Details

analyze690.0ms (7.6%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample139.0ms (1.5%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
3.0ms	26×	body	128	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify158.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1753×	`fma-neg_binary64`
1288×	`fma-def_binary64`
631×	`div-sub_binary64`
512×	`times-frac_binary64`
430×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	118	52
3	269	50
4	429	50
5	743	50
6	1315	50
7	1738	50
8	2176	50
9	2853	50
10	4066	50
11	3523	50
12	3575	50
13	3543	50
14	3557	50
15	4510	50
16	4622	50
17	4761	50

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

19.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 149 to 91 computations (38.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series231.0ms (2.5%)

Counts

4 → 80

Calls

4 calls:

73.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
58.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
54.0ms	(+.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)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 110

Calls

4 calls:

4.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) 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)))

simplify198.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-neg_binary64`
423×	`cancel-sign-sub-inv_binary64`
171×	`distribute-rgt-in_binary64`
160×	`distribute-rgt-neg-in_binary64`
153×	`fma-def_binary64`

Counts

190 → 240

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	5471
1	638	4667
2	2187	4480
3	4402	4480
4	4947	4480
5	4986	4480
6	4872	4480

prune481.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	272	12	284
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	12	285

Error

6.1b

Counts

285 → 12

Alt Table

Status	Error	Program
	22.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	23.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	25.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
▶	19.8b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	29.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 13914 to 8154 computations (41.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series292.0ms (3.2%)

Counts

2 → 29

Calls

2 calls:

274.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
17.0ms	(-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

6.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
4.0ms	(-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

889×	`times-frac_binary64`
412×	`fma-def_binary64`
233×	`fma-neg_binary64`
231×	`associate-/l/_binary64`
107×	`cancel-sign-sub-inv_binary64`

Counts

78 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1986
1	483	1783
2	1693	1695
3	4761	1695
4	4995	1695
5	4913	1695

prune367.0ms (4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	221	13	234

Error

6.1b

Counts

234 → 13

Alt Table

Status	Error	Program
	22.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	23.4b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 -1 (/.f64 c b)))
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	23.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	30.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (pow.f64 (.f64 2 (/.f64 b a)) 3) (pow.f64 (.f64 2 (/.f64 c b)) 3)) (+.f64 (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 b a))) (+.f64 (.f64 (.f64 2 (/.f64 c b)) (.f64 2 (/.f64 c b))) (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (log.f64 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	29.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 10613 to 6185 computations (41.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series75.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

75.0ms

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

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

1 → 98

Calls

1 calls:

10.0ms

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

simplify141.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

589×	`times-frac_binary64`
363×	`associate-/l*_binary64`
343×	`associate-/r*_binary64`
319×	`associate-l_binary64`
271×	`fma-neg_binary64`

Counts

118 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	4048
1	400	3701
2	1206	3497
3	4495	3497
4	4813	3497
5	4940	3497

prune708.0ms (7.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	351	13	364

Error

6.1b

Counts

364 → 13

Alt Table

Status	Error	Program
	22.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	23.4b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 -1 (/.f64 c b)))
✓	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	23.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	30.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (pow.f64 (.f64 2 (/.f64 b a)) 3) (pow.f64 (.f64 2 (/.f64 c b)) 3)) (+.f64 (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 b a))) (+.f64 (.f64 (.f64 2 (/.f64 c b)) (.f64 2 (/.f64 c b))) (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (log.f64 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	29.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
▶	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 18237 to 10944 computations (40% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
	1.2b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series74.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

74.0ms

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

rewrite77.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

357×	`times-frac_binary64`
273×	`*-un-lft-identity_binary64`
208×	`sqrt-prod_binary64`
169×	`add-sqr-sqrt_binary64`
169×	`add-cube-cbrt_binary64`

Counts

1 → 242

Calls

1 calls:

13.0ms

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

simplify420.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
490×	`*-commutative_binary64`
269×	`fma-neg_binary64`
235×	`associate-/r/_binary64`
234×	`cancel-sign-sub-inv_binary64`

Counts

262 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	18734
1	692	16586
2	2265	14390
3	3388	13802
4	4984	13802
5	4933	13802

prune1.6s (17.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	554	13	567

Error

6.1b

Counts

567 → 13

Alt Table

Status	Error	Program
	25.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	23.4b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 -1 (/.f64 c b)))
✓	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.3b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 (cbrt.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))) (cbrt.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))))))) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (cbrt.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	20.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	30.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (-.f64 (pow.f64 (.f64 2 (/.f64 b a)) 3) (pow.f64 (.f64 2 (/.f64 c b)) 3)) (+.f64 (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 b a))) (+.f64 (.f64 (.f64 2 (/.f64 c b)) (.f64 2 (/.f64 c b))) (.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	29.8b	(if (>=.f64 b 0) (.f64 -1/2 (exp.f64 (log.f64 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	29.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
✓	19.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 36219 to 21189 computations (41.5% saved)

regimes1.5s (16.1%)

Accuracy

Total 1.1b remaining (16.6%)

Threshold costs 0b (0%)

Counts

113 → 5

Compiler

Compiled 20438 to 13450 computations (34.2% saved)

bsearch7.0ms (0.1%)

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	439
1	84	373
2	117	373
3	140	371
4	153	371
5	159	371
6	160	371
7	158	371

end3.0ms (0%)

Compiler: Compiled 248 to 151 computations (39.1% saved)

sample1.7s (18.8%)

Algorithm

1×

intervals

Results

902.0ms	8000×	body	128	valid
72.0ms	652×	body	128	nan
43.0ms	383×	body	128	invalid

Compiler

Compiled 880 to 568 computations (35.5% saved)

Details

analyze690.0ms (7.6%)

sample139.0ms (1.5%)

simplify158.0ms (1.7%)

prune6.0ms (0.1%)

localize21.0ms (0.2%)

series231.0ms (2.5%)

rewrite20.0ms (0.2%)

simplify198.0ms (2.2%)

prune481.0ms (5.3%)

localize20.0ms (0.2%)

series292.0ms (3.2%)

rewrite13.0ms (0.1%)

simplify102.0ms (1.1%)

prune367.0ms (4%)

localize21.0ms (0.2%)

series75.0ms (0.8%)

rewrite21.0ms (0.2%)

simplify141.0ms (1.5%)

prune708.0ms (7.8%)

localize22.0ms (0.2%)

series74.0ms (0.8%)

rewrite77.0ms (0.8%)

simplify420.0ms (4.6%)

prune1.6s (17.6%)

regimes1.5s (16.1%)

bsearch7.0ms (0.1%)

simplify13.0ms (0.1%)

end3.0ms (0%)

sample1.7s (18.8%)

Profiling