Details

analyze698.0ms (8.6%)

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)

sample1.8s (22.5%)

Results

1.5s	8256×	body	128	valid
190.0ms	1101×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify156.0ms (1.9%)

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

20.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.5b	(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 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 149 to 91 computations (38.9% saved)

localize20.0ms (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))
✓	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series411.0ms (5%)

Counts

4 → 80

Calls

4 calls:

261.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
53.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
51.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite21.0ms (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:

5.0ms	(/.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)))

simplify144.0ms (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

prune423.0ms (5.2%)

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

4.1b

Counts

279 → 11

Alt Table

Status	Error	Program
	30.4b	(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 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3) (pow.f64 b 3)) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))))
	20.7b	(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))))
	33.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) 3)))
	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (cbrt.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)))
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	22.1b	(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)))
	20.6b	(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)))
	29.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	30.4b	(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)))
	21.6b	(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 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))

Compiler

Compiled 13611 to 7979 computations (41.4% saved)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series71.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

71.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 35

Calls

1 calls:

6.0ms

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

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

411×	`times-frac_binary64`
390×	`unswap-sqr_binary64`
384×	`fma-neg_binary64`
293×	`associate-/l*_binary64`
285×	`associate-r_binary64`

Counts

55 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1633
1	326	1543
2	945	1470
3	4083	1470
4	5217	1470

prune322.0ms (4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	167	13	180

Error

4.1b

Counts

180 → 13

Alt Table

Status	Error	Program
	29.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	27.8b	(if (>=.f64 b 0) (.f64 -1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	30.4b	(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 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3) (pow.f64 b 3)) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))))
	20.7b	(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))))
	30.4b	(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)))
	38.3b	(if (>=.f64 b 0) (.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) a)))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	33.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) 3)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	29.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	21.6b	(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 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))

Compiler

Compiled 7590 to 4811 computations (36.6% saved)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series72.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

72.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 43

Calls

1 calls:

8.0ms

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

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

460×	`times-frac_binary64`
408×	`associate-l_binary64`
317×	`unswap-sqr_binary64`
311×	`associate-/l*_binary64`
305×	`fma-def_binary64`

Counts

63 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1718
1	370	1571
2	1178	1497
3	4445	1497
4	5276	1497

prune339.0ms (4.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	181	14	195

Error

4.0b

Counts

195 → 14

Alt Table

Status	Error	Program
	29.5b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	27.8b	(if (>=.f64 b 0) (.f64 -1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	30.4b	(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 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3) (pow.f64 b 3)) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))))
▶	20.7b	(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))))
	31.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) b))))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	30.4b	(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)))
	38.3b	(if (>=.f64 b 0) (.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) a)))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	33.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) 3)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	29.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	21.6b	(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 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))

Compiler

Compiled 8347 to 5408 computations (35.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 c 2)))
	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series260.0ms (3.2%)

Counts

1 → 20

Calls

1 calls:

260.0ms

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

rewrite15.0ms (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:

7.0ms

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

simplify94.0ms (1.1%)

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

prune835.0ms (10.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	314	3	317
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	318	13	331

Error

4.0b

Counts

331 → 13

Alt Table

Status	Error	Program
	31.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) b))))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	30.4b	(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)))
	38.3b	(if (>=.f64 b 0) (.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) a)))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	33.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) 3)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	21.5b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 2 (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (.f64 -1 b) b)))
	27.8b	(if (>=.f64 b 0) (.f64 -1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	20.4b	(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))))
	20.7b	(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 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	20.7b	(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 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) c)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)))
	21.6b	(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 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))

Compiler

Compiled 15499 to 9365 computations (39.6% saved)

regimes1.8s (22.5%)

Accuracy

Total 1.1b remaining (17.7%)

Threshold costs 0b (0%)

Counts

133 → 3

Compiler

Compiled 23162 to 15326 computations (33.8% saved)

bsearch74.0ms (0.9%)

Steps

Iters	Range		Point
8	5.578383699742264e+77	2.8266591081539867e+80	5.5055700004826897e+79
8	-3.2236795514813885e+159	-1.6736714136635723e+155	-1.7035750295212249e+155

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	129
1	69	129
2	85	129
3	95	129
4	103	129
5	106	129
6	104	129

end285.0ms (3.5%)

Compiler: Compiled 671 to 443 computations (34% saved)

Details

analyze698.0ms (8.6%)

sample1.8s (22.5%)

simplify156.0ms (1.9%)

prune4.0ms (0.1%)

localize20.0ms (0.2%)

series411.0ms (5%)

rewrite21.0ms (0.3%)

simplify144.0ms (1.8%)

prune423.0ms (5.2%)

localize22.0ms (0.3%)

series71.0ms (0.9%)

rewrite8.0ms (0.1%)

simplify68.0ms (0.8%)

prune322.0ms (4%)

localize22.0ms (0.3%)

series72.0ms (0.9%)

rewrite12.0ms (0.1%)

simplify70.0ms (0.9%)

prune339.0ms (4.2%)

localize20.0ms (0.2%)

series260.0ms (3.2%)

rewrite15.0ms (0.2%)

simplify94.0ms (1.1%)

prune835.0ms (10.3%)

regimes1.8s (22.5%)

bsearch74.0ms (0.9%)

simplify9.0ms (0.1%)

end285.0ms (3.5%)

Profiling