Details

analyze346.0ms (5.9%)

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)

sample1.5s (25.4%)

Results

1.2s	7944×	body	128	valid
139.0ms	1049×	body	128	invalid
80.0ms	312×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify357.0ms (6.1%)

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

29.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	29.8b	(/.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)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.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))
✓	29.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series104.0ms (1.8%)

Counts

4 → 100

Calls

4 calls:

54.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite112.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 285

Calls

4 calls:

105.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
105.0ms	(.f64 (.f64 3 a) c)
105.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
105.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify79.0ms (1.4%)

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

385 → 338

Iterations

Useful iterations: 3 (0.0ms)

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

prune208.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	331	7	338
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	333	7	340

Error

0.8b

Counts

340 → 7

Alt Table

Status	Error	Program
	29.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	5.0b	(/.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))
	6.7b	(/.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))
	29.8b	(/.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))
	28.6b	(/.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))
▶	4.7b	(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)))))
	29.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (pow.f64 (sqrt.f64 (.f64 (.f64 3 a) c)) 2)))) (.f64 3 a))

Compiler

Compiled 10254 to 5623 computations (45.2% saved)

localize25.0ms (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 (pow.f64 a 3) (pow.f64 c 4))
✓	0.3b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
✓	0.3b	(.f64 (.f64 a a) (pow.f64 c 3))

series198.0ms (3.4%)

Counts

4 → 120

Calls

4 calls:

90.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
77.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
18.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
13.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite79.0ms (1.4%)

Algorithm

2×	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 → 120

Calls

4 calls:

76.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
76.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
76.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
76.0ms	(.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
0	0	0
1	0	0

simplify140.0ms (2.4%)

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

240 → 126

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

prune204.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	124	9	133

Error

0.8b

Counts

133 → 9

Alt Table

Status	Error	Program
	29.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
▶	5.0b	(/.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))
	6.7b	(/.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))
	29.8b	(/.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))
	28.6b	(/.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))
✓	4.7b	(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)))))
	5.1b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)))) 1) (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)))))
	5.3b	(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)))))
	29.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (pow.f64 (sqrt.f64 (.f64 (.f64 3 a) c)) 2)))) (.f64 3 a))

Compiler

Compiled 6392 to 4006 computations (37.3% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series232.0ms (4%)

Counts

4 → 96

Calls

4 calls:

91.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
66.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
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))
10.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite45.0ms (0.8%)

Algorithm

2×	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 → 66

Calls

4 calls:

43.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
43.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
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	99
1	775	99
2	5239	99
0	0	0
1	0	0

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
399×	`distribute-rgt-neg-in_binary64`
323×	`unswap-sqr_binary64`
280×	`times-frac_binary64`
262×	`distribute-neg-frac_binary64`

Counts

162 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	2262
1	155	2262
2	543	2208
3	2733	2208
4	4814	2208
5	4997	2208

prune140.0ms (2.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	78	14	92

Error

0.7b

Counts

92 → 14

Alt Table

Status	Error	Program
	5.7b	(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)
	29.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
▶	5.0b	(-.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)))
	28.6b	(/.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))
	5.3b	(/.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 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))))) (*.f64 3 a))
✓	4.7b	(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)))))
	10.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 2) (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))
	5.3b	(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)))))
	5.1b	(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))
	29.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (pow.f64 (sqrt.f64 (.f64 (.f64 3 a) c)) 2)))) (.f64 3 a))
	5.0b	(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)
	6.7b	(/.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))
	29.8b	(/.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 (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)

Compiler

Compiled 5159 to 3390 computations (34.3% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 a 3))
✓	0.5b	(pow.f64 (*.f64 c a) 2)
✓	0.7b	(pow.f64 (*.f64 c a) 3)
✓	0.9b	(pow.f64 (*.f64 c a) 4)

series43.0ms (0.7%)

Counts

4 → 108

Calls

4 calls:

