Details

analyze361.0ms (6.1%)

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)

sample1.8s (31%)

Results

808.0ms	2993×	body	256	valid
791.0ms	5263×	body	128	valid
143.0ms	974×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify259.0ms (4.4%)

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

41.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	41.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	41.7b	(/.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))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	37.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series128.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

55.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.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))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify116.0ms (2%)

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

prune143.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	193	13	206
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	13	208

Error

0.5b

Counts

208 → 13

Alt Table

Status	Error	Program
	41.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	41.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.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))))))) (.f64 2 a))
	4.5b	(/.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))
	41.7b	(/.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))
	41.2b	(/.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))
	42.0b	(/.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))
	41.7b	(/.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))))))
	41.7b	(/.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))))))))
	41.7b	(.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))
▶	4.3b	(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))))))
	41.7b	(/.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))
	4.5b	(/.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))
	41.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 c a) (.f64 c a)) -16 (pow.f64 b 4)) (fma.f64 4 (.f64 c a) (.f64 b b))))) (.f64 2 a))

Compiler

Compiled 6426 to 3772 computations (41.3% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series185.0ms (3.1%)

Counts

4 → 120

Calls

4 calls:

92.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
60.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
18.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
14.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 194

Calls

4 calls:

8.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
6.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
6.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
6.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

simplify140.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

314 → 226

Iterations

Useful iterations: 2 (0.0ms)

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

prune342.0ms (5.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	226	13	239

Error

0.5b

Counts

239 → 13

Alt Table

Status	Error	Program
	41.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	41.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.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))))))) (.f64 2 a))
	4.5b	(/.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))
	41.7b	(/.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))
	41.2b	(/.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))
	42.0b	(/.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))
	41.7b	(/.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))))))
	41.7b	(/.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))))))))
	41.7b	(.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))
✓	4.3b	(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))))))
	41.7b	(/.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))
▶	4.5b	(/.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))
	41.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 c a) (.f64 c a)) -16 (pow.f64 b 4)) (fma.f64 4 (.f64 c a) (.f64 b b))))) (.f64 2 a))

Compiler

Compiled 11540 to 6841 computations (40.7% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))

series196.0ms (3.3%)

Counts

4 → 0

Calls

4 calls:

93.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
67.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
19.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
17.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-exp-log_binary64`
72×	`prod-exp_binary64`
68×	`pow-exp_binary64`
68×	`pow-to-exp_binary64`
60×	`add-sqr-sqrt_binary64`

Counts

4 → 233

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
7.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
7.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
5.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

simplify379.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-/r/_binary64`
322×	`associate-l_binary64`
299×	`associate-r_binary64`
229×	`associate-/l*_binary64`
228×	`times-frac_binary64`

Counts

233 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	4102
1	563	3766
2	2829	3612
3	4989	3612

prune475.0ms (8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	226	14	240

Error

0.5b

Counts

240 → 14

Alt Table

Status	Error	Program
	41.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	41.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.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))))))) (.f64 2 a))
▶	4.5b	(/.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))
	41.7b	(/.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))
✓	4.5b	(/.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))
	5.3b	(/.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 (log.f64 (exp.f64 (/.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))
	41.2b	(/.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))
	42.0b	(/.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))
	41.7b	(/.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))))))
	41.7b	(/.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))))))))
	41.7b	(.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))
✓	4.3b	(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))))))
	41.7b	(/.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))
	41.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 c a) (.f64 c a)) -16 (pow.f64 b 4)) (fma.f64 4 (.f64 c a) (.f64 b b))))) (.f64 2 a))

Compiler

Compiled 14884 to 10468 computations (29.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.8b	(pow.f64 (*.f64 c a) 3)

series23.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(pow.f64 (*.f64 c a) 3)
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
18×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(.f64 (.f64 c a) (*.f64 c a))
2.0ms	(pow.f64 (*.f64 c a) 3)

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
401×	`sqr-pow_binary64`
372×	`*-commutative_binary64`
317×	`log-prod_binary64`
316×	`distribute-rgt-in_binary64`

Counts

108 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	836
1	127	719
2	572	711
3	1420	711
4	2523	708
5	4966	708
6	4925	708

prune297.0ms (5%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	159	14	173

Error

0.5b

Counts

173 → 14

Alt Table

Status	Error	Program
	41.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	41.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.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))))))) (.f64 2 a))
✓	4.5b	(/.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))
	41.7b	(/.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))
✓	4.5b	(/.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))
	5.3b	(/.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 (log.f64 (exp.f64 (/.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))
	41.2b	(/.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))
	42.0b	(/.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))
	41.7b	(/.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))))))
	41.7b	(/.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))))))))
	41.7b	(.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))
✓	4.3b	(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))))))
	41.7b	(/.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))
	41.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 c a) (.f64 c a)) -16 (pow.f64 b 4)) (fma.f64 4 (.f64 c a) (.f64 b b))))) (.f64 2 a))

Compiler

Compiled 9206 to 5346 computations (41.9% saved)

regimes379.0ms (6.4%)

Accuracy

Total 2.6b remaining (86.9%)

Threshold costs 0b (0%)

Counts

79 → 1

Compiler

Compiled 10218 to 6928 computations (32.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	91	61
4	121	61
5	154	61
6	176	61
7	189	61
8	193	61
9	191	61

end378.0ms (6.4%)

Compiler: Compiled 726 to 476 computations (34.4% saved)

Details

analyze361.0ms (6.1%)

sample1.8s (31%)

simplify259.0ms (4.4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series128.0ms (2.2%)

rewrite29.0ms (0.5%)

simplify116.0ms (2%)

prune143.0ms (2.4%)

localize24.0ms (0.4%)

series185.0ms (3.1%)

rewrite39.0ms (0.7%)

simplify140.0ms (2.4%)

prune342.0ms (5.8%)

localize31.0ms (0.5%)

series196.0ms (3.3%)

rewrite43.0ms (0.7%)

simplify379.0ms (6.4%)

prune475.0ms (8%)

localize25.0ms (0.4%)

series23.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify72.0ms (1.2%)

prune297.0ms (5%)

regimes379.0ms (6.4%)

simplify5.0ms (0.1%)

end378.0ms (6.4%)

Profiling