Details

analyze346.0ms (5.5%)

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)

sample1.5s (23%)

Results

1.2s	7934×	body	128	valid
120.0ms	878×	body	128	invalid
83.0ms	322×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify258.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	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

27.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	27.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 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
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	27.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series179.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

78.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
50.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
39.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
8.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`
215×	`distribute-rgt-neg-in_binary64`
159×	`associate-r_binary64`
150×	`distribute-rgt-neg-out_binary64`

Counts

186 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4178
1	695	3846
2	2512	3724
3	4692	3704
4	5031	3704

prune147.0ms (2.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	188	18	206
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	190	18	208

Error

1.0b

Counts

208 → 18

Alt Table

Status	Error	Program
	27.9b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	28.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	27.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -64 (pow.f64 b 6)) (fma.f64 4 (.f64 (.f64 c a) (fma.f64 4 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 2 a))
	27.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	27.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	7.8b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))
	27.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
	11.9b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	27.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	5.7b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
	27.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	46.7b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	27.8b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
▶	5.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	27.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	32.3b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	5.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))

Compiler

Compiled 6712 to 3972 computations (40.8% saved)

localize23.0ms (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))
✓	0.4b	(/.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))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

series560.0ms (8.9%)

Counts

4 → 132

Calls

4 calls:

371.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
102.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
67.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
19.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`add-exp-log_binary64`
72×	`prod-exp_binary64`
60×	`div-exp_binary64`
50×	`pow-exp_binary64`
50×	`pow-to-exp_binary64`

Counts

4 → 210

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
7.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
6.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
6.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
406×	`associate-/l*_binary64`
344×	`associate-l_binary64`
300×	`associate-r_binary64`
267×	`associate-/r*_binary64`

Counts

342 → 240

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	5722
1	668	5365
2	3933	5329
3	4956	5329
4	5075	5329

prune495.0ms (7.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	239	19	258

Error

1.0b

Counts

258 → 19

Alt Table

Status	Error	Program
	27.9b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	28.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	27.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -64 (pow.f64 b 6)) (fma.f64 4 (.f64 (.f64 c a) (fma.f64 4 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 2 a))
	27.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	27.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
	11.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	27.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	5.7b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
	27.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	46.7b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	27.8b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
✓	5.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	27.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	27.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	32.3b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	6.9b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	6.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)))) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
▶	5.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))

Compiler

Compiled 12748 to 7631 computations (40.1% saved)

localize31.0ms (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 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))

series325.0ms (5.2%)

Counts

4 → 0

Calls

4 calls:

126.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
105.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
76.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
18.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`add-exp-log_binary64`
90×	`pow-exp_binary64`
90×	`div-exp_binary64`
90×	`prod-exp_binary64`
90×	`pow-to-exp_binary64`

Counts

4 → 248

Calls

4 calls:

7.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
7.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
7.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
6.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))

simplify143.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

340×	`associate-/l*_binary64`
322×	`times-frac_binary64`
288×	`associate-l_binary64`
269×	`associate-r_binary64`
260×	`log-div_binary64`

Counts

248 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	4658
1	619	4222
2	3375	4108
3	4603	4108
4	4998	4108

prune494.0ms (7.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	0	17	17
Picked	0	1	1
Done	0	1	1
Total	231	20	251

Error

1.0b

Counts

251 → 20

Alt Table

Status	Error	Program
	27.8b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	12.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	27.9b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	28.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	27.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -64 (pow.f64 b 6)) (fma.f64 4 (.f64 (.f64 c a) (fma.f64 4 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 2 a))
	27.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	27.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
	11.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	27.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
▶	5.7b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
	27.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	46.7b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	29.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
✓	5.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	27.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	27.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	32.3b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	6.9b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	6.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)))) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
✓	5.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))

Compiler

Compiled 15617 to 11017 computations (29.5% saved)

localize27.0ms (0.4%)

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))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.7b	(pow.f64 (*.f64 c a) 3)

series100.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

75.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
12.0ms	(pow.f64 (*.f64 c a) 3)
12.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
45×	`pow1_binary64`
36×	`add-cbrt-cube_binary64`
33×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 117

Calls

3 calls:

9.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
5.0ms	(.f64 (.f64 c a) (*.f64 c a))
3.0ms	(pow.f64 (*.f64 c a) 3)

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-/r/_binary64`
449×	`unswap-sqr_binary64`
271×	`times-frac_binary64`
213×	`log-div_binary64`
178×	`associate-/l*_binary64`

Counts

201 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2595
1	268	2056
2	1885	2030
3	4538	2030
4	4963	2030

prune338.0ms (5.4%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	17	17
Picked	0	1	1
Done	0	2	2
Total	181	21	202

Error

1.0b

Counts

202 → 21

Alt Table

Status	Error	Program
	27.8b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	12.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	27.9b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	28.3b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	27.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -64 (pow.f64 b 6)) (fma.f64 4 (.f64 (.f64 c a) (fma.f64 4 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 2 a))
	27.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	24.7b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (log.f64 (exp.f64 (pow.f64 (.f64 c a) 2))) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
✓	5.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	27.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
	11.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	27.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.7b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
	27.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	46.7b	(/.f64 (log.f64 (.f64 (exp.f64 (neg.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	29.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
	27.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	27.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	32.3b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	6.9b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	6.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)))) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
✓	5.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))

Compiler

Compiled 10694 to 6219 computations (41.8% saved)

regimes339.0ms (5.4%)

Accuracy

Total 4.9b remaining (86.8%)

Threshold costs 0b (0%)

Counts

62 → 1

Compiler

Compiled 9205 to 6189 computations (32.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	59
1	37	59
2	39	59
3	40	59
4	40	59

end520.0ms (8.3%)

Compiler: Compiled 1006 to 670 computations (33.4% saved)

Details

analyze346.0ms (5.5%)

sample1.5s (23%)

simplify258.0ms (4.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series179.0ms (2.8%)

rewrite29.0ms (0.5%)

simplify116.0ms (1.8%)

prune147.0ms (2.3%)

localize23.0ms (0.4%)

series560.0ms (8.9%)

rewrite41.0ms (0.7%)

simplify160.0ms (2.5%)

prune495.0ms (7.9%)

localize31.0ms (0.5%)

series325.0ms (5.2%)

rewrite49.0ms (0.8%)

simplify143.0ms (2.3%)

prune494.0ms (7.8%)

localize27.0ms (0.4%)

series100.0ms (1.6%)

rewrite24.0ms (0.4%)

simplify89.0ms (1.4%)

prune338.0ms (5.4%)

regimes339.0ms (5.4%)

simplify3.0ms (0%)

end520.0ms (8.3%)

Profiling