Details

analyze849.0ms (6.7%)

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)

sample48.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
3.0ms	23×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify158.0ms (1.3%)

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

prune5.0ms (0%)

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

20.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	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) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
▶	20.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Status

Error

Program

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

▶

20.8b

(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
✓	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series396.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

281.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
60.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 89

Calls

4 calls:

9.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
8.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
212×	`distribute-rgt-neg-in_binary64`
188×	`distribute-lft-neg-in_binary64`
154×	`associate-r_binary64`

Counts

185 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4100
1	684	3745
2	2475	3603
3	4521	3581
4	4989	3581

prune572.0ms (4.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	280	10	290
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	282	10	292

Error

5.5b

Counts

292 → 10

Alt Table

Status	Error	Program
	34.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	23.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	23.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))))
	20.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	24.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	22.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	23.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))))
▶	18.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (*.f64 -1 (/.f64 c b)))
	21.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.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)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.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))))))))

Compiler

Compiled 14408 to 8320 computations (42.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series222.0ms (1.8%)

Counts

2 → 40

Calls

2 calls:

126.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
95.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`prod-diff_binary64`
59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`

Counts

2 → 129

Calls

2 calls:

18.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
16.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify257.0ms (2%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
403×	`fma-neg_binary64`
343×	`div-sub_binary64`
204×	`cancel-sign-sub-inv_binary64`
136×	`sub-neg_binary64`

Counts

169 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	7107
1	675	5059
2	2351	3973
3	4556	3951
4	5099	3951

prune779.0ms (6.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	273	4	277
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	278	9	287

Error

5.3b

Counts

287 → 9

Alt Table

Status	Error	Program
	18.6b	(if (>=.f64 b 0) (.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a)) (*.f64 -1 (/.f64 c b)))
	22.1b	(if (>=.f64 b 0) (-.f64 (/.f64 c b) (/.f64 b a)) (*.f64 -1 (/.f64 c b)))
▶	18.6b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 -1 (/.f64 c b)))
	23.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))))
	23.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))))
	20.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	22.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	22.2b	(if (>=.f64 b 0) (.f64 -1 (/.f64 b a)) (.f64 -1 (/.f64 c b)))
	20.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.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))))))))

Compiler

Compiled 12900 to 7333 computations (43.2% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series124.0ms (1%)

Counts

1 → 20

Calls

1 calls:

123.0ms

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

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`times-frac_binary64`
39×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

1 → 82

Calls

1 calls:

18.0ms

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

simplify172.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/l*_binary64`
321×	`fma-def_binary64`
293×	`fma-neg_binary64`
268×	`associate-/r/_binary64`
191×	`distribute-rgt-in_binary64`

Counts

102 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	3540
1	439	3295
2	1537	3091
3	4697	3085
4	4915	3085

prune904.0ms (7.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	327	2	329
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	329	9	338

Error

5.3b

Counts

338 → 9

Alt Table

Status	Error	Program
▶	18.6b	(if (>=.f64 b 0) (.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a)) (*.f64 -1 (/.f64 c b)))
	22.1b	(if (>=.f64 b 0) (-.f64 (/.f64 c b) (/.f64 b a)) (*.f64 -1 (/.f64 c b)))
	29.7b	(if (>=.f64 b 0) (/.f64 (.f64 (.f64 4 (.f64 a c)) (/.f64 1/2 a)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 -1 (/.f64 c b)))
	23.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))))
	23.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))))
	20.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	22.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	22.3b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2))) (*.f64 -1 (/.f64 c b)))
	20.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.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))))))))

Compiler

Compiled 15793 to 9317 computations (41% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a))
	0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series120.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

119.0ms

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

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 42

Calls

1 calls:

19.0ms

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

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Rules

694×	`times-frac_binary64`
396×	`fma-neg_binary64`
350×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
124×	`distribute-rgt-neg-out_binary64`

Counts

62 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1900
1	442	1745
2	1615	1658
3	4583	1656
4	4926	1656

prune800.0ms (6.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	296	10	306

Error

5.3b

Counts

306 → 10

Alt Table

Status	Error	Program
	22.3b	(if (>=.f64 b 0) (.f64 (.f64 b -2) (/.f64 1/2 a)) (*.f64 -1 (/.f64 c b)))
	22.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	18.6b	(if (>=.f64 b 0) (.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a)) (*.f64 -1 (/.f64 c b)))
	22.1b	(if (>=.f64 b 0) (-.f64 (/.f64 c b) (/.f64 b a)) (*.f64 -1 (/.f64 c b)))
	29.7b	(if (>=.f64 b 0) (/.f64 (.f64 (.f64 4 (.f64 a c)) (/.f64 1/2 a)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 -1 (/.f64 c b)))
	23.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))))
	23.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))))
	20.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	22.3b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2))) (*.f64 -1 (/.f64 c b)))
	20.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.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))))))))

Compiler

Compiled 13330 to 7604 computations (43% saved)

regimes3.4s (27.2%)

Accuracy

Total 1.1b remaining (16.8%)

Threshold costs 0b (0%)

Counts

177 → 3

Compiler

Compiled 24214 to 16786 computations (30.7% saved)

bsearch113.0ms (0.9%)

Steps

Iters	Range		Point
8	2.746859577346239e+89	1.8623847742151241e+93	1.422349730838436e+93
7	-4.294781295811677e+61	-4.351231731861997e+59	-3.96398836197757e+61

Compiler

Compiled 4 to 3 computations (25% saved)

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	124
1	82	122
2	130	120
3	165	120
4	183	120
5	189	120
6	190	120
7	186	120

end2.0ms (0%)

Compiler: Compiled 83 to 50 computations (39.8% saved)

sample3.1s (24.6%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
133.0ms	621×	body	128	nan
126.0ms	386×	body	128	invalid

Compiler

Compiled 491 to 321 computations (34.6% saved)

Details

analyze849.0ms (6.7%)

sample48.0ms (0.4%)

simplify158.0ms (1.3%)

prune5.0ms (0%)

localize24.0ms (0.2%)

series396.0ms (3.1%)

rewrite28.0ms (0.2%)

simplify120.0ms (0.9%)

prune572.0ms (4.5%)

localize34.0ms (0.3%)

series222.0ms (1.8%)

rewrite62.0ms (0.5%)

simplify257.0ms (2%)

prune779.0ms (6.2%)

localize35.0ms (0.3%)

series124.0ms (1%)

rewrite37.0ms (0.3%)

simplify172.0ms (1.4%)

prune904.0ms (7.2%)

localize34.0ms (0.3%)

series120.0ms (0.9%)

rewrite27.0ms (0.2%)

simplify125.0ms (1%)

prune800.0ms (6.3%)

regimes3.4s (27.2%)

bsearch113.0ms (0.9%)

simplify41.0ms (0.3%)

end2.0ms (0%)

sample3.1s (24.6%)

Profiling