Details

sample16.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.003052%

Guaranteed chance to sample good point: 31.284524%

Results

234.0ms	105×	body	5120	exit
149.0ms	116×	body	1280	valid
77.0ms	77×	body	640	valid
59.0ms	56×	body	640	nan
41.0ms	31×	body	1280	nan
27.0ms	40×	body	320	valid
14.0ms	19×	body	320	nan
7.0ms	15×	body	160	valid
6.0ms	12×	body	160	nan
2.0ms	8×	body	80	valid
1.0ms	7×	body	80	nan
1.0ms	4×	body	80	invalid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	133	48
1	453	48
2	2769	47
3	5002	47

prune18.0ms

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: 62.3b

Counts

2 → 2

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (+ (- z 1.0) 7.0) 0.5))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))
5.2b	(+ (- z 1.0) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
19×	`add-log-exp`
13×	`add-sqr-sqrt`
12×	`distribute-lft-out`
11×	`associate-r`
9×	`add-exp-log`
8×	`add-cube-cbrt`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`exp-prod` `add-cbrt-cube`
4×	`associate-+l-` `associate-l` `rem-exp-log`
3×	`prod-exp` `distribute-lft-out--` `unswap-sqr`
2×	`associate-+l+` `sqrt-pow1` `diff-log` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `sub-neg` `flip3-+` `pow1/2` `exp-diff` `associate-r/` `exp-sum` `pow-prod-down` `pow-exp` `-commutative` `cbrt-unprod` `flip-+` `pow-sub`

Counts

4 → 78

Calls

4 calls:

10.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(+ (- z 1.0) 1.0)

series21.0ms

Counts

4 → 10

Calls

4 calls:

2.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
2.0ms	(+ (- z 1.0) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	525	643
1	1922	580
2	5001	575

prune404.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 1.1b

Counts

90 → 3

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

224×	`frac-add`
67×	`associate-*r/`
63×	`*-un-lft-identity`
41×	`distribute-lft-out`
37×	`associate-+l-`
35×	`pow-sub`
33×	`associate-/l/`
32×	`frac-times` `flip3-+` `flip-+`
30×	`add-exp-log`
22×	`associate-r`
20×	`add-cbrt-cube`
17×	`prod-exp`
15×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`unpow-prod-down` `cbrt-unprod`
5×	`div-exp` `associate-l`
4×	`times-frac` `associate-/r*` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `unswap-sqr`
2×	`sqrt-pow1` `exp-sum` `pow-prod-down` `associate-l/` `sqrt-prod` `-commutative` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `exp-diff` `clear-num` `associate-/r/` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 165

Calls

4 calls:

135.0ms	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
143.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))

series101.0ms

Counts

4 → 10

Calls

4 calls:

34.0ms	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
49.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify160.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	3085	10652
1	5003	10244

prune4.6s

Filtered

141 candidates to 175 candidates (-24.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	167	8	175
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	170	8	178

Merged error: 0.0b

Counts

178 → 8

localize78.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
104×	`unpow-prod-down`
84×	`times-frac`
68×	`*-un-lft-identity`
62×	`associate-l`
56×	`add-cube-cbrt`
53×	`add-exp-log`
40×	`sqrt-prod`
38×	`unswap-sqr`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
13×	`div-exp`
12×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `clear-num` `log-pow`

Counts

4 → 210

Calls

4 calls:

5.0ms	(/ (sqrt 2.0) (exp 6.5))
6.0ms	(* (log 6.5) (sqrt 2.0))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify81.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	584	1952
1	2136	1884
2	5001	1813

prune6.5s

Filtered

130 candidates to 214 candidates (-64.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	213	9	222

Merged error: 0.0b

Counts

222 → 9

localize70.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
52×	`unpow-prod-down`
51×	`times-frac`
46×	`*-un-lft-identity`
40×	`add-cube-cbrt`
33×	`associate-l`
31×	`sqrt-prod`
30×	`add-exp-log`
20×	`unswap-sqr`
13×	`pow-exp` `prod-exp`
12×	`associate-r`
10×	`add-cbrt-cube` `sqr-pow`
8×	`pow1`
7×	`div-exp`
6×	`associate-/l*`
4×	`pow-to-exp` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/r*`
2×	`*-commutative` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `log-pow`

Counts

4 → 149

Calls

4 calls:

1.0ms	(sqrt PI)
5.0ms	(/ (sqrt 2.0) (exp 6.5))
6.0ms	(* (log 6.5) (sqrt 2.0))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify71.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	575	1313
1	2085	1282
2	5002	1223

prune1.9s

Filtered

96 candidates to 153 candidates (-59.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	153	9	162

Merged error: 0b

Counts

162 → 9

regimes118.0ms

Accuracy

0% (1.4b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 1.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	75
1	90	75
2	90	75

end0.0ms

sample37.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.003052%

Guaranteed chance to sample good point: 31.284524%

Results

8.4s	3897×	body	5120	exit
4.4s	3399×	body	1280	valid
2.4s	2489×	body	640	valid
2.0s	1495×	body	1280	nan
1.3s	1250×	body	640	nan
852.0ms	1226×	body	320	valid
489.0ms	657×	body	320	nan
286.0ms	626×	body	160	valid
153.0ms	315×	body	160	nan
59.0ms	260×	body	80	valid
58.0ms	276×	body	80	nan
22.0ms	86×	body	80	invalid

Details

sample16.6s

simplify78.0ms

prune18.0ms

localize52.0ms

rewrite39.0ms

series21.0ms

simplify55.0ms

prune404.0ms

localize48.0ms

rewrite311.0ms

series101.0ms

simplify160.0ms

prune4.6s

localize78.0ms

rewrite51.0ms

series0.0ms

simplify81.0ms

prune6.5s

localize70.0ms

rewrite34.0ms

series0.0ms

simplify71.0ms

prune1.9s

regimes118.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample37.3s

Profiling