Details

analyze677.0ms (8.9%)

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)

sample144.0ms (1.9%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid
1.0ms	13×	body	128	nan

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify155.0ms (2%)

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 (0.1%)

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)

localize20.0ms (0.3%)

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)
✓	1.3b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series218.0ms (2.9%)

Counts

4 → 80

Calls

4 calls:

78.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
51.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
48.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite20.0ms (0.3%)

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

simplify193.0ms (2.5%)

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

prune461.0ms (6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	270	14	284
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	271	14	285

Error

6.8b

Counts

285 → 14

Alt Table

Status	Error	Program
	20.0b	(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)))
	28.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (-.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)))
	20.0b	(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)))
	21.4b	(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)))
	36.7b	(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) (/.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
▶	17.6b	(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)))
	27.6b	(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) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.5b	(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)))
	24.2b	(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 2 (/.f64 (.f64 c a) b)) (*.f64 2 b))))
	20.0b	(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 (fma.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)))) (neg.f64 b)) 0)))
	23.6b	(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 (*.f64 -1 b) b)))
	28.5b	(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)))
	20.0b	(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 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	17.7b	(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)))

Compiler

Compiled 14140 to 8284 computations (41.4% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 b a))
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series265.0ms (3.5%)

Counts

2 → 20

Calls

2 calls:

258.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
7.0ms	(*.f64 2 (/.f64 b a))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

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

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary64`
803×	`associate-/l*_binary64`
283×	`associate-/l/_binary64`
242×	`fma-def_binary64`
211×	`associate-/r/_binary64`

Counts

85 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1929
1	501	1739
2	1618	1658
3	5238	1658

prune447.0ms (5.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	238	13	251

Error

6.8b

Counts

251 → 13

Alt Table

Status	Error	Program
	20.0b	(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)))
	28.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (-.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)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	20.0b	(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)))
	21.4b	(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)))
	27.6b	(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) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.5b	(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)))
	28.5b	(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)))
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c 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))))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 -1 (/.f64 c b)))
	36.0b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 (/.f64 (.f64 c 2) (fma.f64 a (.f64 c -4) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b))))
▶	17.7b	(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)))

Compiler

Compiled 11132 to 6502 computations (41.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series10.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

490×	`*-commutative_binary64`
334×	`neg-sub0_binary64`
314×	`neg-mul-1_binary64`
291×	`associate-l_binary64`
290×	`times-frac_binary64`

Counts

46 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	565
1	42	488
2	90	488
3	294	488
4	1369	488
5	2959	488
6	4609	488
7	5240	488

prune368.0ms (4.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	212	12	224

Error

6.8b

Counts

224 → 12

Alt Table

Status	Error	Program
	20.0b	(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)))
	28.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (-.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)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	20.0b	(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)))
	21.4b	(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)))
▶	17.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (.f64 (.f64 c 2) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))
	36.0b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 (/.f64 (.f64 c 2) (fma.f64 a (.f64 c -4) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	27.6b	(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) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.5b	(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)))
	28.5b	(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)))
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c 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))))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))

Compiler

Compiled 8771 to 4828 computations (45% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
✓	0.1b	(.f64 (.f64 c 2) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

series466.0ms (6.1%)

Counts

2 → 40

Calls

2 calls:

260.0ms	(.f64 (.f64 c 2) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
205.0ms	(/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

2 → 98

Calls

2 calls:

11.0ms	(.f64 (.f64 c 2) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
5.0ms	(/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

simplify141.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

912×	`times-frac_binary64`
430×	`fma-def_binary64`
324×	`fma-neg_binary64`
148×	`associate-l_binary64`
144×	`associate-/r/_binary64`

Counts

138 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3846
1	531	3506
2	1826	3316
3	4724	3316
4	4985	3316
5	4935	3316

prune459.0ms (6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	286	13	299

Error

6.8b

Counts

299 → 13

Alt Table

Status	Error	Program
	20.0b	(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)))
	28.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (-.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)))
	33.3b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (exp.f64 (-.f64 (log.f64 (.f64 c 2)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	20.0b	(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)))
	21.4b	(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)))
✓	17.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (.f64 (.f64 c 2) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))
	36.0b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c b)))) (.f64 (/.f64 (.f64 c 2) (fma.f64 a (.f64 c -4) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	27.6b	(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) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.5b	(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)))
	28.5b	(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)))
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (-.f64 (.f64 2 (/.f64 b a)) (.f64 2 (/.f64 c 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))))
	21.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (.f64 (*.f64 c 2) (/.f64 -1/2 b)))
	21.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))

Compiler

Compiled 11989 to 6864 computations (42.7% saved)

regimes1.5s (20.3%)

Accuracy

Total 1.4b remaining (19.8%)

Threshold costs 0b (0%)

Counts

106 → 5

Compiler

Compiled 16474 to 10926 computations (33.7% saved)

bsearch6.0ms (0.1%)

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

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	458
1	74	446
2	98	446
3	118	446
4	132	446
5	138	446
6	139	446
7	138	446

end3.0ms (0%)

Compiler: Compiled 298 to 174 computations (41.6% saved)

sample1.8s (23.2%)

Algorithm

1×

intervals

Results

922.0ms	8000×	body	128	valid
75.0ms	687×	body	128	nan
38.0ms	388×	body	128	invalid

Compiler

Compiled 849 to 535 computations (37% saved)

Details

analyze677.0ms (8.9%)

sample144.0ms (1.9%)

simplify155.0ms (2%)

prune4.0ms (0.1%)

localize20.0ms (0.3%)

series218.0ms (2.9%)

rewrite20.0ms (0.3%)

simplify193.0ms (2.5%)

prune461.0ms (6%)

localize21.0ms (0.3%)

series265.0ms (3.5%)

rewrite15.0ms (0.2%)

simplify66.0ms (0.9%)

prune447.0ms (5.8%)

localize18.0ms (0.2%)

series10.0ms (0.1%)

rewrite1.0ms (0%)

simplify79.0ms (1%)

prune368.0ms (4.8%)

localize21.0ms (0.3%)

series466.0ms (6.1%)

rewrite27.0ms (0.4%)

simplify141.0ms (1.8%)

prune459.0ms (6%)

regimes1.5s (20.3%)

bsearch6.0ms (0.1%)

simplify16.0ms (0.2%)

end3.0ms (0%)

sample1.8s (23.2%)

Profiling