Details

analyze650.0ms (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)

sample3.2s (27.1%)

Results

1.5s	3064×	body	256	valid
1.4s	5187×	body	128	valid
219.0ms	864×	body	128	invalid
3.0ms	5×	body	512	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify394.0ms (3.3%)

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

prune7.0ms (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

43.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	43.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	43.2b	(.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 (0.2%)

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 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	37.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series273.0ms (2.3%)

Counts

4 → 76

Calls

4 calls:

156.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
96.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
17.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
3.0ms	(/.f64 1/3 a)

rewrite217.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

781×	`prod-diff_binary64`
245×	`log1p-udef_binary64`
164×	`egg-rr`
139×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Counts

4 → 164

Calls

4 calls:

209.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
209.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
209.0ms	(/.f64 1/3 a)
208.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	280	53
2	3406	53
3	5118	53
0	0	0
1	0	0

simplify131.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
459×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`
333×	`fma-def_binary64`
308×	`fma-neg_binary64`

Counts

240 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1772
1	368	1700
2	1240	1671
3	4908	1665
4	5068	1665

prune389.0ms (3.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	197	19	216
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	198	20	218

Error

0.5b

Counts

218 → 20

Alt Table

Status	Error	Program
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (/.f64 1/3 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	43.9b	(.f64 (.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b))) (/.f64 1/3 a))
	42.7b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	43.2b	(/.f64 (/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
	42.4b	(.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (/.f64 1 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))))) (/.f64 1/3 a))
▶	2.6b	(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)))))
	42.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (.f64 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))) a))
	43.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 b 4))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (/.f64 1/3 a))
	42.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	43.2b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
✓	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	43.4b	(+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (/.f64 1/3 a)) (.f64 (neg.f64 b) (/.f64 1/3 a)))
	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
	2.9b	(.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))
	43.4b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) 1/3) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) a))
	42.4b	(/.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (.f64 (.f64 a 3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))))
	43.2b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (*.f64 a 3))
	4.2b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (/.f64 1/3 a))
	42.4b	(.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 (neg.f64 b) 3)) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) (neg.f64 b))))) (/.f64 1/3 a))

Compiler

Compiled 6946 to 4098 computations (41% saved)

localize53.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 a a) (pow.f64 c 3))
✓	0.3b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
✓	0.4b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))

series508.0ms (4.2%)

Counts

4 → 132

Calls

4 calls:

189.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
169.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
122.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
27.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite120.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
213×	`add-cbrt-cube_binary64`
212×	`add-log-exp_binary64`

Counts

4 → 123

Calls

4 calls:

116.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
116.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
116.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
115.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	55
1	487	55
2	4934	55
3	5057	55
0	0	0
1	0	0

simplify221.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-l_binary64`
679×	`associate-/r*_binary64`
308×	`associate-/l/_binary64`
297×	`associate-/r/_binary64`
285×	`unswap-sqr_binary64`

Counts

255 → 130

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	1860
1	65	1860
2	212	1860
3	1010	1860
4	4137	1860
5	4230	1860
6	4416	1860
7	4705	1860
8	4974	1860
9	4904	1860

prune517.0ms (4.3%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	127	23	150

Error

0.4b

Counts

150 → 23

Alt Table

Status	Error	Program
	42.7b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	3.4b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (log.f64 (exp.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)))))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (/.f64 1/3 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	43.9b	(.f64 (.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b))) (/.f64 1/3 a))
✓	2.6b	(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)))))
	7.4b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 a c)) (pow.f64 b 3)))) -3/8 (.f64 -1/2 (/.f64 c b)))))
	43.2b	(/.f64 (/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
	42.4b	(.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (/.f64 1 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))))) (/.f64 1/3 a))
	42.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (.f64 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))) a))
	43.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 b 4))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (/.f64 1/3 a))
	42.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	43.2b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
✓	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	43.4b	(+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (/.f64 1/3 a)) (.f64 (neg.f64 b) (/.f64 1/3 a)))
	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
▶	2.9b	(.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))
	3.5b	(fma.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a a) (pow.f64 c 3)))) 1) (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)))))
	43.4b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) 1/3) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) a))
	42.4b	(/.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (.f64 (.f64 a 3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))))
	43.2b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (*.f64 a 3))
	4.2b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (/.f64 1/3 a))
	42.4b	(.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 (neg.f64 b) 3)) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) (neg.f64 b))))) (/.f64 1/3 a))

Compiler

Compiled 7656 to 4751 computations (37.9% saved)

localize59.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))

series230.0ms (1.9%)

Counts

4 → 60

Calls

4 calls:

138.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
36.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
35.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
20.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite118.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
251×	`log-pow_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Counts

4 → 102

Calls

4 calls:

113.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
113.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
113.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
113.0ms	(.f64 (.f64 c a) (*.f64 c a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	346	34
2	3733	34
3	4904	34
0	0	0
1	0	0

simplify224.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

620×	`times-frac_binary64`
581×	`sqr-pow_binary64`
507×	`unswap-sqr_binary64`
460×	`associate-/l*_binary64`
246×	`associate-/r*_binary64`

