Details

analyze759.0ms (9.6%)

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 (23.7%)

Results

1.6s	8256×	body	128	valid
200.0ms	1069×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify161.0ms (2%)

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 (0.1%)

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

21.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.4b	(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)

localize19.0ms (0.2%)

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))
✓	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series418.0ms (5.3%)

Counts

4 → 80

Calls

4 calls:

271.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
53.0ms	(-.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))))
42.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite23.0ms (0.3%)

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))
5.0ms	(-.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)))

simplify139.0ms (1.8%)

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

prune407.0ms (5.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	265	13	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	13	279

Error

6.7b

Counts

279 → 13

Alt Table

Status	Error	Program
	25.5b	(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)))))
	21.8b	(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)))
	20.8b	(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)))
	35.1b	(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 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
▶	19.7b	(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)))
	26.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	26.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
	27.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (expm1.f64 (log1p.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	35.6b	(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)))
	35.9b	(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)))
	26.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.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)))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.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)))
	21.5b	(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 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))

Compiler

Compiled 13805 to 8113 computations (41.2% saved)

localize25.0ms (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))
✓	0.2b	(/.f64 (+.f64 b b) a)
	1.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (+.f64 b b) a)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64`
12×	`associate-/l*_binary64`

Counts

1 → 67

Calls

1 calls:

5.0ms

(/.f64 (+.f64 b b) a)

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

555×	`div-sub_binary64`
500×	`associate-/r*_binary64`
500×	`associate-/r/_binary64`
498×	`fma-neg_binary64`
406×	`associate-*r/_binary64`

Counts

91 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	101	1082
1	188	1046
2	451	1046
3	1314	1046
4	3521	1046
5	4943	1046
6	4994	1046
7	4924	1046

prune515.0ms (6.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	268	5	273
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	271	15	286

Error

6.7b

Counts

286 → 15

Alt Table

Status	Error	Program
	20.1b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 b (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 2 (cbrt.f64 a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	26.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
▶	19.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))
	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b b)) 1) (/.f64 (sqrt.f64 (+.f64 b b)) a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.5b	(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)))))
	21.8b	(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)))
	31.8b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b b)) (log.f64 a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	27.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (expm1.f64 (log1p.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	28.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	21.5b	(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 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	35.6b	(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)))
	35.9b	(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)))
	26.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.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)))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.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)))
	26.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))

Compiler

Compiled 11235 to 6112 computations (45.6% saved)

localize17.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (+.f64 b b) a)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

prune150.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	87	14	101

Error

6.7b

Counts

101 → 14

Alt Table

Status	Error	Program
	25.5b	(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)))))
	21.8b	(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)))
▶	19.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 2 (/.f64 a b))) (/.f64 (.f64 c 2) (*.f64 b -2)))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.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)))
	19.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b b)) (/.f64 (sqrt.f64 (+.f64 b b)) a))) (/.f64 (.f64 c 2) (.f64 b -2)))
	26.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	28.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	21.5b	(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 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	26.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
	31.3b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b b)) (log.f64 a)))) (/.f64 (.f64 c 2) (*.f64 b -2)))
	27.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (expm1.f64 (log1p.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	35.6b	(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)))
	35.9b	(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)))
	26.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.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 3350 to 1975 computations (41% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (/.f64 a b))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 2 (/.f64 a b))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 72

Calls

1 calls:

4.0ms

(/.f64 2 (/.f64 a b))

simplify180.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
416×	`*-commutative_binary64`
303×	`associate-/r/_binary64`
293×	`distribute-rgt-in_binary64`
273×	`fma-neg_binary64`

Counts

96 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1428
1	306	1368
2	832	1365
3	1813	1365
4	2091	1365
5	2287	1365
6	2524	1365
7	3231	1365
8	4656	1365
9	4903	1365

prune171.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Error

6.7b

Counts

125 → 14

Alt Table

Status	Error	Program
	25.5b	(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)))))
	21.8b	(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)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 a) b)))) (/.f64 (.f64 c 2) (.f64 b -2)))
	35.6b	(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)))
	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (/.f64 a b)) (cbrt.f64 (/.f64 a b)))) (/.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 a b))))) (/.f64 (.f64 c 2) (.f64 b -2)))
	26.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.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)))
	28.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	21.5b	(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 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	26.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
	31.3b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b b)) (log.f64 a)))) (/.f64 (.f64 c 2) (*.f64 b -2)))
	27.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (expm1.f64 (log1p.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	35.9b	(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)))
	22.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.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)))
	26.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))

Compiler

Compiled 3555 to 2264 computations (36.3% saved)

regimes2.3s (29.1%)

Accuracy

Total 1.1b remaining (15.7%)

Threshold costs 0b (0%)

Counts

175 → 3

Compiler

Compiled 22394 to 15554 computations (30.5% saved)

bsearch72.0ms (0.9%)

Steps

Iters	Range		Point
7	1.0708155733422024e+121	5.30092268030776e+122	7.250966043701229e+121
8	-2.1488194316017615e+82	-7.183095331642665e+79	-2.1244998464394334e+82

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	123
1	60	123
2	64	123
3	66	123
4	67	123
5	65	123

end513.0ms (6.5%)

Compiler: Compiled 800 to 528 computations (34% saved)

Details

analyze759.0ms (9.6%)

sample1.9s (23.7%)

simplify161.0ms (2%)

prune4.0ms (0.1%)

localize19.0ms (0.2%)

series418.0ms (5.3%)

rewrite23.0ms (0.3%)

simplify139.0ms (1.8%)

prune407.0ms (5.1%)

localize25.0ms (0.3%)

series7.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify104.0ms (1.3%)

prune515.0ms (6.5%)

localize17.0ms (0.2%)

prune150.0ms (1.9%)

localize13.0ms (0.2%)

series7.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify180.0ms (2.3%)

prune171.0ms (2.2%)

regimes2.3s (29.1%)

bsearch72.0ms (0.9%)

simplify5.0ms (0.1%)

end513.0ms (6.5%)

Profiling