Details

analyze369.0ms (6%)

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)

sample1.7s (28.1%)

Results

1.4s	7938×	body	128	valid
186.0ms	993×	body	128	invalid
88.0ms	318×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify346.0ms (5.6%)

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

29.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	29.5b	(/.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)
✓	0.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	29.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series108.0ms (1.8%)

Counts

4 → 100

Calls

4 calls:

57.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
35.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite103.0ms (1.7%)

Algorithm

2×	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:

94.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
94.0ms	(.f64 (.f64 3 a) c)
94.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
94.0ms	(+.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

simplify81.0ms (1.3%)

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

prune220.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	333	8	341
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	333	10	343

Error

0.8b

Counts

343 → 10

Alt Table

Status	Error	Program
	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))
	29.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	6.3b	(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)))))
	8.3b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b))))
	22.3b	(*.f64 -1/2 (/.f64 c b))
	6.6b	(/.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))
	8.5b	(/.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))
	31.1b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.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))
✓	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 10399 to 5710 computations (45.1% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series245.0ms (4%)

Counts

4 → 132

Calls

4 calls:

90.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
78.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
62.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
14.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite82.0ms (1.3%)

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 → 127

Calls

4 calls:

78.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
78.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
78.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
78.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))

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

simplify140.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

259 → 134

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	1860
1	65	1860
2	212	1860
3	1010	1860
4	4138	1860
5	4230	1860
6	4416	1860
7	4705	1860
8	4974	1860
9	4904	1860

prune226.0ms (3.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	134	10	144

Error

0.8b

Counts

144 → 10

Alt Table

Status	Error	Program
	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))
	29.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	6.3b	(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)))))
	11.8b	(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)))))
	6.8b	(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)))))
▶	6.6b	(/.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))
	8.5b	(/.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))
	31.1b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.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))
✓	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 6806 to 4207 computations (38.2% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series263.0ms (4.3%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(/.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))
86.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
78.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
12.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite48.0ms (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 → 69

Calls

4 calls:

46.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
46.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
46.0ms	(/.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))
46.0ms	(.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

simplify88.0ms (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

165 → 86

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

prune157.0ms (2.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	81	15	96

Error

0.7b

Counts

96 → 15

Alt Table

Status	Error	Program
	12.6b	(/.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))
	11.8b	(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)))))
	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))
	7.2b	(.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))))
	29.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 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))
▶	6.6b	(-.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)))
✓	6.3b	(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)))))
	6.8b	(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)))))
	6.7b	(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))
	6.6b	(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)
	7.2b	(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)
	8.5b	(/.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))
	31.1b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
✓	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 5398 to 3538 computations (34.5% saved)

localize28.0ms (0.5%)

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)
✓	0.8b	(pow.f64 (*.f64 c a) 3)
✓	1.0b	(pow.f64 (*.f64 c a) 4)

series50.0ms (0.8%)

Counts

4 → 108

Calls

4 calls:

18.0ms	(pow.f64 (*.f64 c a) 4)
13.0ms	(pow.f64 (*.f64 c a) 3)
12.0ms	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 a 3))
7.0ms	(pow.f64 (*.f64 c a) 2)

rewrite107.0ms (1.7%)

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 → 137

Calls

4 calls:

105.0ms	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 a 3))
105.0ms	(pow.f64 (*.f64 c a) 2)
105.0ms	(pow.f64 (*.f64 c a) 3)
105.0ms	(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

simplify137.0ms (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

245 → 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

prune247.0ms (4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	129	10	139
Fresh	4	8	12
Picked	1	0	1
Done	1	1	2
Total	135	19	154

Error

0.6b

Counts

154 → 19

Alt Table

Status	Error	Program
	12.6b	(/.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))
	21.7b	(-.f64 (log.f64 (exp.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)))
	6.2b	(-.f64 (.f64 -1/2 (/.f64 c b)) (/.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)))
	6.5b	(-.f64 (pow.f64 (.f64 (/.f64 a (/.f64 (.f64 c a) b)) -2) -1) (/.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)))
	6.8b	(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)))))
	7.2b	(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)
	7.3b	(-.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)))
	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))
	7.2b	(.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))))
	29.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	31.1b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	6.6b	(-.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)))
	23.7b	(-.f64 (log.f64 (+.f64 1 (expm1.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)))
	7.1b	(-.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)))
	6.7b	(-.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 a 3))) (/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (sqrt.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)))
	6.5b	(-.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)))
	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))
	6.5b	(-.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)))
✓	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 8332 to 5126 computations (38.5% saved)

regimes738.0ms (12%)

Accuracy

Total 4.2b remaining (85.5%)

Threshold costs 0b (0%)

Counts

67 → 2

Compiler

Compiled 14371 to 9941 computations (30.8% saved)

bsearch28.0ms (0.5%)

Steps

Iters	Range		Point
4	0.9305127278554963	1.3634319583275036	1.3163313487072055

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	110
1	55	110
2	67	110
3	75	110
4	80	110
5	81	110
6	81	110

end538.0ms (8.7%)

Compiler: Compiled 1056 to 705 computations (33.2% saved)

Details

analyze369.0ms (6%)

sample1.7s (28.1%)

simplify346.0ms (5.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series108.0ms (1.8%)

rewrite103.0ms (1.7%)

simplify81.0ms (1.3%)

prune220.0ms (3.6%)

localize26.0ms (0.4%)

series245.0ms (4%)

rewrite82.0ms (1.3%)

simplify140.0ms (2.3%)

prune226.0ms (3.7%)

localize29.0ms (0.5%)

series263.0ms (4.3%)

rewrite48.0ms (0.8%)

simplify88.0ms (1.4%)

prune157.0ms (2.6%)

localize28.0ms (0.5%)

series50.0ms (0.8%)

rewrite107.0ms (1.7%)

simplify137.0ms (2.2%)

prune247.0ms (4%)

regimes738.0ms (12%)

bsearch28.0ms (0.5%)

simplify7.0ms (0.1%)

end538.0ms (8.7%)

Profiling