Details

analyze750.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.9s (19.3%)

Results

1.6s	8256×	body	128	valid
191.0ms	1074×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify157.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1753×	`fma-neg_binary64`
1288×	`fma-def_binary64`
631×	`div-sub_binary64`
512×	`times-frac_binary64`
430×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	118	52
3	269	50
4	429	50
5	743	50
6	1315	50
7	1738	50
8	2176	50
9	2853	50
10	4066	50
11	3523	50
12	3575	50
13	3543	50
14	3557	50
15	4510	50
16	4622	50
17	4761	50

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

18.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 149 to 91 computations (38.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	1.0b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	20.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series426.0ms (4.4%)

Counts

4 → 80

Calls

4 calls:

268.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
58.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
51.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
48.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-neg-in_binary64`
159×	`distribute-rgt-in_binary64`
157×	`distribute-lft-neg-in_binary64`

Counts

186 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	5384
1	686	4516
2	2546	4321
3	4500	4319
4	4865	4319

prune431.0ms (4.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	267	11	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	11	279

Error

4.5b

Counts

279 → 11

Alt Table

Status	Error	Program
	18.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	31.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	18.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	21.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
▶	18.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))

Compiler

Compiled 13587 to 7973 computations (41.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 c 2)))
	1.0b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	20.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series271.0ms (2.8%)

Counts

1 → 20

Calls

1 calls:

270.0ms

(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 c 2)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64`
20×	`add-cube-cbrt_binary64`

Counts

1 → 70

Calls

1 calls:

8.0ms

(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 c 2)))

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
663×	`associate-/l*_binary64`
592×	`associate-/r*_binary64`
349×	`associate-*l/_binary64`
325×	`associate-/r/_binary64`

Counts

90 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	3096
1	385	2703
2	1351	2577
3	4809	2576
4	5338	2576

prune603.0ms (6.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	315	2	317
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	316	12	328

Error

4.5b

Counts

328 → 12

Alt Table

Status	Error	Program
	18.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) b) (.f64 c 2))))
	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) c)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2))))
✓	18.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	31.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	18.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
▶	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))

Compiler

Compiled 15989 to 9673 computations (39.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
	1.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	12.0b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	20.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series94.0ms (1%)

Counts

2 → 40

Calls

2 calls:

52.0ms

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

42.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
61×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
25×	`pow1_binary64`
16×	`rem-sqrt-square_binary64`

Counts

2 → 101

Calls

2 calls:

8.0ms

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

2.0ms

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

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
455×	`times-frac_binary64`
367×	`fma-def_binary64`
278×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`

Counts

141 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	3099
1	389	2882
2	1155	2664
3	4156	2624
4	4958	2624
5	5008	2624

prune824.0ms (8.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	353	1	354
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	353	13	366

Error

4.5b

Counts

366 → 13

Alt Table

Status	Error	Program
	18.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	24.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) 5) (cbrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	21.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) b) (.f64 c 2))))
▶	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) c)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2))))
✓	18.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	31.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	18.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))

Compiler

Compiled 20329 to 12012 computations (40.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) c))
	1.0b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	20.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series829.0ms (8.6%)

Counts

1 → 4

Calls

1 calls:

828.0ms

(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) c))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64`
145×	`add-sqr-sqrt_binary64`
121×	`*-un-lft-identity_binary64`
97×	`add-cube-cbrt_binary64`
84×	`sqrt-prod_binary64`

Counts

1 → 150

Calls

1 calls:

12.0ms

(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) c))

simplify233.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
409×	`associate-/l*_binary64`
356×	`cancel-sign-sub-inv_binary64`
317×	`fma-neg_binary64`
299×	`associate-r_binary64`

Counts

154 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	6297
1	330	5785
2	854	5484
3	2314	5471
4	4483	5471
5	4975	5471

prune1.1s (11.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	491	12	503

Error

4.5b

Counts

503 → 12

Alt Table

Status	Error	Program
	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) c)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2))))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	24.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) 5) (cbrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 2 c) (+.f64 (.f64 a (.f64 c -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	21.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) b) (.f64 c 2))))
	31.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	18.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	18.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
✓	18.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))

Compiler

Compiled 32801 to 19820 computations (39.6% saved)

regimes1.2s (12.4%)

Accuracy

Total 1.0b remaining (14.3%)

Threshold costs 1.0b (14.3%)

Counts

102 → 3

Compiler

Compiled 19302 to 12550 computations (35% saved)

bsearch36.0ms (0.4%)

Steps

Iters	Range		Point
5	2.1665003818594198e+121	7.477859093117982e+121	5.545049901184398e+121
2	-6.23817191079231e+155	-5.018533530183444e+152	-2.9527445303397572e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	148
1	67	146
2	90	146
3	109	146
4	122	146
5	128	146
6	129	146
7	128	146

end288.0ms (3%)

Compiler: Compiled 707 to 454 computations (35.8% saved)

Details

analyze750.0ms (7.8%)

sample1.9s (19.3%)

simplify157.0ms (1.6%)

prune4.0ms (0%)

localize27.0ms (0.3%)

series426.0ms (4.4%)

rewrite22.0ms (0.2%)

simplify146.0ms (1.5%)

prune431.0ms (4.5%)

localize20.0ms (0.2%)

series271.0ms (2.8%)

rewrite16.0ms (0.2%)

simplify97.0ms (1%)

prune603.0ms (6.2%)

localize21.0ms (0.2%)

series94.0ms (1%)

rewrite22.0ms (0.2%)

simplify122.0ms (1.3%)

prune824.0ms (8.5%)

localize22.0ms (0.2%)

series829.0ms (8.6%)

rewrite40.0ms (0.4%)

simplify233.0ms (2.4%)

prune1.1s (11.4%)

regimes1.2s (12.4%)

bsearch36.0ms (0.4%)

simplify6.0ms (0.1%)

end288.0ms (3%)

Profiling