Details

analyze1.0s (8.7%)

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 33 to 24 computations (27.3% saved)

sample101.0ms (0.9%)

Algorithm

1×

intervals

Results

36.0ms	135×	body	256	valid
15.0ms	274×	pre	128	true
13.0ms	35×	body	512	valid
12.0ms	86×	body	128	valid
2.0ms	18×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify313.0ms (2.7%)

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

prune7.0ms (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

52.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	52.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	28.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite59.0ms (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:

20.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
14.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series376.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

146.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
91.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
79.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
59.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify239.0ms (2.1%)

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 → 343

Iterations

Useful iterations: 3 (0.0ms)

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

prune279.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	335	8	343
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	337	8	345

Error

0.2b

Counts

345 → 8

Alt Table

Status	Error	Program
	52.4b	(.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))))
	1.9b	(/.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))
	52.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	52.3b	(/.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))
	52.4b	(/.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))
	51.6b	(/.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))
▶	1.6b	(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))))))
	52.3b	(/.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)))))))

Compiler

Compiled 6090 to 3570 computations (41.4% saved)

localize50.0ms (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 (pow.f64 a 3) (pow.f64 c 4))
✓	0.4b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
30×	`div-exp_binary64`
29×	`unpow-prod-down_binary64`

Counts

4 → 186

Calls

4 calls:

14.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
13.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
12.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
11.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

series687.0ms (6%)

Counts

4 → 120

Calls

4 calls:

286.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
224.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
101.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
77.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

simplify281.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

394×	`times-frac_binary64`
381×	`associate-l_binary64`
327×	`associate-r_binary64`
312×	`log-div_binary64`
299×	`associate-/l*_binary64`

Counts

306 → 566

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4694
1	600	4318
2	3453	4239
3	4707	4239
4	5155	4239

prune636.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	566	0	566
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	566	8	574

Error

0.2b

Counts

574 → 8

Alt Table

Status	Error	Program
	52.4b	(.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))))
▶	1.9b	(/.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))
	52.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	52.3b	(/.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))
	52.4b	(/.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))
	51.6b	(/.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))
✓	1.6b	(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))))))
	52.3b	(/.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)))))))

Compiler

Compiled 11137 to 6570 computations (41% saved)

localize66.0ms (0.6%)

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

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 240

Calls

4 calls:

14.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
12.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
12.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
11.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

series918.0ms (8%)

Counts

4 → 0

Calls

4 calls:

318.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
293.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
246.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
60.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

simplify274.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

464×	`unswap-sqr_binary64`
340×	`times-frac_binary64`
338×	`associate-/l*_binary64`
264×	`log-div_binary64`
225×	`associate-l_binary64`

Counts

240 → 450

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	4272
1	607	3818
2	3147	3765
3	4657	3765
4	5027	3765

prune798.0ms (6.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	450	0	450
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	450	8	458

Error

0.2b

Counts

458 → 8

Alt Table

Status	Error	Program
	52.4b	(.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))))
✓	1.9b	(/.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))
	52.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	52.3b	(/.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))
	52.4b	(/.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))
▶	51.6b	(/.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))
✓	1.6b	(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))))))
	52.3b	(/.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)))))))

Compiler

Compiled 15029 to 10582 computations (29.6% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.1b	(/.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))
✓	51.6b	(fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

5.0ms

(/.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))

1.0ms

(fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

series245.0ms (2.1%)

Counts

2 → 22

Calls

2 calls:

151.0ms

(/.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))

94.0ms

(fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

simplify201.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

673×	`times-frac_binary64`
515×	`associate-/l*_binary64`
398×	`associate-/r*_binary64`
244×	`fma-def_binary64`
200×	`associate-*l/_binary64`

Counts

55 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1876
1	349	1464
2	1178	1361
3	4851	1361
4	5000	1361
5	4995	1361
6	5000	1361
7	4997	1361
8	4958	1361

prune207.0ms (1.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	263	7	270
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	266	12	278

Error

0.2b

Counts

278 → 12

Alt Table

Status	Error	Program
	51.8b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)) 3)))) (*.f64 2 a))
	52.3b	(/.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))
	52.3b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) b) a)))
	52.3b	(/.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)))))))
	52.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) b) (*.f64 a 2)) 3))
✓	1.9b	(/.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))
	52.4b	(/.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))
	51.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	52.1b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (.f64 2 a))
✓	1.6b	(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))))))
	1.7b	(/.f64 (-.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 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))
	52.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) b) (.f64 a 2))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) b) (.f64 a 2)))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) b) (*.f64 a 2))))

Compiler

Compiled 4995 to 2620 computations (47.5% saved)

regimes860.0ms (7.5%)

Accuracy

Total 1.3b remaining (85.5%)

Threshold costs 0b (0%)

Compiler

Compiled 12150 to 8016 computations (34% saved)

simplify8.0ms (0.1%)

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

end2.0ms (0%)

Compiler: Compiled 43 to 30 computations (30.2% saved)

sample3.7s (32%)

Algorithm

1×

intervals

Results

961.0ms	3797×	body	256	valid
552.0ms	1475×	body	512	valid
492.0ms	8844×	pre	128	true
337.0ms	2728×	body	128	valid
100.0ms	844×	body	128	nan

Compiler

Compiled 607 to 392 computations (35.4% saved)

Details

analyze1.0s (8.7%)

sample101.0ms (0.9%)

simplify313.0ms (2.7%)

prune7.0ms (0.1%)

localize23.0ms (0.2%)

rewrite59.0ms (0.5%)

series376.0ms (3.3%)

simplify239.0ms (2.1%)

prune279.0ms (2.4%)

localize50.0ms (0.4%)

rewrite70.0ms (0.6%)

series687.0ms (6%)

simplify281.0ms (2.4%)

prune636.0ms (5.5%)

localize66.0ms (0.6%)

rewrite79.0ms (0.7%)

series918.0ms (8%)

simplify274.0ms (2.4%)

prune798.0ms (6.9%)

localize25.0ms (0.2%)

rewrite10.0ms (0.1%)

series245.0ms (2.1%)

simplify201.0ms (1.8%)

prune207.0ms (1.8%)

regimes860.0ms (7.5%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample3.7s (32%)

Profiling