Counts

162 → 106

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	816
1	29	816
2	88	816
3	390	816
4	2482	816
5	3415	816
6	3369	816
7	3508	816
8	3672	816
9	3838	816
10	3998	816
11	4170	816
12	4395	816
13	4601	816
14	4900	816
15	4892	816

prune435.0ms (3.6%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	20	20
Picked	0	1	1
Done	0	2	2
Total	106	23	129

Error

0.4b

Counts

129 → 23

Alt Table

Status	Error	Program
	42.7b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
▶	3.4b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (log.f64 (exp.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)))))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (/.f64 1/3 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	43.9b	(.f64 (.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b))) (/.f64 1/3 a))
✓	2.6b	(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)))))
	7.4b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 a c)) (pow.f64 b 3)))) -3/8 (.f64 -1/2 (/.f64 c b)))))
	43.2b	(/.f64 (/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
	42.4b	(.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (/.f64 1 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))))) (/.f64 1/3 a))
	42.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (.f64 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))) a))
	43.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 b 4))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (/.f64 1/3 a))
	42.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	43.2b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
✓	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	43.4b	(+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (/.f64 1/3 a)) (.f64 (neg.f64 b) (/.f64 1/3 a)))
	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
✓	2.9b	(.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))
	3.5b	(fma.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a a) (pow.f64 c 3)))) 1) (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)))))
	43.4b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) 1/3) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) a))
	42.4b	(/.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (.f64 (.f64 a 3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))))
	43.2b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (*.f64 a 3))
	4.2b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (/.f64 1/3 a))
	42.4b	(.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 (neg.f64 b) 3)) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) (neg.f64 b))))) (/.f64 1/3 a))

Compiler

Compiled 7149 to 4579 computations (35.9% saved)

localize58.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
	0.4b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
✓	15.6b	(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))

series193.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

193.0ms

(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))

rewrite95.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

603×	`log-prod_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
205×	`log-pow_binary64`
128×	`add-sqr-sqrt_binary64`

Counts

1 → 66

Calls

1 calls:

92.0ms

(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	277	16
2	3057	16
3	5135	16
0	0	0
1	0	0

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1397×	`associate-/r/_binary64`
532×	`times-frac_binary64`
493×	`unswap-sqr_binary64`
378×	`associate-/l*_binary64`
219×	`sqr-pow_binary64`

Counts

102 → 67

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	576
1	30	576
2	91	576
3	361	576
4	2264	576
5	3155	576
6	3107	576
7	3236	576
8	3390	576
9	3537	576
10	5216	576

prune994.0ms (8.3%)

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	19	19
Picked	0	1	1
Done	0	3	3
Total	180	23	203

Error

0.4b

Counts

203 → 23

Alt Table

Status	Error	Program
	42.7b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
✓	3.4b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (log.f64 (exp.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)))))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (/.f64 1/3 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	43.9b	(.f64 (.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 1/4) (sqrt.f64 b))) (/.f64 1/3 a))
✓	2.6b	(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)))))
	7.4b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 a c)) (pow.f64 b 3)))) -3/8 (.f64 -1/2 (/.f64 c b)))))
	43.2b	(/.f64 (/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
	42.4b	(.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (/.f64 1 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))))) (/.f64 1/3 a))
	42.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (.f64 (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))))) a))
	43.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 b 4))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 b) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 b 4)))))) (/.f64 1/3 a))
	42.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	43.2b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
✓	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	43.4b	(+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (/.f64 1/3 a)) (.f64 (neg.f64 b) (/.f64 1/3 a)))
	43.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 1/3 a))))
✓	2.9b	(.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))
	3.5b	(fma.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a a) (pow.f64 c 3)))) 1) (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)))))
	43.4b	(.f64 (+.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) 1/3) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) a))
	42.4b	(/.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) (.f64 (.f64 a 3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))))
	43.2b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (*.f64 a 3))
	4.2b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (/.f64 1/3 a))
	42.4b	(.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 (neg.f64 b) 3)) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) (neg.f64 b))))) (/.f64 1/3 a))

Compiler

Compiled 9466 to 5906 computations (37.6% saved)

regimes1.5s (12.6%)

Accuracy

Total 2.7b remaining (88.6%)

Threshold costs 0b (0%)

Counts

70 → 1

Compiler

Compiled 13961 to 9516 computations (31.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	61
1	36	61
2	36	61

end1.2s (9.8%)

Compiler: Compiled 946 to 620 computations (34.5% saved)

Details

analyze650.0ms (5.4%)

sample3.2s (27.1%)

simplify394.0ms (3.3%)

prune7.0ms (0.1%)

localize19.0ms (0.2%)

series273.0ms (2.3%)

rewrite217.0ms (1.8%)

simplify131.0ms (1.1%)

prune389.0ms (3.3%)

localize53.0ms (0.4%)

series508.0ms (4.2%)

rewrite120.0ms (1%)

simplify221.0ms (1.9%)

prune517.0ms (4.3%)

localize59.0ms (0.5%)

series230.0ms (1.9%)

rewrite118.0ms (1%)

simplify224.0ms (1.9%)

prune435.0ms (3.6%)

localize58.0ms (0.5%)

series193.0ms (1.6%)

rewrite95.0ms (0.8%)

simplify121.0ms (1%)

prune994.0ms (8.3%)

regimes1.5s (12.6%)

simplify5.0ms (0%)

end1.2s (9.8%)

Profiling