Details

analyze2.5s (23.1%)

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
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
0%	93.6%	6.4%	8
0%	91.3%	8.7%	9
0%	86.6%	13.4%	10
0%	85.8%	14.2%	11
1.6%	81.5%	16.9%	12
2.3%	78.3%	19.4%	13
2.3%	77.1%	20.6%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample2.4s (22.4%)

Results

1.7s	8256×	body	128	valid
406.0ms	337×	body	8192	exit
172.0ms	892×	body	128	invalid

Compiler

Compiled 83 to 53 computations (36.1% saved)

simplify141.0ms (1.3%)

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

21.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	21.2b	(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)))
	21.3b	(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)))

Status

Error

Program

▶

21.2b

(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)))

21.3b

(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)))

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	2.0b	(+.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 1536 to 1280 computations (16.7% saved)

series177.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

61.0ms	(+.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))

rewrite45.0ms (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:

10.0ms	(+.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)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify208.0ms (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	7258
1	613	6063
2	2119	4942
3	4406	4869
4	4870	4869
5	4825	4869

prune517.0ms (4.8%)

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

5.9b

Counts

329 → 10

Alt Table

Status	Error	Program
	30.4b	(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)))
	23.5b	(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)))
	34.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.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 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
▶	20.7b	(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 (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)))
	24.3b	(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) (.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 2 a)))
	21.3b	(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)))
	29.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.0b	(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 c (.f64 a -4))) b)))) (*.f64 2 a)))
	24.4b	(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)))
	22.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))

Compiler

Compiled 18581 to 10752 computations (42.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	6.7b	(+.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))))
✓	13.8b	(sqrt.f64 (.f64 c (.f64 a -4)))
	22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series180.0ms (1.7%)

Counts

2 → 12

Calls

2 calls:

158.0ms	(+.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))))
22.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`fma-def_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
4.0ms	(+.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))))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-neg_binary64`
484×	`associate-r_binary64`
367×	`associate-l_binary64`
352×	`associate-/l*_binary64`
265×	`associate-/r*_binary64`

Counts

51 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	925
1	288	841
2	864	812
3	4332	810
4	4981	810
5	4914	810

prune463.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	251	11	262

Error

5.9b

Counts

262 → 11

Alt Table

Status	Error	Program
	30.4b	(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)))
	23.5b	(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)))
	34.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.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 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
✓	20.7b	(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 (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)))
	33.8b	(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 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)))) (.f64 2 a)))
	24.3b	(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) (.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 2 a)))
▶	21.3b	(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)))
	29.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.0b	(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 c (.f64 a -4))) b)))) (*.f64 2 a)))
	24.4b	(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)))
	22.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a)))

Compiler

Compiled 17248 to 10654 computations (38.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	1.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	2.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	22.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series254.0ms (2.4%)

Counts

4 → 80

Calls

4 calls:

93.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
65.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
52.0ms	(+.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 (0.2%)

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:

10.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))

simplify150.0ms (1.4%)

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

prune477.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	293	5	298
Fresh	3	6	9
Picked	1	0	1
Done	1	0	1
Total	298	11	309

Error

5.8b

Counts

309 → 11

Alt Table

Status	Error	Program
	30.4b	(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)))
	23.5b	(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)))
	24.4b	(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)))
	32.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (/.f64 (.f64 1/2 (+.f64 (.f64 a (.f64 c -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	25.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
	23.5b	(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)))
	34.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.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 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	33.8b	(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 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)))) (.f64 2 a)))
▶	21.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 (sqrt.f64 1/2) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a))))
	29.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.1b	(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)))

Compiler

Compiled 14442 to 8479 computations (41.3% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
	1.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	13.8b	(sqrt.f64 (.f64 a (.f64 c -4)))
	22.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series251.0ms (2.3%)

Counts

2 → 12

Calls

2 calls:

229.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
22.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

2 → 44

Calls

2 calls:

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

simplify177.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-neg_binary64`
479×	`associate-/l*_binary64`
391×	`associate-/r*_binary64`
369×	`fma-def_binary64`
176×	`cancel-sign-sub-inv_binary64`

Counts

56 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1471
1	281	1063
2	962	1009
3	3745	998
4	4678	998
5	4866	998
6	4993	998
7	4842	998

prune291.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	172	13	185

Error

4.3b

Counts

185 → 13

Alt Table

Status	Error	Program
	33.8b	(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 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)))) (.f64 2 a)))
	28.3b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))) b) (/.f64 (sqrt.f64 1/2) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a))))
	30.4b	(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)))
	23.5b	(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)))
	24.4b	(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)))
	32.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (/.f64 (.f64 1/2 (+.f64 (.f64 a (.f64 c -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	25.7b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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)))
	23.5b	(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)))
	34.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.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 (+.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 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (.f64 -2 b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a))))
✓	21.0b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 (sqrt.f64 1/2) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a))))
	29.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	24.1b	(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)))

Compiler

Compiled 10142 to 5975 computations (41.1% saved)

regimes1.8s (16.8%)

Accuracy

Total 2.5b remaining (36.4%)

Threshold costs 0b (0%)

Counts

140 → 3

Compiler

Compiled 23894 to 15702 computations (34.3% saved)

bsearch91.0ms (0.8%)

Steps

Iters	Range		Point
9	3.2671344679182654e+108	2.5675625145885843e+113	1.9314596379250625e+113
7	-5.901242717073054e+92	-8.606228378406822e+90	-5.777484400075436e+92

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	148
1	62	144
2	88	144
3	107	144
4	119	144
5	123	144
6	122	144

end388.0ms (3.6%)

Compiler: Compiled 768 to 495 computations (35.5% saved)

Details

analyze2.5s (23.1%)

sample2.4s (22.4%)

simplify141.0ms (1.3%)

prune5.0ms (0%)

localize20.0ms (0.2%)

series177.0ms (1.6%)

rewrite45.0ms (0.4%)

simplify208.0ms (1.9%)

prune517.0ms (4.8%)

localize27.0ms (0.3%)

series180.0ms (1.7%)

rewrite11.0ms (0.1%)

simplify76.0ms (0.7%)

prune463.0ms (4.3%)

localize20.0ms (0.2%)

series254.0ms (2.4%)

rewrite26.0ms (0.2%)

simplify150.0ms (1.4%)

prune477.0ms (4.4%)

localize31.0ms (0.3%)

series251.0ms (2.3%)

rewrite9.0ms (0.1%)

simplify177.0ms (1.7%)

prune291.0ms (2.7%)

regimes1.8s (16.8%)

bsearch91.0ms (0.8%)

simplify6.0ms (0.1%)

end388.0ms (3.6%)

Profiling