Details

analyze676.0ms (6.3%)

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)

sample2.4s (22.7%)

Results

735.0ms	5345×	body	128	valid
651.0ms	1199×	body	2048	valid
328.0ms	762×	body	1024	valid
251.0ms	394×	body	4096	valid
142.0ms	1057×	body	128	invalid
127.0ms	365×	body	512	valid
44.0ms	191×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify142.0ms (1.3%)

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

34.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.9b	(.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)
✓	1.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	22.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series162.0ms (1.5%)

Counts

3 → 60

Calls

3 calls:

71.0ms	(/.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))))
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite18.0ms (0.2%)

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:

9.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify96.0ms (0.9%)

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

prune134.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

6.1b

Counts

170 → 10

Alt Table

Status	Error	Program
	45.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	31.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	49.1b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a))))
	38.6b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	51.2b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
	46.1b	(.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))
	33.1b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	31.4b	(.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)))
	35.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))

Compiler

Compiled 4776 to 2894 computations (39.4% saved)

localize11.0ms (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)))))))
✓	0.5b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	15.9b	(sqrt.f64 (.f64 a (.f64 c -4)))

series1.1s (10.1%)

Counts

4 → 42

Calls

4 calls:

475.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
471.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
131.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
19.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite37.0ms (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)))))))
4.0ms	(+.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)))

simplify163.0ms (1.5%)

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

prune260.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	291	10	301

Error

2.2b

Counts

301 → 10

Alt Table

Status	Error	Program
	45.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	31.3b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
	49.1b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a))))
	46.2b	(.f64 -1/2 (.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 b b) (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
▶	31.1b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	38.6b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	46.1b	(.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))
	46.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.3b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))

Compiler

Compiled 9153 to 6051 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))
✓	0.2b	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
✓	0.5b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
✓	15.9b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series356.0ms (3.3%)

Counts

4 → 28

Calls

4 calls:

193.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
138.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
20.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
5.0ms	(.f64 -4 (.f64 c a))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`pow1_binary64`
16×	`associate-l_binary64`

Counts

4 → 95

Calls

4 calls:

7.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
5.0ms	(.f64 -4 (.f64 c a))
2.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r*_binary64`
447×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`
157×	`associate-r_binary64`

Counts

123 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	2765
1	587	2488
2	1863	2447
3	4942	2447
4	4995	2447
5	4936	2447

prune142.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	167	10	177

Error

2.2b

Counts

177 → 10

Alt Table

Status	Error	Program
	45.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	31.3b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
	49.1b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a))))
	46.2b	(.f64 -1/2 (.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 b b) (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
✓	31.1b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	38.6b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	46.1b	(.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))
	46.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.3b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))

Compiler

Compiled 4859 to 3107 computations (36.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	0.5b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	15.9b	(sqrt.f64 (.f64 a (.f64 c -4)))

series1.1s (10.2%)

Counts

2 → 28

Calls

2 calls:

712.0ms	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
385.0ms	(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 82

Calls

2 calls:

7.0ms	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
4.0ms	(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

572×	`associate-/l*_binary64`
523×	`associate-/r*_binary64`
483×	`fma-neg_binary64`
385×	`associate-l_binary64`
271×	`fma-def_binary64`

Counts

110 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	3001
1	465	2662
2	1474	2628
3	4851	2624
4	5108	2624

prune248.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	229	11	240

Error

2.2b

Counts

240 → 11

Alt Table

Status	Error	Program
	45.5b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	31.3b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
	49.1b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a))))
	46.0b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 -4 c)))))))))
	45.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	46.2b	(.f64 -1/2 (.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 b b) (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
✓	31.1b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	38.6b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.1b	(.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))
	46.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	38.3b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))

Compiler

Compiled 7102 to 4922 computations (30.7% saved)

regimes3.2s (29.6%)

Accuracy

Total 7.5b remaining (70.2%)

Threshold costs 0b (0%)

Counts

230 → 3

Compiler

Compiled 23348 to 16722 computations (28.4% saved)

bsearch82.0ms (0.8%)

Steps

Iters	Range		Point
7	9.220427097593508e+87	5.967502722357334e+89	5.847885655853759e+89
8	-2.249005245629534e-55	-3.5022497682459474e-59	-1.2017854710556e-58

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	60
1	42	60
2	48	60
3	52	60
4	55	60
5	56	60
6	55	60

end165.0ms (1.5%)

Compiler: Compiled 330 to 229 computations (30.6% saved)

Details

analyze676.0ms (6.3%)

sample2.4s (22.7%)

simplify142.0ms (1.3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series162.0ms (1.5%)

rewrite18.0ms (0.2%)

simplify96.0ms (0.9%)

prune134.0ms (1.2%)

localize11.0ms (0.1%)

series1.1s (10.1%)

rewrite37.0ms (0.3%)

simplify163.0ms (1.5%)

prune260.0ms (2.4%)

localize10.0ms (0.1%)

series356.0ms (3.3%)

rewrite21.0ms (0.2%)

simplify107.0ms (1%)

prune142.0ms (1.3%)

localize12.0ms (0.1%)

series1.1s (10.2%)

rewrite18.0ms (0.2%)

simplify91.0ms (0.8%)

prune248.0ms (2.3%)

regimes3.2s (29.6%)

bsearch82.0ms (0.8%)

simplify5.0ms (0%)

end165.0ms (1.5%)

Profiling