Details

analyze374.0ms (5.5%)

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)

sample2.1s (30.4%)

Results

898.0ms	5153×	body	128	valid
871.0ms	3101×	body	256	valid
196.0ms	892×	body	128	invalid
1.0ms	2×	body	512	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify346.0ms (5.1%)

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

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

46.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	46.7b	(.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)

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))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	40.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series159.0ms (2.3%)

Counts

4 → 76

Calls

4 calls:

90.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
58.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
10.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.f64 1/3 a)

rewrite24.0ms (0.4%)

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))

simplify108.0ms (1.6%)

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

prune157.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	212	9	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	214	9	223

Error

0.1b

Counts

223 → 9

Alt Table

Status	Error	Program
	47.9b	(.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (cbrt.f64 b) (.f64 (cbrt.f64 b) (cbrt.f64 b))))) (fma.f64 (neg.f64 (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))) (/.f64 1/3 a))
	3.7b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
▶	0.6b	(/.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))
	46.7b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/3) (cbrt.f64 a)))
	46.0b	(.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (/.f64 1/3 a))
	2.8b	(.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))
	46.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (/.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 1/3) (cbrt.f64 a))))
	46.7b	(/.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (.f64 b b)) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))
	2.3b	(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)))))))

Compiler

Compiled 6341 to 3683 computations (41.9% 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))
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
✓	0.3b	(fma.f64 a (*.f64 c -3) 0)
	0.4b	(/.f64 1/3 a)

series14.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
6.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite8.0ms (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:

6.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify97.0ms (1.4%)

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

prune147.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	137	8	145

Error

0.0b

Counts

145 → 8

Alt Table

Status	Error	Program
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))) (+.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))
	1.6b	(/.f64 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) 0)) (cbrt.f64 (fma.f64 a (.f64 c -3) 0))) (cbrt.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))
	0.9b	(/.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))
	0.2b	(/.f64 (/.f64 (.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	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))
	1.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (exp.f64 (log.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))
	2.3b	(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)))))))

Compiler

Compiled 4211 to 2623 computations (37.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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))

series211.0ms (3.1%)

Counts

3 → 60

Calls

3 calls:

149.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
33.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
28.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite20.0ms (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:

6.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify165.0ms (2.4%)

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

prune205.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	245	7	252

Error

Counts

252 → 7

Alt Table

Status	Error	Program
	1.3b	(/.f64 (/.f64 (neg.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)))) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	2.3b	(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)))))
	1.6b	(/.f64 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) 0)) (cbrt.f64 (fma.f64 a (.f64 c -3) 0))) (cbrt.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))
	0.9b	(/.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))
▶	0.2b	(/.f64 (/.f64 (.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	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))
	0.5b	(/.f64 (neg.f64 c) (.f64 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))

Compiler

Compiled 6606 to 3603 computations (45.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series133.0ms (1.9%)

Counts

2 → 44

Calls

2 calls:

130.0ms	(/.f64 (/.f64 (.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
3.0ms	(/.f64 (*.f64 a (neg.f64 c)) a)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
38×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 85

Calls

2 calls:

8.0ms	(/.f64 (/.f64 (.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
4.0ms	(/.f64 (*.f64 a (neg.f64 c)) a)

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

760×	`div-sub_binary64`
526×	`fma-def_binary64`
347×	`distribute-frac-neg_binary64`
197×	`distribute-rgt-neg-out_binary64`
167×	`distribute-rgt-in_binary64`

Counts

129 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	3665
1	576	2956
2	2108	2854
3	4250	2848
4	5613	2848

prune195.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f64 (/.f64 (.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (*.f64 b b)) 3))) b))
	0.4b	(.f64 (/.f64 (/.f64 a 1) 1) (/.f64 (/.f64 (neg.f64 c) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	1.3b	(/.f64 (/.f64 (neg.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)))) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	2.3b	(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)))))
	0.9b	(/.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))
	0.3b	(.f64 (/.f64 (.f64 a (neg.f64 c)) a) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))

Compiler

Compiled 6481 to 3027 computations (53.3% saved)

regimes2.1s (30.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Counts

331 → 1

Compiler

Compiled 46053 to 29846 computations (35.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	14	21
1	24	21
2	28	21
3	31	21
4	32	21
5	31	21

end130.0ms (1.9%)

Compiler: Compiled 222 to 147 computations (33.8% saved)

Details

analyze374.0ms (5.5%)

sample2.1s (30.4%)

simplify346.0ms (5.1%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series159.0ms (2.3%)

rewrite24.0ms (0.4%)

simplify108.0ms (1.6%)

prune157.0ms (2.3%)

localize13.0ms (0.2%)

series14.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify97.0ms (1.4%)

prune147.0ms (2.2%)

localize10.0ms (0.1%)

series211.0ms (3.1%)

rewrite20.0ms (0.3%)

simplify165.0ms (2.4%)

prune205.0ms (3%)

localize12.0ms (0.2%)

series133.0ms (1.9%)

rewrite20.0ms (0.3%)

simplify107.0ms (1.6%)

prune195.0ms (2.9%)

regimes2.1s (30.3%)

simplify2.0ms (0%)

end130.0ms (1.9%)

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