Details

analyze380.0ms (5.8%)

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)

sample1.6s (23.9%)

Results

1.2s	7913×	body	128	valid
145.0ms	999×	body	128	invalid
96.0ms	343×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify351.0ms (5.3%)

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

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

27.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	27.8b	(/.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
✓	0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.3b	(.f64 (.f64 3 a) c)
✓	0.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	27.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series108.0ms (1.6%)

Counts

4 → 100

Calls

4 calls:

58.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
36.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(.f64 (.f64 3 a) c)

rewrite107.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`fma-def_binary64`
366×	`fma-neg_binary64`
288×	`egg-rr`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`

Counts

4 → 288

Calls

4 calls:

100.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
100.0ms	(.f64 (.f64 3 a) c)
100.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
100.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	297	56
2	3769	56
3	5480	56

simplify79.0ms (1.2%)

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

388 → 341

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1940
1	368	1868
2	1240	1839
3	4908	1833
4	5068	1833

prune215.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	334	7	341
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	335	8	343

Error

0.8b

Counts

343 → 8

Alt Table

Status	Error	Program
	27.8b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	8.3b	(/.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 3 a))
	28.2b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	26.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	5.9b	(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)))))
	23.5b	(*.f64 -1/2 (/.f64 c b))
	6.1b	(/.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 3 a))

Compiler

Compiled 10307 to 5648 computations (45.2% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series202.0ms (3.1%)

Counts

4 → 120

Calls

4 calls:

91.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
79.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
19.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
13.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite76.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

311×	`log1p-udef_binary64`
181×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
173×	`add-cbrt-cube_binary64`

Counts

4 → 124

Calls

4 calls:

74.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
74.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
74.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
73.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	397	52
2	4535	52
3	5081	52

simplify142.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-/l*_binary64`
441×	`associate-/r*_binary64`
413×	`associate-l_binary64`
371×	`associate-r_binary64`
353×	`sqr-pow_binary64`

Counts

244 → 130

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1632
1	52	1632
2	165	1632
3	705	1632
4	3868	1632
5	3945	1632
6	4120	1632
7	4416	1632
8	4685	1632
9	4997	1632
10	4873	1632

prune220.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Error

0.8b

Counts

138 → 10

Alt Table

Status	Error	Program
	7.4b	(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)))))
	23.5b	(*.f64 -1/2 (/.f64 c b))
	27.8b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	8.3b	(/.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 3 a))
	28.2b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	26.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	5.9b	(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)))))
	6.3b	(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)))))
▶	6.1b	(/.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 3 a))

Compiler

Compiled 6566 to 4108 computations (37.4% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.4b	(/.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 3 a))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))

series175.0ms (2.7%)

Counts

4 → 60

Calls

4 calls:

84.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
65.0ms	(/.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 3 a))
16.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
10.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

356×	`log1p-expm1-u_binary64`
356×	`expm1-log1p-u_binary64`
343×	`add-cbrt-cube_binary64`
340×	`add-log-exp_binary64`
339×	`add-exp-log_binary64`

Counts

4 → 64

Calls

4 calls:

43.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
43.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
43.0ms	(/.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 3 a))
43.0ms	(.f64 (.f64 c a) (*.f64 c a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	93
1	775	93
2	5239	93

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
399×	`distribute-rgt-neg-in_binary64`
305×	`unswap-sqr_binary64`
284×	`neg-mul-1_binary64`
262×	`distribute-neg-frac_binary64`

Counts

124 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	1686
1	152	1686
2	511	1632
3	2537	1632
4	4583	1632
5	4985	1632

prune141.0ms (2.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	74	15	89

Error

0.8b

Counts

89 → 15

Alt Table

Status	Error	Program
	21.6b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))))
✓	5.9b	(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)))))
	26.2b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3)))) 1)
✓	6.1b	(/.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 3 a))
	28.2b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	26.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	6.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3)) 3))
	6.2b	(pow.f64 (/.f64 (.f64 a 3) (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (*.f64 c a) 4) (pow.f64 b 7))))))) -1)
	6.9b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))) 3)
	6.3b	(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)))))
	6.9b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (.f64 a 3))) 2) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))))
	6.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (/.f64 1 (.f64 a 3)))
▶	6.1b	(-.f64 (/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (.f64 a 3)) (/.f64 (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7))))) (.f64 a 3)))
	27.8b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))

