Details

analyze594.0ms (6.6%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample205.0ms (2.3%)

Algorithm

1×

intervals

Results

15.0ms	45×	body	2048	valid
11.0ms	159×	body	128	valid
6.0ms	26×	body	1024	valid
4.0ms	10×	body	4096	valid
3.0ms	12×	body	128	invalid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify142.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune3.0ms (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

32.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.7b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.4b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	20.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series570.0ms (6.3%)

Counts

3 → 60

Calls

3 calls:

449.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
70.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
50.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 67

Calls

3 calls:

4.0ms	(/.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)))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
539×	`associate-/l*_binary64`
458×	`fma-def_binary64`
246×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

127 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3311
1	510	3170
2	1534	3008
3	4840	3008
4	4954	3008

prune162.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

4.3b

Counts

170 → 8

Alt Table

Status	Error	Program
	41.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	33.0b	(.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))))))))
	32.8b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
▶	31.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	48.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	43.5b	(.f64 -1/2 (.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	38.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	50.0b	(.f64 -1/2 (cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))))

Compiler

Compiled 4736 to 2852 computations (39.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	12.1b	(sqrt.f64 (.f64 a (.f64 c -4)))

series766.0ms (8.5%)

Counts

4 → 42

Calls

4 calls:

407.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
193.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
144.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
22.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
99×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

4 → 164

Calls

4 calls:

6.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
3.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))

simplify172.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-*l/_binary64`
496×	`fma-def_binary64`
478×	`fma-neg_binary64`
422×	`associate-/r/_binary64`
308×	`cancel-sign-sub-inv_binary64`

Counts

206 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	6330
1	644	5816
2	2163	5690
3	4938	5684
4	5187	5684

prune238.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	287	4	291
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	290	9	299

Error

2.2b

Counts

299 → 9

Alt Table

Status	Error	Program
	41.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
▶	31.0b	(.f64 -1/2 (.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)))
	48.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	45.8b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	38.0b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
	33.0b	(.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))))))))
	47.2b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))) a) 3)))
✓	31.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

Compiler

Compiled 9052 to 5981 computations (33.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 c a))
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
✓	12.1b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series387.0ms (4.3%)

Counts

4 → 28

Calls

4 calls:

199.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)
163.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
19.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
5.0ms	(.f64 -4 (.f64 c a))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
15×	`pow1_binary64`
12×	`times-frac_binary64`

Counts

4 → 86

Calls

4 calls:

4.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)
4.0ms	(.f64 -4 (.f64 c a))
3.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

777×	`associate-l_binary64`
692×	`associate-/r*_binary64`
333×	`fma-def_binary64`
238×	`associate-*r/_binary64`
226×	`associate-*l/_binary64`

Counts

114 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2620
1	506	2410
2	1572	2364
3	5036	2364

prune110.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Error

2.2b

Counts

139 → 9

Alt Table

Status	Error	Program
	41.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
✓	31.0b	(.f64 -1/2 (.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)))
	48.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	45.8b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	38.0b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
▶	33.0b	(.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))))))))
	47.2b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))) a) 3)))
✓	31.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

Compiler

Compiled 3896 to 2507 computations (35.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
✓	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)))))))
	1.4b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	20.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series707.0ms (7.8%)

Counts

2 → 32

Calls

2 calls:

639.0ms

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

68.0ms

(/.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)))))))

rewrite86.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac_binary64`
298×	`*-un-lft-identity_binary64`
224×	`sqrt-prod_binary64`
186×	`add-sqr-sqrt_binary64`
186×	`add-cube-cbrt_binary64`

Counts

2 → 289

Calls

2 calls:

14.0ms

(/.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)))))))

5.0ms

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

simplify527.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
311×	`fma-neg_binary64`
260×	`associate-/r/_binary64`
245×	`associate-/l/_binary64`
213×	`cancel-sign-sub-inv_binary64`

Counts

321 → 349

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	387	21192
1	934	18842
2	3173	16705
3	4685	16265
4	4981	16265
5	4946	16265

prune550.0ms (6.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	532	1	533
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	533	9	542

Error

2.2b

Counts

542 → 9

Alt Table

Status	Error	Program
	41.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
✓	31.0b	(.f64 -1/2 (.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))) a)))
	48.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	45.8b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	38.0b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
✓	33.0b	(.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))))))))
	42.7b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 a (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (.f64 c -4))))))))
✓	31.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

Compiler

Compiled 25076 to 14975 computations (40.3% saved)

regimes1.9s (20.8%)

Accuracy

Total 7.0b remaining (70.3%)

Threshold costs 0b (0%)

Counts

124 → 3

Compiler

Compiled 12476 to 8634 computations (30.8% saved)

bsearch71.0ms (0.8%)

Steps

Iters	Range		Point
8	3.3995058031280872e+87	7.243765641083012e+90	6.451056025612858e+90
10	-4.16103480341049e-95	-4.279334544435657e-106	-3.255073772856574e-95

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
11×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	58
1	47	58
2	60	58
3	79	58
4	91	58
5	99	58
6	102	58
7	101	58

end1.0ms (0%)

Compiler: Compiled 42 to 29 computations (31% saved)

sample1.6s (17.8%)

Algorithm

1×

intervals

Results

357.0ms	1142×	body	2048	valid
347.0ms	5202×	body	128	valid
171.0ms	707×	body	1024	valid
154.0ms	399×	body	4096	valid
69.0ms	380×	body	512	valid
42.0ms	687×	body	128	nan
25.0ms	391×	body	128	invalid
22.0ms	170×	body	256	valid

Compiler

Compiled 254 to 179 computations (29.5% saved)

Details

analyze594.0ms (6.6%)

sample205.0ms (2.3%)

simplify142.0ms (1.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series570.0ms (6.3%)

rewrite11.0ms (0.1%)

simplify100.0ms (1.1%)

prune162.0ms (1.8%)

localize10.0ms (0.1%)

series766.0ms (8.5%)

rewrite31.0ms (0.3%)

simplify172.0ms (1.9%)

prune238.0ms (2.6%)

localize10.0ms (0.1%)

series387.0ms (4.3%)

rewrite16.0ms (0.2%)

simplify69.0ms (0.8%)

prune110.0ms (1.2%)

localize11.0ms (0.1%)

series707.0ms (7.8%)

rewrite86.0ms (1%)

simplify527.0ms (5.8%)

prune550.0ms (6.1%)

regimes1.9s (20.8%)

bsearch71.0ms (0.8%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.6s (17.8%)

Profiling