Details

analyze378.0ms (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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (33.8%)

Results

1.3s	8255×	body	128	valid
4.0ms	32×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify124.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)

Compiler

Compiled 56 to 35 computations (37.5% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
✓	0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

series100.0ms (2.4%)

Counts

2 → 36

Calls

2 calls:

81.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
19.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`
6×	`log-prod_binary64`

Counts

2 → 54

Calls

2 calls:

8.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
5.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

simplify131.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-neg_binary64`
596×	`distribute-rgt-in_binary64`
561×	`distribute-lft-in_binary64`
428×	`fma-def_binary64`
287×	`associate-l_binary64`

Counts

90 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	139	1318
1	361	1151
2	1074	1106
3	3774	1106
4	4986	1101
5	4991	1101
6	4998	1101
7	4944	1101

prune99.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	6	106

Error

0.0b

Counts

106 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
▶	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	17.3b	(-.f64 (+.f64 (-.f64 x (/.f64 (.f64 (log.f64 y) (+.f64 (pow.f64 y 3) 1/8)) (+.f64 (.f64 y y) (-.f64 (.f64 1/2 1/2) (.f64 y 1/2))))) y) z)
	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y) z)
	34.2b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)

Compiler

Compiled 2205 to 1248 computations (43.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
✓	0.1b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series52.0ms (1.2%)

Counts

2 → 36

Calls

2 calls:

44.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
8.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

593×	`sub-neg_binary64`
376×	`unsub-neg_binary64`
363×	`+-commutative_binary64`
356×	`associate-l_binary64`
324×	`associate-r_binary64`

Counts

64 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	895
1	221	860
2	548	791
3	1679	791
4	3642	791
5	5049	791

prune50.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Error

0.0b

Counts

60 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	17.3b	(-.f64 (+.f64 (-.f64 x (/.f64 (.f64 (log.f64 y) (+.f64 (pow.f64 y 3) 1/8)) (+.f64 (.f64 y y) (-.f64 (.f64 1/2 1/2) (.f64 y 1/2))))) y) z)
	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
▶	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y) z)
	34.2b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)

Compiler

Compiled 1175 to 670 computations (43% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y)
✓	0.1b	(*.f64 (log.f64 y) (+.f64 y 1/2))

series87.0ms (2.1%)

Counts

2 → 36

Calls

2 calls:

79.0ms	(+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y)
9.0ms	(*.f64 (log.f64 y) (+.f64 y 1/2))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
5×	`associate-+l+_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(*.f64 (log.f64 y) (+.f64 y 1/2))
5.0ms	(+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y)

simplify105.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-neg_binary64`
624×	`distribute-rgt-in_binary64`
597×	`distribute-lft-in_binary64`
455×	`fma-def_binary64`
359×	`associate-l_binary64`

Counts

86 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1281
1	340	1125
2	1053	1057
3	4084	1057
4	4943	1051
5	5073	1051

prune111.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	100	6	106

Error

0.0b

Counts

106 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	17.3b	(-.f64 (+.f64 (-.f64 x (/.f64 (.f64 (log.f64 y) (+.f64 (pow.f64 y 3) 1/8)) (+.f64 (.f64 y y) (-.f64 (.f64 1/2 1/2) (.f64 y 1/2))))) y) z)
▶	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
✓	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (log.f64 y) (+.f64 y 1/2))) y) z)
	34.2b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)

Compiler

Compiled 2054 to 1158 computations (43.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
✓	0.1b	(.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2))
✓	0.3b	(+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
✓	0.6b	(cbrt.f64 y)

series615.0ms (14.6%)

Counts

4 → 48

Calls

4 calls:

270.0ms	(+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
162.0ms	(.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2))
147.0ms	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
35.0ms	(cbrt.f64 y)

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`cbrt-prod_binary64`

Counts

4 → 104

Calls

4 calls:

10.0ms	(+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
6.0ms	(.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2))
6.0ms	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-neg_binary64`
293×	`associate-+l+_binary64`
274×	`associate-+r+_binary64`
272×	`associate-l_binary64`
252×	`associate-r_binary64`

Counts

152 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2836
1	537	2384
2	2134	2178
3	4795	2178
4	5521	2178

prune285.0ms (6.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	217	5	222

Error

Counts

222 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	17.3b	(-.f64 (+.f64 (-.f64 x (/.f64 (.f64 (log.f64 y) (+.f64 (pow.f64 y 3) 1/8)) (+.f64 (.f64 y y) (-.f64 (.f64 1/2 1/2) (.f64 y 1/2))))) y) z)
	0.2b	(-.f64 (+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y) z)
✓	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
	34.2b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)

Compiler

Compiled 6437 to 3638 computations (43.5% saved)

regimes283.0ms (6.7%)

Accuracy

Total 0.1b remaining (80.3%)

Threshold costs 0.1b (80.3%)

Counts

46 → 1

Compiler

Compiled 4610 to 3206 computations (30.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	23	16
3	27	16
4	29	16
5	29	16

end95.0ms (2.3%)

Compiler: Compiled 139 to 94 computations (32.4% saved)

Details

analyze378.0ms (9%)

sample1.4s (33.8%)

simplify124.0ms (2.9%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series100.0ms (2.4%)

rewrite16.0ms (0.4%)

simplify131.0ms (3.1%)

prune99.0ms (2.3%)

localize10.0ms (0.2%)

series52.0ms (1.2%)

rewrite4.0ms (0.1%)

simplify64.0ms (1.5%)

prune50.0ms (1.2%)

localize9.0ms (0.2%)

series87.0ms (2.1%)

rewrite11.0ms (0.3%)

simplify105.0ms (2.5%)

prune111.0ms (2.6%)

localize14.0ms (0.3%)

series615.0ms (14.6%)

rewrite33.0ms (0.8%)

simplify104.0ms (2.5%)

prune285.0ms (6.7%)

regimes283.0ms (6.7%)

simplify3.0ms (0.1%)

end95.0ms (2.3%)

Profiling