Details

analyze291.0ms (4.7%)

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)

sample1.3s (21.3%)

Results

1.0s	7953×	body	128	valid
126.0ms	1014×	body	128	invalid
69.0ms	303×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify350.0ms (5.7%)

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

27.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	27.1b	(/.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)

localize11.0ms (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))
✓	26.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series167.0ms (2.7%)

Counts

4 → 100

Calls

4 calls:

93.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
57.0ms	(+.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))
5.0ms	(.f64 (.f64 3 a) c)

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
10×	`add-log-exp_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(.f64 (.f64 3 a) c)
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify119.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
309×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
189×	`associate-r_binary64`
182×	`associate-l_binary64`

Counts

193 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	3732
1	687	3410
2	2579	3302
3	4808	3302
4	4889	3302

prune149.0ms (2.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	168	19	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	19	189

Error

0.8b

Counts

189 → 19

Alt Table

Status	Error	Program
	27.2b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
▶	7.8b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	26.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (neg.f64 (.f64 c (.f64 3 a)))) (fma.f64 (neg.f64 c) (.f64 3 a) (.f64 c (.f64 3 a)))))) (.f64 3 a))
	27.0b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
	27.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	27.0b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	31.4b	(/.f64 (log.f64 (exp.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	27.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) 3) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) a))
	8.0b	(/.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 (pow.f64 (.f64 c 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))
	27.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 6) (.f64 -27 (pow.f64 (.f64 c a) 3))) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (*.f64 3 a))
	28.4b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	9.8b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	27.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	29.5b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	31.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	27.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
	27.2b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 3 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
	46.1b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (*.f64 3 a))
	27.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 6052 to 3596 computations (40.6% saved)

localize27.0ms (0.4%)

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))
✓	0.3b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
✓	0.4b	(.f64 (.f64 a a) (pow.f64 c 3))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

series245.0ms (4%)

Counts

4 → 120

Calls

4 calls:

113.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
92.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
21.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
19.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`pow-exp_binary64`
39×	`div-exp_binary64`

Counts

4 → 194

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
7.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
6.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
6.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

simplify149.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

382×	`associate-l_binary64`
354×	`times-frac_binary64`
322×	`associate-r_binary64`
274×	`log-div_binary64`
271×	`associate-/l*_binary64`

Counts

314 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	4804
1	586	4461
2	3216	4382
3	4601	4382
4	5008	4382

prune351.0ms (5.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	224	20	244

Error

0.8b

Counts

244 → 20

Alt Table

Status	Error	Program
	27.2b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
✓	7.8b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	26.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (neg.f64 (.f64 c (.f64 3 a)))) (fma.f64 (neg.f64 c) (.f64 3 a) (.f64 c (.f64 3 a)))))) (.f64 3 a))
	27.0b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
	27.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	27.0b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	31.4b	(/.f64 (log.f64 (exp.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	13.6b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	27.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) 3) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) a))
▶	8.0b	(/.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 (pow.f64 (.f64 c 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))
	27.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 6) (.f64 -27 (pow.f64 (.f64 c a) 3))) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (*.f64 3 a))
	28.4b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	9.8b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	27.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	29.5b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	31.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	27.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
	27.2b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 3 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
	46.1b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (*.f64 3 a))
	27.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 12526 to 7746 computations (38.2% saved)

localize28.0ms (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 (*.f64 c a) 3) (pow.f64 b 5))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.7b	(pow.f64 (*.f64 c a) 3)

series211.0ms (3.4%)

Counts

4 → 120

Calls

4 calls:

105.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
81.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
14.0ms	(pow.f64 (*.f64 c a) 3)
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-exp-log_binary64`
68×	`times-frac_binary64`
46×	`pow1_binary64`
42×	`unpow-prod-down_binary64`
39×	`add-cbrt-cube_binary64`

Counts

4 → 213

Calls

4 calls:

8.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
6.0ms	(.f64 (.f64 c a) (*.f64 c a))
5.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
3.0ms	(pow.f64 (*.f64 c a) 3)

simplify153.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

506×	`unswap-sqr_binary64`
466×	`times-frac_binary64`
437×	`associate-/l*_binary64`
329×	`log-div_binary64`
211×	`associate-/r*_binary64`

