Details

analyze1.5s (16.2%)

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
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample44.0ms (0.5%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
2.0ms	15×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify133.0ms (1.4%)

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

prune6.0ms (0.1%)

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

20.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.4b	(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)))
▶	20.3b	(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

20.4b

(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)))

▶

20.3b

(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)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`prod-diff_binary64`
58×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
37×	`sqrt-prod_binary64`

Counts

3 → 139

Calls

3 calls:

14.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(-.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)))

series131.0ms (1.4%)

Counts

3 → 60

Calls

3 calls:

47.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
46.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
38.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify227.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

413×	`neg-mul-1_binary64`
405×	`fma-neg_binary64`
340×	`cancel-sign-sub-inv_binary64`
221×	`distribute-rgt-in_binary64`
217×	`distribute-rgt-neg-in_binary64`

Counts

199 → 372

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	7433
1	582	5432
2	2019	4330
3	4384	4274
4	4974	4274
5	4910	4274

prune624.0ms (6.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	425	10	435
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	426	11	437

Error

5.6b

Counts

437 → 11

Alt Table

Status	Error	Program
	23.0b	(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 a (.f64 c -4))) b)))) (*.f64 2 a)))
	31.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	20.4b	(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)))
	20.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	21.9b	(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 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)))) (.f64 2 a)))
	24.5b	(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 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
	20.4b	(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)))
	22.1b	(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 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (*.f64 2 a)))
▶	20.0b	(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 -2 b) (.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	23.7b	(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)))

Compiler

Compiled 16682 to 9687 computations (41.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

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

series269.0ms (2.9%)

Counts

2 → 56

Calls

2 calls:

238.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
31.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-/l*_binary64`
467×	`fma-def_binary64`
205×	`cancel-sign-sub-inv_binary64`
182×	`associate-/r/_binary64`
159×	`distribute-rgt-neg-in_binary64`

Counts

105 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2383
1	471	2176
2	1770	2083
3	5310	2083

prune624.0ms (6.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	549	5	554
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	553	12	565

Error

5.6b

Counts

565 → 12

Alt Table

Status	Error	Program
	23.0b	(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 a (.f64 c -4))) b)))) (*.f64 2 a)))
	36.2b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 2 c) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	31.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	23.4b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	21.9b	(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 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)))) (.f64 2 a)))
	20.4b	(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)))
	24.5b	(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 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
▶	20.1b	(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 -2 b) (.f64 2 a)))
	22.1b	(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 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.2b	(if (>=.f64 b 0) (/.f64 2 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) c)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	35.3b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 (.f64 c a) 4)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 -2 b) (*.f64 2 a)))

Compiler

Compiled 13869 to 8482 computations (38.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.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)))))
✓	9.4b	(-.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))))))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
67×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
25×	`pow1_binary64`
24×	`sqrt-div_binary64`

Counts

2 → 130

Calls

2 calls:

13.0ms

(*.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)))))

6.0ms

(-.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))))))

series89.0ms (0.9%)

Counts

2 → 40

Calls

2 calls:

48.0ms

(-.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))))))

40.0ms

(*.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)))))

simplify164.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
762×	`fma-neg_binary64`
269×	`cancel-sign-sub-inv_binary64`
212×	`distribute-rgt-neg-in_binary64`
187×	`distribute-lft-neg-in_binary64`

Counts

170 → 324

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	4481
1	552	3931
2	1892	3488
3	4517	3476
4	4939	3476

prune612.0ms (6.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	1080	0	1080
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	1080	12	1092

Error

5.6b

Counts

1092 → 12

Alt Table

Status	Error	Program
	23.0b	(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 a (.f64 c -4))) b)))) (*.f64 2 a)))
	36.2b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 2 c) (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	31.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	23.4b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	21.9b	(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 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)))) (.f64 2 a)))
	20.4b	(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)))
	24.5b	(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 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
✓	20.1b	(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 -2 b) (.f64 2 a)))
	22.1b	(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 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
▶	20.2b	(if (>=.f64 b 0) (/.f64 2 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) c)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	35.3b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 (.f64 c a) 4)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 -2 b) (*.f64 2 a)))

