Details

analyze767.0ms (7.2%)

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)

sample2.0s (18.4%)

Results

1.6s	8256×	body	128	valid
214.0ms	1164×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify155.0ms (1.5%)

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

prune4.0ms (0%)

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

20.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.8b	(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)

localize19.0ms (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)
✓	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series229.0ms (2.2%)

Counts

4 → 80

Calls

4 calls:

72.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
59.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
54.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite21.0ms (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:

5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) 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)))

simplify202.0ms (1.9%)

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

prune435.0ms (4.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	271	13	284
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	13	285

Error

7.9b

Counts

285 → 13

Alt Table

Status	Error	Program
	23.0b	(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)))
	24.3b	(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)))
	21.6b	(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)))
	21.6b	(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)))
▶	20.9b	(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)))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.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)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	21.3b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.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)))
	22.0b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.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)))
	29.9b	(if (>=.f64 b 0) (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)) (sqrt.f64 (/.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)))
	35.8b	(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))))))))
	24.5b	(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)))))
	22.8b	(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)))

Compiler

Compiled 14050 to 8250 computations (41.3% saved)

localize20.0ms (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))))))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series85.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

85.0ms

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

rewrite25.0ms (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))))))

simplify143.0ms (1.3%)

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

prune645.0ms (6.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	347	4	351
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	352	12	364

Error

7.9b

Counts

364 → 12

Alt Table

Status	Error	Program
	23.0b	(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)))
	24.3b	(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)))
	21.6b	(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)))
	21.6b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b b)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	24.5b	(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)))))
	21.3b	(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)))
▶	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.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)))
	32.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) 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)))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.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)))
	35.8b	(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))))))))
	22.8b	(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)))

Compiler

Compiled 18110 to 10865 computations (40% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.2b	(/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series358.0ms (3.4%)

Counts

2 → 31

Calls

2 calls:

276.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
82.0ms	(/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 109

Calls

2 calls:

6.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
5.0ms	(/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

simplify157.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/r*_binary64`
376×	`associate-*l/_binary64`
351×	`associate-/r/_binary64`
316×	`fma-def_binary64`
300×	`associate-/l/_binary64`

Counts

140 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	5187
1	555	4144
2	1787	3915
3	4751	3915
4	4965	3915
5	4937	3915

prune867.0ms (8.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	347	4	351
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	349	14	363

Error

7.9b

Counts

363 → 14

Alt Table

Status	Error	Program
	23.0b	(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)))
	24.3b	(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)))
	21.6b	(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)))
	21.6b	(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)))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (/.f64 (.f64 c 2) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))
	36.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (.f64 (/.f64 (.f64 2 c) (fma.f64 a (.f64 c -4) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	37.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (.f64 2 (fma.f64 (/.f64 c (.f64 a (.f64 c -4))) b (/.f64 c (sqrt.f64 (.f64 a (.f64 c -4)))))))
	22.8b	(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)))
	21.3b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) b)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	32.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) 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)))
▶	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.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)))
	35.8b	(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))))))))
	24.5b	(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)))))

Compiler

Compiled 19177 to 10855 computations (43.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series77.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

77.0ms

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

rewrite80.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

573×	`times-frac_binary64`
330×	`*-un-lft-identity_binary64`
246×	`add-sqr-sqrt_binary64`
246×	`add-cube-cbrt_binary64`
42×	`distribute-lft-out_binary64`

Counts

1 → 299

Calls

1 calls:

14.0ms

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

simplify463.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-/r*_binary64`
473×	`associate-/l*_binary64`
325×	`associate-/l/_binary64`
309×	`fma-def_binary64`
251×	`associate-/r/_binary64`

Counts

319 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	13472
1	600	12377
2	1793	11741
3	4600	11741
4	4981	11741

prune1.1s (10.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	525	1	526
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	526	14	540

Error

7.9b

Counts

540 → 14

Alt Table

Status	Error	Program
	23.0b	(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)))
	24.3b	(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)))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (/.f64 (/.f64 (.f64 c 2) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))
	36.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (.f64 (/.f64 (.f64 2 c) (fma.f64 a (.f64 c -4) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	37.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (.f64 2 (fma.f64 (/.f64 c (.f64 a (.f64 c -4))) b (/.f64 c (sqrt.f64 (.f64 a (.f64 c -4)))))))
	22.8b	(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)))
	21.6b	(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)))
	21.3b	(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)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b b)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 (sqrt.f64 b) (sqrt.f64 b) b)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	32.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) 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)))
✓	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.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)))
	35.8b	(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))))))))
	24.5b	(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)))))

Compiler

Compiled 29463 to 18266 computations (38% saved)

regimes2.4s (22.2%)

Accuracy

Total 1.3b remaining (19.6%)

Threshold costs 0b (0%)

Counts

193 → 3

Compiler

Compiled 33598 to 22218 computations (33.9% saved)

bsearch67.0ms (0.6%)

Steps

Iters	Range		Point
6	2.0154796778266114e+65	1.913690069440372e+66	1.8712767159114232e+66
8	-8.472965000569034e+94	-4.587689578604787e+91	-9.602324171183254e+93

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
1×	`distribute-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	145
1	50	145
2	53	145
3	56	145
4	59	145
5	60	145
6	60	145

end322.0ms (3%)

Compiler: Compiled 773 to 496 computations (35.8% saved)

Details

analyze767.0ms (7.2%)

sample2.0s (18.4%)

simplify155.0ms (1.5%)

prune4.0ms (0%)

localize19.0ms (0.2%)

series229.0ms (2.2%)

rewrite21.0ms (0.2%)

simplify202.0ms (1.9%)

prune435.0ms (4.1%)

localize20.0ms (0.2%)

series85.0ms (0.8%)

rewrite25.0ms (0.2%)

simplify143.0ms (1.3%)

prune645.0ms (6.1%)

localize25.0ms (0.2%)

series358.0ms (3.4%)

rewrite25.0ms (0.2%)

simplify157.0ms (1.5%)

prune867.0ms (8.2%)

localize22.0ms (0.2%)

series77.0ms (0.7%)

rewrite80.0ms (0.8%)

simplify463.0ms (4.4%)

prune1.1s (10.3%)

regimes2.4s (22.2%)

bsearch67.0ms (0.6%)

simplify6.0ms (0.1%)

end322.0ms (3%)

Profiling