Details

analyze374.0ms (6.5%)

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)

sample1.6s (27.5%)

Results

1.2s	7929×	body	128	valid
145.0ms	984×	body	128	invalid
92.0ms	327×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify356.0ms (6.2%)

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 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	29.6b	(.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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 a) c)
✓	0.3b	(-.f64 (.f64 b b) (.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))
✓	29.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series110.0ms (1.9%)

Counts

4 → 100

Calls

4 calls:

61.0ms	(/.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))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite109.0ms (1.9%)

Algorithm

1×	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:

101.0ms	(.f64 (.f64 3 a) c)
101.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
101.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
101.0ms	(+.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

simplify85.0ms (1.5%)

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

prune211.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	328	10	338
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	329	11	340

Error

0.8b

Counts

340 → 11

Alt Table

Status	Error	Program
	29.4b	(/.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))
	11.8b	(/.f64 (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 -3/2 (/.f64 (.f64 c a) 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))
	22.4b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 -3 (.f64 a c))))) (*.f64 3 a))
	6.5b	(/.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))
	29.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	8.1b	(/.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))
	30.9b	(/.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 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))) b) (*.f64 3 a))
▶	6.2b	(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)))))

Compiler

Compiled 10408 to 5719 computations (45.1% saved)

localize30.0ms (0.5%)

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

series209.0ms (3.6%)

Counts

4 → 120

Calls

4 calls:

92.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
81.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
20.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
15.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite80.0ms (1.4%)

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 → 120

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify154.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-/l*_binary64`
441×	`associate-/r*_binary64`
414×	`associate-l_binary64`
372×	`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

prune191.0ms (3.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	125	12	137

Error

0.8b

Counts

137 → 12

Alt Table

Status	Error	Program
	29.4b	(/.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))
	11.8b	(/.f64 (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 -3/2 (/.f64 (.f64 c a) 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))
	22.4b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 -3 (.f64 a c))))) (*.f64 3 a))
▶	6.5b	(/.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))
	29.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	8.1b	(/.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))
	30.9b	(/.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 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))) b) (*.f64 3 a))
✓	6.2b	(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)))))
	7.8b	(fma.f64 (log.f64 (exp.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)))))

Compiler

Compiled 6448 to 4030 computations (37.5% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series169.0ms (3%)

Counts

4 → 96

Calls

4 calls:

74.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
67.0ms	(/.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))
17.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
10.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite46.0ms (0.8%)

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 → 65

Calls

4 calls:

44.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
44.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
44.0ms	(/.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))
44.0ms	(.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

simplify92.0ms (1.6%)

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

161 → 82

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

prune145.0ms (2.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	79	15	94

Error

0.7b

Counts

94 → 15

Alt Table

Status	Error	Program
	6.5b	(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)
	9.4b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 c a) 2))) 1) (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))
	6.5b	(.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)))
	29.4b	(/.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))
▶	6.5b	(-.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)))
	30.9b	(/.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))
	22.2b	(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))))
	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 -3 (.f64 a c))))) (*.f64 3 a))
	29.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 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))))
	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 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))) b) (*.f64 3 a))
✓	6.2b	(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)))))
	12.3b	(/.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))
	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))

Compiler

Compiled 5185 to 3403 computations (34.4% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series166.0ms (2.9%)

Counts

4 → 108

Calls

4 calls:

135.0ms	(/.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))
14.0ms	(pow.f64 (*.f64 c a) 4)
11.0ms	(pow.f64 (*.f64 c a) 3)
7.0ms	(pow.f64 (*.f64 c a) 2)

rewrite69.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`log1p-expm1-u_binary64`
273×	`expm1-log1p-u_binary64`
263×	`add-cbrt-cube_binary64`
262×	`add-log-exp_binary64`
261×	`add-exp-log_binary64`

Counts

4 → 65

Calls

4 calls:

67.0ms	(/.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))
67.0ms	(pow.f64 (*.f64 c a) 2)
67.0ms	(pow.f64 (*.f64 c a) 3)
67.0ms	(pow.f64 (*.f64 c a) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	75
1	601	75
2	4887	75
3	4863	75

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
515×	`associate-/r/_binary64`
504×	`associate-*l/_binary64`
429×	`associate-/l/_binary64`
413×	`associate-*r/_binary64`

Counts

173 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	2181
1	101	2181
2	346	2181
3	1732	2082
4	4990	2082

prune126.0ms (2.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	76	15	91

Error

0.7b

Counts

91 → 15

Alt Table

Status	Error	Program
	6.5b	(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)
	9.4b	(-.f64 (/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (.f64 a 3)) (/.f64 (fma.f64 9/8 (/.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 c a) 2))) 1) (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 (.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)))
	29.4b	(/.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))
✓	6.5b	(-.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)))
	30.9b	(/.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))
	22.2b	(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))))
	29.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 -3 (.f64 a c))))) (*.f64 3 a))
	29.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 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))))
	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 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))) b) (*.f64 3 a))
✓	6.2b	(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)))))
	12.3b	(/.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))
	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))

Compiler

Compiled 4560 to 2886 computations (36.7% saved)

regimes901.0ms (15.7%)

Accuracy

Total 4.6b remaining (85.9%)

Threshold costs 0b (0%)

Counts

88 → 2

Compiler

Compiled 18918 to 13445 computations (28.9% saved)

bsearch5.0ms (0.1%)

Steps

Iters	Range		Point
0	2.43817991435438	2.4889860501533208	2.4635829822538504

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
4×	`+-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	45	108
1	56	108
2	63	108
3	67	108
4	69	108
5	69	108

end382.0ms (6.7%)

Compiler: Compiled 792 to 524 computations (33.8% saved)

Details

analyze374.0ms (6.5%)

sample1.6s (27.5%)

simplify356.0ms (6.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series110.0ms (1.9%)

rewrite109.0ms (1.9%)

simplify85.0ms (1.5%)

prune211.0ms (3.7%)

localize30.0ms (0.5%)

series209.0ms (3.6%)

rewrite80.0ms (1.4%)

simplify154.0ms (2.7%)

prune191.0ms (3.3%)

localize29.0ms (0.5%)

series169.0ms (3%)

rewrite46.0ms (0.8%)

simplify92.0ms (1.6%)

prune145.0ms (2.5%)

localize26.0ms (0.5%)

series166.0ms (2.9%)

rewrite69.0ms (1.2%)

simplify65.0ms (1.1%)

prune126.0ms (2.2%)

regimes901.0ms (15.7%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end382.0ms (6.7%)

Profiling