Details

analyze370.0ms (4.5%)

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)

sample2.4s (28.5%)

Results

1.1s	3897×	body	256	valid
601.0ms	1535×	body	512	valid
449.0ms	2824×	body	128	valid
131.0ms	851×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify344.0ms (4.2%)

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

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

52.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	52.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	52.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 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
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	27.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series149.0ms (1.8%)

Counts

4 → 76

Calls

4 calls:

84.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
52.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
11.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
2.0ms	(/.f64 1/3 a)

rewrite23.0ms (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:

10.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
2.0ms	(/.f64 1/3 a)
0.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify115.0ms (1.4%)

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

prune152.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Error

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
	52.4b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/3 (cbrt.f64 a)))
	1.9b	(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)))))))
	52.2b	(.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (*.f64 b b)) 3))) b) (/.f64 1/3 a))
	2.4b	(.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))
	52.4b	(.f64 (.f64 (.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))) (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))) (/.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))

Compiler

Compiled 6049 to 3521 computations (41.8% saved)

localize13.0ms (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)

series16.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
5.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite7.0ms (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:

5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify96.0ms (1.2%)

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

prune146.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	137	5	142

Error

Counts

142 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (cbrt.f64 (/.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.9b	(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)))))))
	0.8b	(/.f64 (.f64 (cbrt.f64 (.f64 -27 (pow.f64 (.f64 c a) 3))) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	2.4b	(.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))
▶	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))

Compiler

Compiled 4083 to 2537 computations (37.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.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))
✓	0.1b	(/.f64 (*.f64 (neg.f64 c) a) a)

series285.0ms (3.4%)

Counts

3 → 64

Calls

3 calls:

234.0ms	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
48.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
3.0ms	(/.f64 (*.f64 (neg.f64 c) a) a)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 105

Calls

3 calls:

7.0ms	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
4.0ms	(/.f64 (*.f64 (neg.f64 c) a) a)
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

477×	`distribute-frac-neg_binary64`
427×	`fma-def_binary64`
398×	`div-sub_binary64`
212×	`associate-/l*_binary64`
196×	`times-frac_binary64`

Counts

169 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	4065
1	684	3807
2	2673	3673
3	4971	3673

prune184.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
	1.9b	(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)))))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
▶	0.3b	(.f64 (/.f64 (/.f64 (neg.f64 c) 1) 1) (/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
✓	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))

Compiler

Compiled 6537 to 3063 computations (53.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series421.0ms (5.1%)

Counts

2 → 40

Calls

2 calls:

231.0ms	(.f64 (/.f64 (/.f64 (neg.f64 c) 1) 1) (/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
190.0ms	(/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

rewrite141.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

428×	`times-frac_binary64`
266×	`add-sqr-sqrt_binary64`
257×	`*-un-lft-identity_binary64`
188×	`add-cube-cbrt_binary64`
106×	`associate-l_binary64`

Counts

2 → 318

Calls

2 calls:

74.0ms	(.f64 (/.f64 (/.f64 (neg.f64 c) 1) 1) (/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
7.0ms	(/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

simplify265.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary64`
246×	`associate-*l/_binary64`
246×	`associate-/l*_binary64`
211×	`associate-*r/_binary64`
191×	`associate-l_binary64`

Counts

358 → 525

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	10858
1	854	9916
2	3309	9525
3	4835	9525
4	4979	9525

prune487.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	599	0	599
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	599	4	603

Error

Counts

603 → 4

Alt Table

Status	Error	Program
	1.9b	(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)))))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
✓	0.3b	(.f64 (/.f64 (/.f64 (neg.f64 c) 1) 1) (/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
✓	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))

Compiler

Compiled 20295 to 11280 computations (44.4% saved)

regimes2.4s (29.5%)

Accuracy

Total 0.1b remaining (73.6%)

Threshold costs 0.1b (73.6%)

Counts

314 → 1

Compiler

Compiled 48139 to 32077 computations (33.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	28	27
2	33	27
3	40	27
4	48	27
5	55	27
6	59	27
7	60	27
8	59	27

end96.0ms (1.2%)

Compiler: Compiled 171 to 112 computations (34.5% saved)

Details

analyze370.0ms (4.5%)

sample2.4s (28.5%)

simplify344.0ms (4.2%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series149.0ms (1.8%)

rewrite23.0ms (0.3%)

simplify115.0ms (1.4%)

prune152.0ms (1.8%)

localize13.0ms (0.2%)

series16.0ms (0.2%)

rewrite7.0ms (0.1%)

simplify96.0ms (1.2%)

prune146.0ms (1.8%)

localize12.0ms (0.2%)

series285.0ms (3.4%)

rewrite24.0ms (0.3%)

simplify96.0ms (1.2%)

prune184.0ms (2.2%)

localize15.0ms (0.2%)

series421.0ms (5.1%)

rewrite141.0ms (1.7%)

simplify265.0ms (3.2%)

prune487.0ms (5.9%)

regimes2.4s (29.5%)

simplify3.0ms (0%)

end96.0ms (1.2%)

Profiling