Details

analyze374.0ms (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)

sample144.0ms (2.1%)

Algorithm

1×

intervals

Results

17.0ms	129×	body	256	valid
11.0ms	276×	pre	128	true
8.0ms	43×	body	512	valid
6.0ms	84×	body	128	valid
1.0ms	20×	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

53.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
▶	53.1b	(.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 (0.2%)

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))
✓	26.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series476.0ms (6.9%)

Counts

4 → 96

Calls

4 calls:

363.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
55.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
46.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite22.0ms (0.3%)

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))
5.0ms	(-.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))

simplify191.0ms (2.8%)

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

prune214.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	222	4	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	4	228

Error

0.0b

Counts

228 → 4

Alt Table

Status	Error	Program
	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))
	53.1b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
	1.4b	(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))))))
▶	0.4b	(/.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))

Compiler

Compiled 6177 to 3592 computations (41.8% saved)

localize16.0ms (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	(fma.f64 a (.f64 c -4) (.f64 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))
✓	0.3b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series332.0ms (4.8%)

Counts

3 → 64

Calls

3 calls:

276.0ms

(/.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)

4.0ms

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

rewrite31.0ms (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))

10.0ms

(*.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)

simplify115.0ms (1.7%)

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

prune245.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	216	5	221

Error

0.0b

Counts

221 → 5

Alt Table

Status	Error	Program
	1.4b	(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))))))
	0.4b	(/.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))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.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)) (/.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))) (/.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))))
	0.5b	(.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)))
▶	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 7238 to 4554 computations (37.1% 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	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

series284.0ms (4.1%)

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))

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

prune162.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
	1.3b	(/.f64 (.f64 -2 c) (fma.f64 2 (-.f64 b (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (/.f64 -4 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3)))))
	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.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)))
	1.4b	(-.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))))
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 4766 to 2868 computations (39.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series481.0ms (7%)

Counts

2 → 40

Calls

2 calls:

277.0ms	(.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)))
203.0ms	(/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
33×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
24×	`times-frac_binary64`
20×	`prod-exp_binary64`

Counts

2 → 100

Calls

2 calls:

16.0ms	(.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)))
5.0ms	(/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

simplify129.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

445×	`distribute-rgt-in_binary64`
389×	`associate-l_binary64`
387×	`fma-neg_binary64`
359×	`distribute-lft-in_binary64`
265×	`associate-r_binary64`

Counts

140 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4664
1	697	3930
2	2742	3781
3	4786	3781
4	4948	3781

prune259.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	271	5	276

Error

Counts

276 → 5

Alt Table

Status	Error	Program
	1.3b	(/.f64 (.f64 -2 c) (fma.f64 2 (-.f64 b (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (/.f64 -4 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3)))))
	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.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)))
	1.4b	(-.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))))
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 9524 to 6186 computations (35% saved)

regimes1.1s (16.2%)

Accuracy

Total 0.1b remaining (79.9%)

Threshold costs 0.1b (79.9%)

Counts

203 → 1

Compiler

Compiled 25400 to 17374 computations (31.6% 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 (27.2%)

Algorithm

1×

intervals

Results

505.0ms	3751×	body	256	valid
332.0ms	8849×	pre	128	true
295.0ms	1489×	body	512	valid
193.0ms	2760×	body	128	valid
55.0ms	849×	body	128	nan

Compiler

Compiled 242 to 164 computations (32.2% saved)

Details

analyze374.0ms (5.4%)

sample144.0ms (2.1%)

simplify262.0ms (3.8%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series476.0ms (6.9%)

rewrite22.0ms (0.3%)

simplify191.0ms (2.8%)

prune214.0ms (3.1%)

localize16.0ms (0.2%)

series332.0ms (4.8%)

rewrite31.0ms (0.5%)

simplify115.0ms (1.7%)

prune245.0ms (3.6%)

localize10.0ms (0.1%)

series284.0ms (4.1%)

rewrite8.0ms (0.1%)

simplify64.0ms (0.9%)

prune162.0ms (2.4%)

localize16.0ms (0.2%)

series481.0ms (7%)

rewrite32.0ms (0.5%)

simplify129.0ms (1.9%)

prune259.0ms (3.8%)

regimes1.1s (16.2%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.9s (27.2%)

Profiling