Details

sample1.7s

Algorithm

intervals

Results

1.4s	104×	body	5120	exit
104.0ms	48×	body	1280	nan
84.0ms	257×	body	80	valid
51.0ms	34×	body	640	nan
24.0ms	22×	body	320	nan
5.0ms	9×	body	160	nan
1.0ms	5×	body	80	nan

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5174	87

prune16.0ms

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: 1.5b

Counts

2 → 2

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
1.0b	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
103×	`distribute-lft-out`
27×	`times-frac`
20×	`associate-r`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`distribute-rgt-neg-in` `add-log-exp`
5×	`associate-l`
3×	`flip3-+` `exp-diff` `associate-/r` `flip-+` `associate-/l`
2×	`frac-times` `sqrt-pow1` `associate-*r/` `exp-sum` `pow-prod-down`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `div-exp` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `sqrt-prod` `-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
1.2s	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
34.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series28.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
17.0ms	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
4.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5038	2798

prune511.0ms

Filtered

73 candidates to 114 candidates (-56.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	12	114
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Merged error: 0.3b

Counts

116 → 13

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))
6.2b	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
6.2b	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

4596×	`*-un-lft-identity`
1800×	`times-frac`
1611×	`distribute-lft-out`
900×	`distribute-lft-out--`
169×	`frac-add`
96×	`add-log-exp`
71×	`sum-log`
45×	`flip3-+` `flip-+`
7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
3×	`+-commutative`
2×	`associate-+l+` `associate-+r+` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 402

Calls

4 calls:

26.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))
132.0ms	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
131.0ms	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))

series42.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))
13.0ms	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
24.0ms	(+ (+ (/ -176.6150291621406 (- 4.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))

simplify148.0ms

Algorithm

egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5289	25406

prune3.1s

Filtered

113 candidates to 412 candidates (-264.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	412	13	425

Merged error: 0.3b

Counts

425 → 13

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

207×	`frac-add`
70×	`flip3-+` `flip-+`
62×	`associate-*l/` `associate-/l/`
36×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`add-cbrt-cube`
8×	`add-exp-log`
7×	`pow1` `associate-/r*`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`associate-/l*` `distribute-lft-out--`
3×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `sqrt-pow1` `exp-sum` `clear-num` `div-inv`
1×	`+-commutative` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `sqrt-prod` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
162.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
26.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series30.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
19.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5387	6840

prune3.2s

Filtered

132 candidates to 150 candidates (-13.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	152	11	163

Merged error: 0.3b

Counts

163 → 11

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

303×	`*-un-lft-identity`
229×	`distribute-lft-out`
128×	`frac-add`
66×	`add-log-exp`
49×	`sum-log`
44×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
16×	`associate-/l/`
12×	`exp-sum`
11×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`associate-/r*`
2×	`+-commutative` `associate-+r+` `sqrt-pow1`
1×	`cbrt-undiv` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `associate-/r/` `div-inv`

Counts

4 → 169

Calls

4 calls:

125.0ms	(/ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099)))))))) (exp (+ 7.0 (- 0.5 z))))
2.0ms	(sqrt (* PI 2.0))
93.0ms	(+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099)))))))
80.0ms	(+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))))

series48.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(/ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099)))))))) (exp (+ 7.0 (- 0.5 z))))
0.0ms	(sqrt (* PI 2.0))
18.0ms	(+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099)))))))
11.0ms	(+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))))

simplify84.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5058	13283

prune1.6s

Filtered

109 candidates to 179 candidates (-64.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	179	11	190

Merged error: 0.3b

Counts

190 → 11

regimes113.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	181
1	95	181

end0.0ms

sample55.0s

Algorithm

intervals

Results

46.3s	3847×	body	5120	exit
3.0s	1534×	body	1280	nan
2.5s	8100×	body	80	valid
1.8s	1260×	body	640	nan
611.0ms	612×	body	320	nan
207.0ms	330×	body	160	nan
87.0ms	293×	body	80	nan
1.0ms	1×	body	160	valid

Details

sample1.7s

simplify32.0ms

prune16.0ms

localize54.0ms

rewrite1.3s

series28.0ms

simplify36.0ms

prune511.0ms

localize77.0ms

rewrite404.0ms

series42.0ms

simplify148.0ms

prune3.1s

localize57.0ms

rewrite209.0ms

series30.0ms

simplify51.0ms

prune3.2s

localize54.0ms

rewrite312.0ms

series48.0ms

simplify84.0ms

prune1.6s

regimes113.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample55.0s

Profiling