
✓	25.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series201.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

88.0ms	(.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)
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 (0.4%)

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:

8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
6.0ms	(-.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))

simplify224.0ms (3.4%)

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

prune154.0ms (2.3%)

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
	53.6b	(/.f64 (.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3) (pow.f64 b 3)) (/.f64 1/2 a)) (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))
	2.1b	(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))))))
	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))
	53.6b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 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))

Compiler

Compiled 6297 to 3672 computations (41.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))

series359.0ms (5.4%)

Counts

3 → 64

Calls

3 calls:

300.0ms

(/.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))

56.0ms

(+.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:

13.0ms

(/.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))

8.0ms

(*.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)

simplify122.0ms (1.9%)

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

prune197.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	217	5	222

Error

Counts

222 → 5

Alt Table

Status	Error	Program
	0.4b	(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (.f64 (+.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (-.f64 (.f64 0 0) (.f64 (.f64 c (.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.9b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
▶	0.0b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.5b	(/.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)))

Compiler

Compiled 7202 to 4540 computations (37% saved)

localize10.0ms (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)))
	0.0b	(+.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))

series285.0ms (4.3%)

Counts

1 → 20

Calls

1 calls:

284.0ms

(/.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:

6.0ms

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

simplify67.0ms (1%)

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

prune184.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
▶	0.1b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	0.4b	(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (.f64 (+.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (-.f64 (.f64 0 0) (.f64 (.f64 c (.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.5b	(/.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)))
	0.5b	(/.f64 (/.f64 (.f64 -2 c) (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)))

Compiler

Compiled 4760 to 2872 computations (39.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series422.0ms (6.4%)

Counts

3 → 108

Calls

3 calls:

254.0ms

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

111.0ms

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

56.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 54

Calls

3 calls:

4.0ms

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

1.0ms

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

0.0ms

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

simplify188.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
332×	`fma-def_binary64`
205×	`*-commutative_binary64`
174×	`fma-neg_binary64`
136×	`distribute-neg-in_binary64`

Counts

162 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	610	8925
1	2099	8542
2	4978	8534
3	5076	8534

prune468.0ms (7.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	359	1	360
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	360	5	365

Error

Counts

365 → 5

Alt Table

Status	Error	Program
	0.4b	(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (.f64 (+.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (-.f64 (.f64 0 0) (.f64 (.f64 c (.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	3.4b	(neg.f64 (+.f64 (/.f64 c b) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))))
✓	0.0b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.1b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	0.5b	(/.f64 (/.f64 (.f64 -2 c) (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)))

Compiler

Compiled 18104 to 12201 computations (32.6% saved)

regimes708.0ms (10.7%)

Accuracy

Total 0.1b remaining (76.8%)

Threshold costs 0.1b (76.8%)

Counts

130 → 1

Compiler

Compiled 15996 to 10682 computations (33.2% 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)

sample1.9s (28.9%)

Algorithm

1×

intervals

Results

524.0ms	3797×	body	256	valid
332.0ms	8847×	pre	128	true
295.0ms	1471×	body	512	valid
192.0ms	2732×	body	128	valid
58.0ms	847×	body	128	nan

Compiler

Compiled 214 to 147 computations (31.3% saved)

Details

analyze355.0ms (5.4%)

sample365.0ms (5.5%)

simplify259.0ms (3.9%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series201.0ms (3.1%)

rewrite23.0ms (0.4%)

simplify224.0ms (3.4%)

prune154.0ms (2.3%)

localize15.0ms (0.2%)

series359.0ms (5.4%)

rewrite32.0ms (0.5%)

simplify122.0ms (1.9%)

prune197.0ms (3%)

localize10.0ms (0.1%)

series285.0ms (4.3%)

rewrite8.0ms (0.1%)

simplify67.0ms (1%)

prune184.0ms (2.8%)

localize13.0ms (0.2%)

series422.0ms (6.4%)

rewrite10.0ms (0.1%)

simplify188.0ms (2.9%)

prune468.0ms (7.1%)

regimes708.0ms (10.7%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.9s (28.9%)

Profiling