Details

analyze9.0ms

Algorithm

sampling

Space saved by range analysis: 74.975586%

Space saved by search: 99.861009%

Guaranteed chance to sample good point: 99.450549%

sample69.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
3.0ms	257×	pre	80	true
0.0ms	1×	body	80	invalid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 2.6b

Counts

2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
2.5b	(exp (* (fabs x) (fabs x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow1/2` `rem-exp-log`

Counts

4 → 157

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)
2.0ms	(exp (* (fabs x) (fabs x)))

series29.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
10.0ms	(exp (* (fabs x) (fabs x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	437	1271
1	2104	1091
2	5001	993

prune640.0ms

Filtered

109 candidates to 167 candidates (-53.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	153	14	167
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	15	169

Merged error: 0.9b

Counts

169 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
1.0b	(pow (exp (fabs x)) (fabs x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
80×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`pow-pow` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)
3.0ms	(pow (exp (fabs x)) (fabs x))

series50.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
31.0ms	(pow (exp (fabs x)) (fabs x))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	413	1275
1	2257	1097
2	5001	1015

prune820.0ms

Filtered

116 candidates to 177 candidates (-52.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	168	9	177
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	170	22	192

Merged error: 0.5b

Counts

192 → 22

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(pow (exp (fabs x)) (/ (fabs x) 2))
0.6b	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0b	(sqrt PI)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`times-frac`
51×	`add-cube-cbrt` `*-un-lft-identity`
26×	`pow-unpow`
16×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`pow-pow`
6×	`unpow-prod-down` `exp-prod` `div-inv`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`pow-to-exp` `pow-exp` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 140

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0ms	(sqrt PI)

series71.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
29.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
0.0ms	(sqrt PI)

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	499	1039
1	2498	929
2	5002	895

prune902.0ms

Filtered

108 candidates to 150 candidates (-38.9%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	138	12	150
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	142	30	172

Merged error: 0.4b

Counts

172 → 30

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
0.6b	(pow (exp (fabs x)) (/ (fabs x) 2))
0.6b	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0b	(sqrt PI)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`pow-pow`
7×	`pow1`
6×	`unpow-prod-down` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `sqrt-prod`
2×	`pow-to-exp` `pow-exp` `div-inv` `sqr-pow`
1×	`cbrt-prod` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-r/` `associate-l/`

Counts

4 → 85

Calls

4 calls:

5.0ms	(cbrt (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0ms	(sqrt PI)

series101.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(cbrt (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
29.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
34.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
0.0ms	(sqrt PI)

simplify79.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	205	596
1	626	570
2	2873	563
3	5001	551

prune585.0ms

Filtered

74 candidates to 95 candidates (-28.4%)

Pruning

30 alts after pruning (28 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	27	28
Picked	0	1	1
Done	0	1	1
Total	95	30	125

Merged error: 0.4b

Counts

125 → 30

regimes442.0ms

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	61
1	44	61

end0.0ms

analyze11.0ms

Algorithm

sampling

Space saved by range analysis: 74.975586%

Space saved by search: 99.861009%

Guaranteed chance to sample good point: 99.450549%

sample1.9s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
96.0ms	8043×	pre	80	true
9.0ms	43×	body	80	invalid

Details

analyze9.0ms

sample69.0ms

simplify65.0ms

prune15.0ms

localize29.0ms

rewrite32.0ms

series29.0ms

simplify68.0ms

prune640.0ms

localize34.0ms

rewrite31.0ms

series50.0ms

simplify66.0ms

prune820.0ms

localize39.0ms

rewrite25.0ms

series71.0ms

simplify65.0ms

prune902.0ms

localize49.0ms

rewrite17.0ms

series101.0ms

simplify79.0ms

prune585.0ms

regimes442.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze11.0ms

sample1.9s

Profiling