Details

analyze576.0ms (3.7%)

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)

sample3.6s (23.7%)

Results

1.6s	3921×	body	256	valid
943.0ms	1526×	body	512	valid
685.0ms	2809×	body	128	valid
221.0ms	840×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify477.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

prune8.0ms (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

52.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	52.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	26.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series335.0ms (2.2%)

Counts

4 → 76

Calls

4 calls:

176.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
130.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
23.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
5.0ms	(/.f64 1/3 a)

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 123

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
5.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
4.0ms	(/.f64 1/3 a)
1.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify202.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
340×	`distribute-rgt-in_binary64`
235×	`cancel-sign-sub-inv_binary64`
185×	`fma-neg_binary64`
160×	`associate-r_binary64`

Counts

199 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	5008
1	661	4039
2	2464	3848
3	4911	3848

prune250.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	219	4	223

Error

0.0b

Counts

223 → 4

Alt Table

Status	Error	Program
	2.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
▶	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
✓	52.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 5881 to 3415 computations (41.9% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.2b	(fma.f64 a (*.f64 c -3) 0)
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.3b	(/.f64 1/3 a)

series26.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
10.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
1.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify170.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-rgt-in_binary64`
506×	`associate-/l/_binary64`
492×	`associate-l_binary64`
430×	`associate-/r/_binary64`
383×	`associate-r_binary64`

Counts

92 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1049
1	175	901
2	597	847
3	2395	797
4	4205	797
5	4724	797
6	5000	797
7	4845	797

prune274.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Status	Error	Program
	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.6b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1 (/.f64 a 1/3))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.5b	(/.f64 (/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 1/3 (/.f64 1 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
✓	52.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 4021 to 2495 computations (38% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))

series620.0ms (4%)

Counts

3 → 60

Calls

3 calls:

455.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
85.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
80.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

3 → 107

Calls

3 calls:

13.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
12.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify260.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-def_binary64`
278×	`div-sub_binary64`
247×	`associate-/l/_binary64`
187×	`cancel-sign-sub-inv_binary64`
166×	`distribute-rgt-neg-out_binary64`

Counts

167 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	4899
1	638	4739
2	2058	4559
3	4528	4553
4	4983	4553
5	4903	4553

prune409.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	4	0	4
Picked	0	1	1
Done	0	1	1
Total	245	5	250

Error

Counts

250 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 (sqrt.f64 c) (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 (neg.f64 (sqrt.f64 c)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	1.7b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
▶	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	52.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 6435 to 3472 computations (46% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.4b	(.f64 (.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))
✓	0.5b	(.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
✓	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))

series3.8s (25%)

Counts

3 → 60

Calls

3 calls:

2.1s

(*.f64 (*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))

1.2s

(*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))

586.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))

rewrite329.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

338×	`*-un-lft-identity_binary64`
269×	`times-frac_binary64`
149×	`add-sqr-sqrt_binary64`
134×	`add-cube-cbrt_binary64`
92×	`associate-r_binary64`

Counts

3 → 324

Calls

3 calls:

80.0ms

(*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))

59.0ms

(*.f64 (*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))

43.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))

simplify567.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

509×	`associate-/l*_binary64`
417×	`associate-*l/_binary64`
340×	`fma-def_binary64`
262×	`times-frac_binary64`
197×	`distribute-rgt-neg-out_binary64`

Counts

384 → 440

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	490	21998
1	1512	18006
2	4901	18000
3	5097	18000

prune994.0ms (6.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	512	5	517

Error

Counts

517 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 (sqrt.f64 c) (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 (neg.f64 (sqrt.f64 c)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	1.7b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	52.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 29766 to 14880 computations (50% saved)

regimes2.1s (13.5%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Counts

217 → 1

Compiler

Compiled 34042 to 22496 computations (33.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	20	21
2	24	21
3	27	21
4	28	21
5	28	21

end113.0ms (0.7%)

Compiler: Compiled 210 to 131 computations (37.6% saved)

Details

analyze576.0ms (3.7%)

sample3.6s (23.7%)

simplify477.0ms (3.1%)

prune8.0ms (0.1%)

localize19.0ms (0.1%)

series335.0ms (2.2%)

rewrite44.0ms (0.3%)

simplify202.0ms (1.3%)

prune250.0ms (1.6%)

localize25.0ms (0.2%)

series26.0ms (0.2%)

rewrite16.0ms (0.1%)

simplify170.0ms (1.1%)

prune274.0ms (1.8%)

localize15.0ms (0.1%)

series620.0ms (4%)

rewrite48.0ms (0.3%)

simplify260.0ms (1.7%)

prune409.0ms (2.7%)

localize31.0ms (0.2%)

series3.8s (25%)

rewrite329.0ms (2.1%)

simplify567.0ms (3.7%)

prune994.0ms (6.5%)

regimes2.1s (13.5%)

simplify3.0ms (0%)

end113.0ms (0.7%)

Profiling