Details

analyze800.0ms (8.3%)

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)

sample2.2s (22.8%)

Results

1.8s	8256×	body	128	valid
239.0ms	1074×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% 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

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

17.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.4b	(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)))
▶	17.2b	(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

17.4b

(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)))

▶

17.2b

(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)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(+.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))
✓	1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series174.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

62.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
54.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite40.0ms (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))

simplify214.0ms (2.2%)

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

prune569.0ms (5.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	319	8	327
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	320	9	329

Error

4.2b

Counts

329 → 9

Alt Table

Status	Error	Program
	17.4b	(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)))
	25.8b	(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 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (neg.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)))
	20.1b	(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)))
▶	17.3b	(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)))
	34.4b	(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)))
	22.1b	(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)))
	23.0b	(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)))
	18.2b	(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)))

Compiler

Compiled 18513 to 10700 computations (42.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	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)))))
✓	7.3b	(-.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))))))
	22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series106.0ms (1.1%)

Counts

2 → 40

Calls

2 calls:

58.0ms

(-.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))))))

48.0ms

(*.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)))))

rewrite45.0ms (0.5%)

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:

18.0ms

(*.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)))))

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))))))

simplify137.0ms (1.4%)

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 → 199

Iterations

Useful iterations: 3 (0.0ms)

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

prune825.0ms (8.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	442	0	442
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	442	9	451

Error

4.2b

Counts

451 → 9

Alt Table

Status	Error	Program
▶	17.4b	(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)))
	25.8b	(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 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
	21.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (neg.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)))
	20.1b	(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)))
✓	17.3b	(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)))
	34.4b	(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)))
	22.1b	(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)))
	23.0b	(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)))
	18.2b	(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)))

Compiler

Compiled 26630 to 15604 computations (41.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.3b	(-.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))))
✓	22.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series239.0ms (2.5%)

Counts

4 → 80

Calls

4 calls:

86.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
57.0ms	(-.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))))
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify154.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-neg_binary64`
376×	`cancel-sign-sub-inv_binary64`
373×	`distribute-rgt-in_binary64`
165×	`associate-r_binary64`
164×	`distribute-rgt-neg-in_binary64`

Counts

196 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	5766
1	733	4840
2	2707	4645
3	4911	4645
4	5121	4645

prune703.0ms (7.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	294	4	298
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	298	9	307

Error

4.2b

Counts

307 → 9

Alt Table

Status	Error	Program
▶	17.4b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.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)))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
	34.4b	(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)))
	20.2b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b b))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	18.2b	(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)))
	25.8b	(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 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
✓	17.3b	(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)))
	23.3b	(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)))
	20.1b	(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)))
	18.4b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) (-.f64 (/.f64 c b) (/.f64 b a)))

Compiler

Compiled 14132 to 8275 computations (41.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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)))))
✓	6.8b	(+.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))))))
	22.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	23.5b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series258.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

99.0ms

(+.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))))))

94.0ms

(*.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)))))

64.0ms

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

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
16×	`sqrt-prod_binary64`
15×	`unswap-sqr_binary64`
12×	`fabs-mul_binary64`

Counts

3 → 80

Calls

3 calls:

7.0ms

(*.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)))))

2.0ms

(+.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))))))

1.0ms

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

simplify177.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-r_binary64`
365×	`associate-l_binary64`
351×	`times-frac_binary64`
272×	`associate-/r*_binary64`
243×	`fma-def_binary64`

Counts

188 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	459	11692
1	1481	10603
2	5273	10603

prune812.0ms (8.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	372	2	374
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	372	11	383

Error

4.2b

Counts

383 → 11

Alt Table

Status	Error	Program
✓	17.4b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.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)))))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
	34.4b	(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)))
	20.2b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b b))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)))
	18.2b	(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)))
	37.9b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) 3))))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
	25.8b	(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 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a)))
✓	17.3b	(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)))
	23.3b	(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)))
	40.5b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (.f64 (fabs.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a)))))) (sqrt.f64 (cbrt.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)))
	20.1b	(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)))
	18.4b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) (-.f64 (/.f64 c b) (/.f64 b a)))

Compiler

Compiled 27497 to 17490 computations (36.4% saved)

regimes1.6s (16.2%)

Accuracy

Total 1.0b remaining (15.8%)

Threshold costs 1.0b (15.8%)

Counts

109 → 3

Compiler

Compiled 18834 to 12334 computations (34.5% saved)

bsearch41.0ms (0.4%)

Steps

Iters	Range		Point
6	3.7860061035834417e+93	2.0802435370307088e+94	1.921741260874318e+94
2	-4.0572577234280044e+147	-3.3386390074051144e+147	-3.428466346907976e+147

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
15×	`*-commutative_binary64`
13×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	152
1	64	148
2	92	148
3	111	148
4	123	148
5	127	148
6	126	148

end272.0ms (2.8%)

Compiler: Compiled 663 to 422 computations (36.3% saved)

Details

analyze800.0ms (8.3%)

sample2.2s (22.8%)

simplify133.0ms (1.4%)

prune5.0ms (0.1%)

localize21.0ms (0.2%)

series174.0ms (1.8%)

rewrite40.0ms (0.4%)

simplify214.0ms (2.2%)

prune569.0ms (5.9%)

localize23.0ms (0.2%)

series106.0ms (1.1%)

rewrite45.0ms (0.5%)

simplify137.0ms (1.4%)

prune825.0ms (8.5%)

localize20.0ms (0.2%)

series239.0ms (2.5%)

rewrite26.0ms (0.3%)

simplify154.0ms (1.6%)

prune703.0ms (7.3%)

localize26.0ms (0.3%)

series258.0ms (2.7%)

rewrite70.0ms (0.7%)

simplify177.0ms (1.8%)

prune812.0ms (8.4%)

regimes1.6s (16.2%)

bsearch41.0ms (0.4%)

simplify8.0ms (0.1%)

end272.0ms (2.8%)

Profiling