Counts

333 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	5256
1	451	4597
2	3152	4443
3	4700	4443
4	5156	4443

prune428.0ms (7%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	232	23	255

Error

0.8b

Counts

255 → 23

Alt Table

Status	Error	Program
	29.5b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	25.5b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (log.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 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	27.2b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
✓	7.8b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	24.6b	(/.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 (log.f64 (exp.f64 (pow.f64 (.f64 c 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))
	26.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (neg.f64 (.f64 c (.f64 3 a)))) (fma.f64 (neg.f64 c) (.f64 3 a) (.f64 c (.f64 3 a)))))) (.f64 3 a))
	27.0b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
	27.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	27.0b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	31.4b	(/.f64 (log.f64 (exp.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	13.6b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	27.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) 3) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) a))
✓	8.0b	(/.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 (pow.f64 (.f64 c 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))
	14.4b	(/.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 (pow.f64 (.f64 c 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))
	27.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 6) (.f64 -27 (pow.f64 (.f64 c a) 3))) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (*.f64 3 a))
	28.4b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
▶	9.8b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	27.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	31.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	27.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
	27.2b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 3 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
	46.1b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (*.f64 3 a))
	27.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 15021 to 8801 computations (41.4% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c 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))
	0.7b	(pow.f64 (*.f64 c a) 3)

series177.0ms (2.9%)

Counts

1 → 36

Calls

1 calls:

176.0ms

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

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
35×	`unpow-prod-down_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`

Counts

1 → 96

Calls

1 calls:

6.0ms

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

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

737×	`associate-l_binary64`
590×	`associate-r_binary64`
361×	`associate-*l/_binary64`
327×	`log-prod_binary64`
312×	`associate-*r/_binary64`

Counts

132 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2687
1	243	2633
2	1169	2505
3	4639	2505
4	5344	2505

prune330.0ms (5.4%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	20	20
Picked	0	1	1
Done	0	2	2
Total	229	23	252

Error

0.8b

Counts

252 → 23

Alt Table

Status	Error	Program
	29.5b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	25.5b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (log.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 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	27.2b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
✓	7.8b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	24.6b	(/.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 (log.f64 (exp.f64 (pow.f64 (.f64 c 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))
	26.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (neg.f64 (.f64 c (.f64 3 a)))) (fma.f64 (neg.f64 c) (.f64 3 a) (.f64 c (.f64 3 a)))))) (.f64 3 a))
	27.0b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))) 3) a)
	27.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	27.0b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	31.4b	(/.f64 (log.f64 (exp.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	13.6b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	27.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) 3) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) a))
✓	8.0b	(/.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 (pow.f64 (.f64 c 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))
	14.4b	(/.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 (pow.f64 (.f64 c 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))
	27.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 6) (.f64 -27 (pow.f64 (.f64 c a) 3))) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (*.f64 3 a))
	28.4b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
✓	9.8b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	27.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	31.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	27.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
	27.2b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 3 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
	46.1b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (*.f64 3 a))
	27.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 10658 to 5553 computations (47.9% saved)

regimes824.0ms (13.4%)

Accuracy

Total 5.7b remaining (87.7%)

Threshold costs 0b (0%)

Counts

90 → 2

Compiler

Compiled 15864 to 10802 computations (31.9% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 20 to 14 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	138
1	78	132
2	98	132
3	106	132
4	109	132
5	110	132
6	109	132

end564.0ms (9.2%)

Compiler: Compiled 1099 to 727 computations (33.8% saved)

Details

analyze291.0ms (4.7%)

sample1.3s (21.3%)

simplify350.0ms (5.7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series167.0ms (2.7%)

rewrite30.0ms (0.5%)

simplify119.0ms (1.9%)

prune149.0ms (2.4%)

localize27.0ms (0.4%)

series245.0ms (4%)

rewrite39.0ms (0.6%)

simplify149.0ms (2.4%)

prune351.0ms (5.7%)

localize28.0ms (0.5%)

series211.0ms (3.4%)

rewrite36.0ms (0.6%)

simplify153.0ms (2.5%)

prune428.0ms (7%)

localize28.0ms (0.4%)

series177.0ms (2.9%)

rewrite13.0ms (0.2%)

simplify104.0ms (1.7%)

prune330.0ms (5.4%)

regimes824.0ms (13.4%)

bsearch5.0ms (0.1%)

simplify6.0ms (0.1%)

end564.0ms (9.2%)

Profiling