Details

analyze343.0ms (4.8%)

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)

sample2.5s (35.8%)

Results

1.0s	3894×	body	256	valid
656.0ms	1531×	body	512	valid
655.0ms	2831×	body	128	valid
123.0ms	862×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify257.0ms (3.6%)

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

52.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	52.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	52.3b	(/.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)

localize9.0ms (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))
✓	27.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series208.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

100.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
53.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(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:

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))

simplify188.0ms (2.7%)

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

prune152.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	6	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	222	6	228

Error

0.0b

Counts

228 → 6

Alt Table

Status	Error	Program
	52.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))) (cbrt.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))))
	1.8b	(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))))))
	6.1b	(neg.f64 (/.f64 c b))
	2.2b	(.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))
▶	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))
	52.3b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (*.f64 (/.f64 1/2 a) (/.f64 1/2 a)) (/.f64 1/2 a))))

Compiler

Compiled 6347 to 3694 computations (41.8% saved)

localize15.0ms (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	(+.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))

series312.0ms (4.4%)

Counts

3 → 64

Calls

3 calls:

257.0ms

(/.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))

51.0ms

(+.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))

rewrite29.0ms (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))

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)

simplify112.0ms (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

prune210.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (/.f64 (.f64 (.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.4b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))))
	0.5b	(/.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))
	1.8b	(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 7044 to 4424 computations (37.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series267.0ms (3.8%)

Counts

2 → 44

Calls

2 calls:

264.0ms	(/.f64 (/.f64 (.f64 (.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
3.0ms	(/.f64 (.f64 (.f64 c a) -2) a)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
38×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`

Counts

2 → 87

Calls

2 calls:

10.0ms	(/.f64 (/.f64 (.f64 (.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
5.0ms	(/.f64 (.f64 (.f64 c a) -2) a)

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
760×	`associate-*l/_binary64`
560×	`associate-/r/_binary64`
201×	`associate-/l*_binary64`
171×	`fma-neg_binary64`

Counts

131 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3858
1	590	3469
2	2203	2939
3	4868	2939
4	5525	2939

prune208.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	226	4	230

Error

Counts

230 → 4

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (.f64 (.f64 c a) -2) a)))
	0.5b	(/.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))
	1.8b	(-.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))))
✓	0.1b	(/.f64 (/.f64 (.f64 (.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

Compiler

Compiled 6660 to 3656 computations (45.1% saved)

localize14.0ms (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	(fma.f64 a (.f64 c -4) (.f64 b b))
	0.1b	(/.f64 (.f64 (.f64 c a) -2) a)
✓	0.3b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (.f64 (.f64 c a) -2) a)))

series263.0ms (3.7%)

Counts

1 → 20

Calls

1 calls:

263.0ms

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

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

259×	`times-frac_binary64`
155×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`
51×	`add-exp-log_binary64`

Counts

1 → 170

Calls

1 calls:

12.0ms

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

simplify221.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

458×	`fma-neg_binary64`
251×	`sub-neg_binary64`
208×	`fma-def_binary64`
201×	`associate-/r/_binary64`
158×	`associate-/l*_binary64`

Counts

190 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	8609
1	634	7870
2	2445	7459
3	3985	7459
4	4916	7459
5	4953	7459

prune300.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	333	4	337

Error

Counts

337 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (.f64 (.f64 c a) -2) a)))
	1.8b	(-.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))))
✓	0.1b	(/.f64 (/.f64 (.f64 (.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.5b	(/.f64 (/.f64 1 (/.f64 1 (/.f64 (.f64 c a) 1))) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 -2 a)))

Compiler

Compiled 11570 to 6611 computations (42.9% saved)

regimes1.1s (16%)

Accuracy

Total 0.1b remaining (71.5%)

Threshold costs 0.1b (71.5%)

Counts

245 → 1

Compiler

Compiled 30260 to 20306 computations (32.9% 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

end90.0ms (1.3%)

Compiler: Compiled 152 to 103 computations (32.2% saved)

Details

analyze343.0ms (4.8%)

sample2.5s (35.8%)

simplify257.0ms (3.6%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series208.0ms (2.9%)

rewrite22.0ms (0.3%)

simplify188.0ms (2.7%)

prune152.0ms (2.1%)

localize15.0ms (0.2%)

series312.0ms (4.4%)

rewrite29.0ms (0.4%)

simplify112.0ms (1.6%)

prune210.0ms (3%)

localize13.0ms (0.2%)

series267.0ms (3.8%)

rewrite22.0ms (0.3%)

simplify107.0ms (1.5%)

prune208.0ms (2.9%)

localize14.0ms (0.2%)

series263.0ms (3.7%)

rewrite43.0ms (0.6%)

simplify221.0ms (3.1%)

prune300.0ms (4.2%)

regimes1.1s (16%)

simplify2.0ms (0%)

end90.0ms (1.3%)

Profiling