Details

analyze775.0ms (9.3%)

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)

sample2.3s (27.3%)

Results

2.0s	8256×	body	128	valid
192.0ms	1117×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify129.0ms (1.6%)

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 (0.1%)

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

18.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	18.9b	(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)))
▶	18.8b	(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

18.9b

(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)))

▶

18.8b

(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
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.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))))
✓	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series165.0ms (2%)

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))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite41.0ms (0.5%)

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:

14.0ms	(-.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))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify205.0ms (2.5%)

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	8106
1	613	6063
2	2119	4942
3	4406	4869
4	4870	4869
5	4825	4869

prune552.0ms (6.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	318	9	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	319	10	329

Error

6.5b

Counts

329 → 10

Alt Table

Status	Error	Program
	31.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (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)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (cbrt.f64 (-.f64 (neg.f64 b) (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)))
▶	18.5b	(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)))
	18.8b	(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) (.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 2 a)))
	18.9b	(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)))
	21.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
	22.8b	(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)))
	24.0b	(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)))
	23.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (+.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.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)))

Compiler

Compiled 18823 to 10886 computations (42.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a))
	0.8b	(-.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))))
	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-/l*_binary64`
6×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 34

Calls

1 calls:

6.0ms

(/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

930×	`div-sub_binary64`
882×	`fma-def_binary64`
606×	`times-frac_binary64`
347×	`fma-neg_binary64`
338×	`associate-/l*_binary64`

Counts

58 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	737
1	205	509
2	599	432
3	2746	432
4	5554	432

prune519.0ms (6.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	260	4	264
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	262	12	274

Error

6.5b

Counts

274 → 12

Alt Table

Status	Error	Program
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	31.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (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)))
▶	18.7b	(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 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (*.f64 b -2)) a)))
	22.8b	(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)))
	23.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (+.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.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)))
	28.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (*.f64 -1 b))) (+.f64 (log.f64 2) (log.f64 a)))))
	18.8b	(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) (.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 2 a)))
	18.9b	(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)))
	21.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (cbrt.f64 (-.f64 (neg.f64 b) (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)))
	18.9b	(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 (.f64 (cbrt.f64 (.f64 b -2)) (cbrt.f64 (.f64 b -2))) 2) (/.f64 (cbrt.f64 (*.f64 b -2)) a)))

Compiler

Compiled 13961 to 8355 computations (40.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (*.f64 b -2)) a))
	0.8b	(-.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))))
	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series27.0ms (0.3%)

Counts

1 → 16

Calls

1 calls:

27.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 b -2)) 2) (/.f64 (sqrt.f64 (*.f64 b -2)) a))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

1 → 58

Calls

1 calls:

14.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 b -2)) 2) (/.f64 (sqrt.f64 (*.f64 b -2)) a))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Rules

609×	`associate-*l/_binary64`
578×	`associate-/l*_binary64`
555×	`associate-*r/_binary64`
509×	`associate-l_binary64`
421×	`associate-r_binary64`

Counts

74 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1464
1	350	1147
2	1093	1084
3	4205	1042
4	4705	1042
5	4962	1042

prune586.0ms (7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	299	14	313

Error

6.5b

Counts

313 → 14

Alt Table

Status	Error	Program
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	31.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (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)))
	23.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (+.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.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)))
	28.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (*.f64 -1 b))) (+.f64 (log.f64 2) (log.f64 a)))))
	34.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (.f64 b -2)) 2)) (/.f64 (sqrt.f64 (.f64 b -2)) 2)) (.f64 (.f64 (/.f64 (sqrt.f64 (.f64 b -2)) a) (/.f64 (sqrt.f64 (.f64 b -2)) a)) (/.f64 (sqrt.f64 (*.f64 b -2)) a)))))
▶	18.8b	(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) (.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 2 a)))
	18.9b	(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)))
	21.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
	22.8b	(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)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (cbrt.f64 (-.f64 (neg.f64 b) (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)))
	18.9b	(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 (/.f64 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 b -2))) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 b -2))) (cbrt.f64 a))))
	28.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (+.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 b -2))) (log.f64 2)) (log.f64 (/.f64 (sqrt.f64 (.f64 b -2)) a)))))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) b) a)))

Compiler

Compiled 16733 to 10784 computations (35.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(-.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))))
✓	10.3b	(+.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))))))
	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series52.0ms (0.6%)

Counts

1 → 20

Calls

1 calls:

52.0ms

(+.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))))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 25

Calls

1 calls:

4.0ms

(+.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))))))

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

739×	`times-frac_binary64`
486×	`fma-neg_binary64`
353×	`fma-def_binary64`
314×	`associate-l_binary64`
308×	`associate-/r*_binary64`

Counts

45 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1095
1	325	993
2	1016	945
3	4881	945
4	5204	945

prune1.3s (15.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	424	0	424
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	424	14	438

Error

6.5b

Counts

438 → 14

Alt Table

Status	Error	Program
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (*.f64 2 a)))
	31.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (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)))
	23.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (+.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.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)))
	28.5b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (-.f64 (log.f64 (+.f64 (neg.f64 b) (*.f64 -1 b))) (+.f64 (log.f64 2) (log.f64 a)))))
	34.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (.f64 b -2)) 2)) (/.f64 (sqrt.f64 (.f64 b -2)) 2)) (.f64 (.f64 (/.f64 (sqrt.f64 (.f64 b -2)) a) (/.f64 (sqrt.f64 (.f64 b -2)) a)) (/.f64 (sqrt.f64 (*.f64 b -2)) a)))))
✓	18.8b	(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) (.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 2 a)))
	18.9b	(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)))
	21.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))
	22.8b	(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)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (cbrt.f64 (-.f64 (neg.f64 b) (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)))
	18.9b	(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 (/.f64 (sqrt.f64 (.f64 b -2)) 2) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 b -2))) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 b -2))) (cbrt.f64 a))))
	28.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (exp.f64 (+.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 b -2))) (log.f64 2)) (log.f64 (/.f64 (sqrt.f64 (.f64 b -2)) a)))))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) b) a)))

Compiler

Compiled 28183 to 16476 computations (41.5% saved)

regimes928.0ms (11.1%)

Accuracy

Total 1.1b remaining (16.3%)

Threshold costs 0b (0%)

Counts

90 → 5

Compiler

Compiled 16110 to 10958 computations (32% saved)

bsearch6.0ms (0.1%)

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

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	483
1	69	469
2	93	469
3	117	469
4	132	469
5	139	469
6	140	469
7	139	469

end462.0ms (5.5%)

Compiler: Compiled 1367 to 863 computations (36.9% saved)

Details

analyze775.0ms (9.3%)

sample2.3s (27.3%)

simplify129.0ms (1.6%)

prune5.0ms (0.1%)

localize19.0ms (0.2%)

series165.0ms (2%)

rewrite41.0ms (0.5%)

simplify205.0ms (2.5%)

prune552.0ms (6.6%)

localize20.0ms (0.2%)

series8.0ms (0.1%)

rewrite8.0ms (0.1%)

simplify53.0ms (0.6%)

prune519.0ms (6.2%)

localize21.0ms (0.3%)

series27.0ms (0.3%)

rewrite18.0ms (0.2%)

simplify85.0ms (1%)

prune586.0ms (7%)

localize22.0ms (0.3%)

series52.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify63.0ms (0.8%)

prune1.3s (15.2%)

regimes928.0ms (11.1%)

bsearch6.0ms (0.1%)

simplify15.0ms (0.2%)

end462.0ms (5.5%)

Profiling