Compiler

Compiled 15462 to 9670 computations (37.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 2 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`times-frac_binary64`
119×	`*-un-lft-identity_binary64`
119×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
25×	`associate-/r*_binary64`

Counts

1 → 120

Calls

1 calls:

11.0ms

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

series355.0ms (3.8%)

Counts

1 → 20

Calls

1 calls:

355.0ms

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

simplify184.0ms (2%)

Algorithm

1×	egg-herbie

Rules

754×	`times-frac_binary64`
572×	`associate-/l*_binary64`
454×	`associate-/r/_binary64`
306×	`associate-/l/_binary64`
182×	`fma-def_binary64`

Counts

140 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	5866
1	606	5672
2	1827	5455
3	5040	5455

prune730.0ms (7.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1835	3	1838
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	1838	12	1850

Error

5.6b

Counts

1850 → 12

Alt Table

Status	Error	Program
	23.0b	(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 a (.f64 c -4))) b)))) (*.f64 2 a)))
	31.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (fma.f64 (.f64 4 (.f64 c a)) (fma.f64 4 (.f64 c a) (.f64 b b)) (pow.f64 b 4))))) (*.f64 2 a)))
	23.4b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	21.9b	(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 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)))) (.f64 2 a)))
	20.3b	(if (>=.f64 b 0) (.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 2) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) c))) (/.f64 (.f64 -2 b) (.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	20.4b	(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)))
	24.5b	(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 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)))
	29.2b	(if (>=.f64 b 0) (/.f64 2 (/.f64 (cbrt.f64 (pow.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b)) 3)) c)) (/.f64 (.f64 -2 b) (.f64 2 a)))
	22.1b	(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 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (.f64 c -4))) b) b))) (*.f64 2 a)))
	23.6b	(if (>=.f64 b 0) (/.f64 2 (/.f64 (.f64 -2 b) c)) (/.f64 (.f64 -2 b) (*.f64 2 a)))
	35.3b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 (.f64 c a) 4)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 -2 b) (*.f64 2 a)))

Compiler

Compiled 18507 to 11360 computations (38.6% saved)

regimes1.7s (17.7%)

Accuracy

Total 1.2b remaining (18.3%)

Threshold costs 0b (0%)

Compiler

Compiled 20838 to 14450 computations (30.7% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	445
1	77	433
2	109	433
3	131	433
4	143	433
5	147	433
6	146	433

end4.0ms (0%)

Compiler: Compiled 287 to 176 computations (38.7% saved)

sample1.7s (18.4%)

Algorithm

1×

intervals

Results

946.0ms	8000×	body	128	valid
68.0ms	610×	body	128	nan
44.0ms	395×	body	128	invalid

Compiler

Compiled 862 to 562 computations (34.8% saved)

Details

analyze1.5s (16.2%)

sample44.0ms (0.5%)

simplify133.0ms (1.4%)

prune6.0ms (0.1%)

localize25.0ms (0.3%)

rewrite39.0ms (0.4%)

series131.0ms (1.4%)

simplify227.0ms (2.4%)

prune624.0ms (6.6%)

localize22.0ms (0.2%)

rewrite15.0ms (0.2%)

series269.0ms (2.9%)

simplify83.0ms (0.9%)

prune624.0ms (6.6%)

localize23.0ms (0.2%)

rewrite32.0ms (0.3%)

series89.0ms (0.9%)

simplify164.0ms (1.7%)

prune612.0ms (6.5%)

localize21.0ms (0.2%)

rewrite24.0ms (0.3%)

series355.0ms (3.8%)

simplify184.0ms (2%)

prune730.0ms (7.7%)

regimes1.7s (17.7%)

bsearch9.0ms (0.1%)

simplify16.0ms (0.2%)

end4.0ms (0%)

sample1.7s (18.4%)

Profiling