Details

analyze2.5s (22.4%)

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)

sample2.5s (22.4%)

Results

1.7s	8256×	body	128	valid
565.0ms	390×	body	8192	exit
175.0ms	940×	body	128	invalid

Compiler

Compiled 83 to 53 computations (36.1% saved)

simplify129.0ms (1.1%)

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

19.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.0b	(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)))
▶	19.9b	(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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))

Status

Error

Program

20.0b

(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)))

▶

19.9b

(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) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 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
✓	0.4b	(/.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))))
✓	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series447.0ms (4%)

Counts

4 → 80

Calls

4 calls:

272.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
71.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(+.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)))

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
60×	`prod-diff_binary64`
53×	`add-cube-cbrt_binary64`
39×	`sqrt-prod_binary64`

Counts

4 → 172

Calls

4 calls:

19.0ms	(/.f64 (.f64 2 c) (-.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))))
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)))

simplify201.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

462×	`fma-neg_binary64`
417×	`cancel-sign-sub-inv_binary64`
186×	`sub-neg_binary64`
180×	`associate-r_binary64`
169×	`unswap-sqr_binary64`

Counts

252 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	9152
1	826	6984
2	2995	5850
3	4857	5850
4	4898	5850

prune523.0ms (4.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	323	9	332
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	324	10	334

Error

6.2b

Counts

334 → 10

Alt Table

Status	Error	Program
▶	20.0b	(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)))
	23.2b	(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)))
	32.6b	(if (>=.f64 b 0) (cbrt.f64 (pow.f64 (/.f64 (.f64 c 2) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) 3)) (/.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) 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 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 4 (.f64 c a))) (+.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)))
	21.7b	(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) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b)))) (*.f64 2 a)))
	24.4b	(if (>=.f64 b 0) (expm1.f64 (log1p.f64 (/.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)))
	27.5b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) (*.f64 2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 19125 to 10931 computations (42.8% saved)

localize19.0ms (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))
✓	1.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	1.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	23.5b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series242.0ms (2.2%)

Counts

4 → 80

Calls

4 calls:

85.0ms	(.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)
55.0ms	(+.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)))

rewrite28.0ms (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:

12.0ms	(.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)))

simplify143.0ms (1.3%)

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

prune504.0ms (4.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	293	5	298
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	295	13	308

Error

6.1b

Counts

308 → 13

Alt Table

Status	Error	Program
	32.6b	(if (>=.f64 b 0) (cbrt.f64 (pow.f64 (/.f64 (.f64 c 2) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) 3)) (/.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) 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 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 4 (.f64 c a))) (+.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)))
	20.9b	(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 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))))
	23.2b	(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)))
	23.3b	(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)))
▶	20.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)) (/.f64 1/2 a))))
	24.4b	(if (>=.f64 b 0) (expm1.f64 (log1p.f64 (/.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)))
	27.5b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) (*.f64 2 a)))
	29.7b	(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))))))))
	23.3b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b) 3)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 14534 to 8543 computations (41.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (/.f64 1/2 a)))
	1.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	1.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	23.5b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series90.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

89.0ms

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-div_binary64`
16×	`frac-times_binary64`
12×	`flip--_binary64`
12×	`flip3--_binary64`
10×	`add-cbrt-cube_binary64`

Counts

1 → 45

Calls

1 calls:

13.0ms

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

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

449×	`times-frac_binary64`
336×	`associate-/l*_binary64`
333×	`associate-*r/_binary64`
296×	`associate-*l/_binary64`
284×	`associate-/r*_binary64`

Counts

65 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2753
1	467	2454
2	1328	2266
3	4899	2266
4	4950	2266

prune788.0ms (7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	412	1	413
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	413	13	426

Error

6.1b

Counts

426 → 13

Alt Table

Status	Error	Program
	32.6b	(if (>=.f64 b 0) (cbrt.f64 (pow.f64 (/.f64 (.f64 c 2) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) 3)) (/.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) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	29.7b	(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 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b) 3)))) (/.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 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 4 (.f64 c a))) (+.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)))
	20.9b	(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 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))))
	23.2b	(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)))
	23.3b	(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)))
✓	20.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)) (/.f64 1/2 a))))
	24.4b	(if (>=.f64 b 0) (expm1.f64 (log1p.f64 (/.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)))
	27.5b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) (*.f64 2 a)))
	23.3b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))

Compiler

Compiled 25927 to 14998 computations (42.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 2 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.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))))
	23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series285.0ms (2.5%)

Counts

1 → 20

Calls

1 calls:

284.0ms

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

rewrite32.0ms (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))

simplify135.0ms (1.2%)

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 → 179

Iterations

Useful iterations: 2 (0.0ms)

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

prune991.0ms (8.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	439	1	440
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	441	12	453

Error

6.1b

Counts

453 → 12

Alt Table

Status	Error	Program
	21.9b	(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)))
	20.3b	(if (>=.f64 b 0) (/.f64 (sqrt.f64 2) (/.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) c) (sqrt.f64 2))) (/.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 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	35.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (.f64 4 (.f64 c a))) (+.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)))
	20.9b	(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 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))))
	23.2b	(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)))
	23.3b	(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)))
✓	20.1b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)) (/.f64 1/2 a))))
	24.4b	(if (>=.f64 b 0) (expm1.f64 (log1p.f64 (/.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)))
	27.5b	(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 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -4)) b))) (*.f64 2 a)))
	23.3b	(if (>=.f64 b 0) (.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (.f64 (-.f64 (*.f64 -1 b) b) (/.f64 1/2 a)))
	29.7b	(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 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))

Compiler

Compiled 25129 to 14423 computations (42.6% saved)

regimes1.1s (9.4%)

Accuracy

Total 1.1b remaining (16.6%)

Threshold costs 0b (0%)

Counts

103 → 3

Compiler

Compiled 17694 to 11678 computations (34% saved)

bsearch84.0ms (0.7%)

Steps

Iters	Range		Point
4	1.3489364754836958e+119	1.1824665961964641e+122	7.523821768677853e+121
11	-3.2033102230879885e+77	-5.3930075293582715e+53	-1.3083832570146259e+77

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (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

end276.0ms (2.5%)

Compiler: Compiled 692 to 443 computations (36% saved)

Details

analyze2.5s (22.4%)

sample2.5s (22.4%)

simplify129.0ms (1.1%)

prune5.0ms (0%)

localize20.0ms (0.2%)

series447.0ms (4%)

rewrite55.0ms (0.5%)

simplify201.0ms (1.8%)

prune523.0ms (4.6%)

localize19.0ms (0.2%)

series242.0ms (2.2%)

rewrite28.0ms (0.3%)

simplify143.0ms (1.3%)

prune504.0ms (4.5%)

localize22.0ms (0.2%)

series90.0ms (0.8%)

rewrite23.0ms (0.2%)

simplify88.0ms (0.8%)

prune788.0ms (7%)

localize21.0ms (0.2%)

series285.0ms (2.5%)

rewrite32.0ms (0.3%)

simplify135.0ms (1.2%)

prune991.0ms (8.8%)

regimes1.1s (9.4%)

bsearch84.0ms (0.7%)

simplify7.0ms (0.1%)

end276.0ms (2.5%)

Profiling