13.0ms	(pow.f64 (*.f64 c a) 4)
11.0ms	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 a 3))
11.0ms	(pow.f64 (*.f64 c a) 3)
8.0ms	(pow.f64 (*.f64 c a) 2)

rewrite104.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

281×	`log1p-udef_binary64`
280×	`expm1-udef_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
160×	`add-sqr-sqrt_binary64`

Counts

4 → 134

Calls

4 calls:

102.0ms	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 a 3))
102.0ms	(pow.f64 (*.f64 c a) 2)
102.0ms	(pow.f64 (*.f64 c a) 3)
102.0ms	(pow.f64 (*.f64 c a) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	359	34
2	4316	34
3	4988	34
4	5175	34
0	0	0
1	0	0

simplify131.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

651×	`sqr-pow_binary64`
633×	`associate-/r*_binary64`
536×	`associate-*l/_binary64`
399×	`*-commutative_binary64`
303×	`unswap-sqr_binary64`

Counts

242 → 139

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	19	972
1	46	972
2	118	972
3	405	972
4	688	828
5	724	828
6	949	756
7	1562	756
8	2226	756
9	3919	756
10	3985	756
11	4183	756
12	4434	756
13	4681	756
14	4852	756

prune221.0ms (3.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	138	15	153

Error

0.7b

Counts

153 → 15

Alt Table

Status	Error	Program
	5.7b	(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)
	5.0b	(-.f64 (.f64 -3/2 (/.f64 1 (.f64 (.f64 a 3) (/.f64 b (.f64 c a))))) (/.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)))
	29.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	5.7b	(-.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 a 3)) 2)) (/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (cbrt.f64 (.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)))
	28.6b	(/.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))
	5.3b	(/.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 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)))))))) (*.f64 3 a))
✓	4.7b	(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)))))
	5.1b	(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))
	5.8b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 -3/2 (/.f64 (.f64 c a) b))) 2) (.f64 (cbrt.f64 (.f64 -3/2 (/.f64 (.f64 c a) b))) (/.f64 1/3 a))) (/.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)))
	29.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (pow.f64 (sqrt.f64 (.f64 (.f64 3 a) c)) 2)))) (.f64 3 a))
	5.0b	(-.f64 (.f64 -3/2 (.f64 (/.f64 (.f64 c a) b) (/.f64 1/3 a))) (/.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)))
	4.9b	(-.f64 (.f64 -1/2 (/.f64 (/.f64 (.f64 c a) b) a)) (/.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)))
	29.8b	(/.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))
	5.7b	(-.f64 (pow.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (/.f64 (.f64 c a) b) 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)))
	10.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 2) (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 8118 to 4981 computations (38.6% saved)

regimes999.0ms (17.1%)

Accuracy

Total 5.0b remaining (88.1%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 17043 to 11846 computations (30.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	63
1	37	63
2	44	63
3	48	63
4	51	63
5	52	63
6	52	63

end435.0ms (7.4%)

Compiler: Compiled 778 to 530 computations (31.9% saved)

Details

analyze346.0ms (5.9%)

sample1.5s (25.4%)

simplify357.0ms (6.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series104.0ms (1.8%)

rewrite112.0ms (1.9%)

simplify79.0ms (1.4%)

prune208.0ms (3.6%)

localize25.0ms (0.4%)

series198.0ms (3.4%)

rewrite79.0ms (1.4%)

simplify140.0ms (2.4%)

prune204.0ms (3.5%)

localize28.0ms (0.5%)

series232.0ms (4%)

rewrite45.0ms (0.8%)

simplify85.0ms (1.4%)

prune140.0ms (2.4%)

localize26.0ms (0.4%)

series43.0ms (0.7%)

rewrite104.0ms (1.8%)

simplify131.0ms (2.2%)

prune221.0ms (3.8%)

regimes999.0ms (17.1%)

simplify3.0ms (0.1%)

end435.0ms (7.4%)

Profiling