Compiler

Compiled 5068 to 3241 computations (36% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
✓	0.5b	(pow.f64 (*.f64 c a) 2)
✓	0.8b	(pow.f64 (*.f64 c a) 3)
✓	0.9b	(pow.f64 (*.f64 c a) 4)

series116.0ms (1.8%)

Counts

4 → 108

Calls

4 calls:

84.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
15.0ms	(pow.f64 (*.f64 c a) 4)
11.0ms	(pow.f64 (*.f64 c a) 3)
7.0ms	(pow.f64 (*.f64 c a) 2)

rewrite64.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`log-prod_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
207×	`log-pow_binary64`
138×	`log1p-expm1-u_binary64`

Counts

4 → 137

Calls

4 calls:

62.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
62.0ms	(pow.f64 (*.f64 c a) 2)
62.0ms	(pow.f64 (*.f64 c a) 3)
62.0ms	(pow.f64 (*.f64 c a) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	307	34
2	3085	34
3	5105	34

simplify112.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1529×	`associate-*l/_binary64`
736×	`associate-/l*_binary64`
398×	`associate-/r*_binary64`
327×	`unswap-sqr_binary64`
290×	`sqr-pow_binary64`

Counts

245 → 139

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	19	1296
1	49	1296
2	152	1296
3	728	1296
4	3112	1044
5	3185	1044
6	3301	972
7	3459	972
8	3606	972
9	3787	972
10	5743	972

prune268.0ms (4.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	12	12
Picked	1	0	1
Done	0	2	2
Total	139	15	154

Error

0.8b

Counts

154 → 15

Alt Table

Status	Error	Program
	21.6b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))))
✓	5.9b	(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)))))
	6.9b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (.f64 a 3))) 2) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))))
	24.0b	(-.f64 (/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (.f64 a 3)) (/.f64 (fma.f64 9/8 (/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 c a) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 c a) 2))))) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7))))) (*.f64 a 3)))
	26.2b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3)))) 1)
✓	6.1b	(/.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 3 a))
	28.2b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	26.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	6.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3)) 3))
	6.2b	(pow.f64 (/.f64 (.f64 a 3) (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (*.f64 c a) 4) (pow.f64 b 7))))))) -1)
	6.9b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (*.f64 a 3))) 3)
	6.3b	(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)))))
	6.2b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))) (/.f64 1 (.f64 a 3)))
	27.8b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))

Compiler

Compiled 8240 to 5107 computations (38% saved)

regimes1.5s (22.6%)

Accuracy

Total 5.1b remaining (87.5%)

Threshold costs 0b (0%)

Counts

123 → 1

Compiler

Compiled 30266 to 20656 computations (31.8% saved)

simplify4.0ms (0.1%)

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

end538.0ms (8.2%)

Compiler: Compiled 793 to 539 computations (32% saved)

Details

analyze380.0ms (5.8%)

sample1.6s (23.9%)

simplify351.0ms (5.3%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series108.0ms (1.6%)

rewrite107.0ms (1.6%)

simplify79.0ms (1.2%)

prune215.0ms (3.3%)

localize27.0ms (0.4%)

series202.0ms (3.1%)

rewrite76.0ms (1.1%)

simplify142.0ms (2.2%)

prune220.0ms (3.3%)

localize29.0ms (0.4%)

series175.0ms (2.7%)

rewrite45.0ms (0.7%)

simplify74.0ms (1.1%)

prune141.0ms (2.1%)

localize26.0ms (0.4%)

series116.0ms (1.8%)

rewrite64.0ms (1%)

simplify112.0ms (1.7%)

prune268.0ms (4.1%)

regimes1.5s (22.6%)

simplify4.0ms (0.1%)

end538.0ms (8.2%)

Profiling