Details

analyze492.0ms (4.7%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
34.3%	65.5%	0.1%	6
37.4%	56.2%	6.4%	7
41.3%	52.3%	6.4%	8
50.7%	40.6%	8.7%	9
54.2%	32.4%	13.4%	10
58.9%	26.9%	14.2%	11
62.7%	20.7%	16.5%	12
64.5%	16.6%	19%	13
67.1%	13.5%	19.4%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample2.0s (18.7%)

Infinites

91.7% of outputs are infinite.

Results

1.7s	8256×	body	128	valid
107.0ms	694×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1002×	`fma-def_binary64`
782×	`fma-neg_binary64`
748×	`distribute-rgt-in_binary64`
560×	`div-sub_binary64`
469×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	44	52
2	94	52
3	211	50
4	341	50
5	594	50
6	1082	50
7	1702	50
8	2066	50
9	2870	50
10	3495	50
11	3501	50
12	3503	50
13	4196	50
14	4249	50
15	4881	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

16.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.8b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
▶	16.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Status

Error

Program

16.8b

(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))

▶

16.8b

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

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.0b	(-.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))
✓	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series173.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

58.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
53.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
51.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`prod-diff_binary64`
59×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
37×	`sqrt-prod_binary64`

Counts

4 → 155

Calls

4 calls:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(+.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))

simplify200.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
235×	`exp-prod_binary64`
216×	`distribute-rgt-neg-in_binary64`
177×	`distribute-lft-neg-in_binary64`

Counts

251 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	7252
1	613	5514
2	2119	4942
3	4406	4869
4	4870	4869
5	4825	4869

prune617.0ms (5.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	316	11	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	317	12	329

Error

5.0b

Counts

329 → 12

Alt Table

Status	Error	Program
	16.8b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	18.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	28.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 4 a) c) (.f64 (.f64 4 a) c))) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a)))
	25.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 3))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
	16.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	23.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	20.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	23.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
▶	16.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Compiler

Compiled 18795 to 10872 computations (42.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
	1.0b	(-.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))
	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series271.0ms (2.6%)

Counts

1 → 20

Calls

1 calls:

271.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`associate-/r*_binary64`
7×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

11.0ms

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

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
432×	`associate-/r*_binary64`
238×	`fma-neg_binary64`
221×	`associate-*l/_binary64`
220×	`fma-def_binary64`

Counts

53 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1740
1	388	1573
2	1316	1490
3	4772	1490
4	4988	1490
5	4912	1490

prune824.0ms (7.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	352	5	357
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	357	12	369

Error

4.7b

Counts

369 → 12

Alt Table

Status	Error	Program
	20.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	17.1b	(if (>=.f64 b 0) (/.f64 (/.f64 (.f64 2 c) (.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))))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
▶	16.8b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	28.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 4 a) c) (.f64 (.f64 4 a) c))) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a)))
	26.6b	(if (>=.f64 b 0) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
	17.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (neg.f64 b)) (*.f64 2 a)))
	23.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	23.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 c))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Compiler

Compiled 21864 to 11799 computations (46% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.4b	(-.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))))
✓	23.3b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series528.0ms (5%)

Counts

4 → 80

Calls

4 calls:

378.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
54.0ms	(-.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))))
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 110

Calls

4 calls:

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

simplify192.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-neg_binary64`
459×	`cancel-sign-sub-inv_binary64`
173×	`associate-/r/_binary64`
157×	`distribute-rgt-neg-in_binary64`
155×	`distribute-rgt-in_binary64`

Counts

190 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	5502
1	628	4671
2	2148	4484
3	4334	4468
4	4901	4468
5	4980	4468
6	4843	4468

prune684.0ms (6.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	283	2	285
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	284	13	297

Error

4.7b

Counts

297 → 13

Alt Table

Status	Error	Program
	28.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 4 a) c) (.f64 (.f64 4 a) c))) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a)))
	19.6b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	20.6b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (neg.f64 b)) (*.f64 2 a)))
	20.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	17.1b	(if (>=.f64 b 0) (/.f64 (/.f64 (.f64 2 c) (.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))))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	26.6b	(if (>=.f64 b 0) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
	17.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	23.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	23.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
▶	16.9b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 c))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Compiler

Compiled 14212 to 8389 computations (41% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 c))
	1.0b	(-.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))
	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series83.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

83.0ms

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`associate-/l*_binary64`
7×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 34

Calls

1 calls:

12.0ms

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

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

808×	`times-frac_binary64`
474×	`associate-/l*_binary64`
375×	`fma-neg_binary64`
321×	`fma-def_binary64`
168×	`distribute-rgt-in_binary64`

Counts

54 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	1677
1	399	1518
2	1337	1451
3	4874	1449
4	5098	1449

prune893.0ms (8.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	356	1	357
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	358	12	370

Error

4.7b

Counts

370 → 12

Alt Table

Status	Error	Program
	28.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 4 a) c) (.f64 (.f64 4 a) c))) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a)))
	19.6b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	17.9b	(if (>=.f64 b 0) (/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	26.6b	(if (>=.f64 b 0) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	16.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)))
	17.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	19.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (neg.f64 b)) (*.f64 2 a)))
	23.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	17.1b	(if (>=.f64 b 0) (/.f64 (/.f64 (.f64 2 c) (.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))))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	23.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a)))
✓	16.9b	(if (>=.f64 b 0) (/.f64 1 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 c))) (/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Compiler

Compiled 21957 to 12119 computations (44.8% saved)

regimes2.6s (25.3%)

Accuracy

Total 0.8b remaining (14.1%)

Threshold costs 0.8b (14.1%)

Counts

190 → 3

Compiler

Compiled 34518 to 22222 computations (35.6% saved)

bsearch59.0ms (0.6%)

Steps

Iters	Range		Point
6	1.588209678957361e+104	2.0927799489779192e+105	1.7930757211015575e+105
8	-4.684101613605904e+108	-9.922587655201207e+104	-4.402828950487531e+108

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
14×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	166
1	61	164
2	82	164
3	102	164
4	116	164
5	122	164
6	123	164
7	122	164

end368.0ms (3.5%)

Compiler: Compiled 783 to 478 computations (39% saved)

Details

analyze492.0ms (4.7%)

sample2.0s (18.7%)

simplify128.0ms (1.2%)

prune5.0ms (0%)

localize19.0ms (0.2%)

series173.0ms (1.7%)

rewrite39.0ms (0.4%)

simplify200.0ms (1.9%)

prune617.0ms (5.9%)

localize22.0ms (0.2%)

series271.0ms (2.6%)

rewrite14.0ms (0.1%)

simplify91.0ms (0.9%)

prune824.0ms (7.9%)

localize21.0ms (0.2%)

series528.0ms (5%)

rewrite19.0ms (0.2%)

simplify192.0ms (1.8%)

prune684.0ms (6.5%)

localize23.0ms (0.2%)

series83.0ms (0.8%)

rewrite15.0ms (0.1%)

simplify75.0ms (0.7%)

prune893.0ms (8.5%)

regimes2.6s (25.3%)

bsearch59.0ms (0.6%)

simplify7.0ms (0.1%)

end368.0ms (3.5%)

Profiling