Details

analyze1.8s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.9s

Algorithm

intervals

Results

1.8s	151×	body	5120	exit
77.0ms	256×	body	80	valid
7.0ms	413×	pre	80	true
2.0ms	6×	body	80	invalid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5022	78

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: 1.2b

Counts

2 → 2

localize55.0ms

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 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
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

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

Counts

4 → 98

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
175.0ms	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 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	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series31.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
21.0ms	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	2689

prune459.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 0.1b

Counts

110 → 11

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
0.9b	(/ (* (+ (+ (/ 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))

rewrite167.0ms

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)))
126.0ms	(/ (* (+ (+ (/ 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))

simplify56.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5486	6839

prune3.4s

Filtered

132 candidates to 150 candidates (-13.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	146	15	161

Merged error: 0.0b

Counts

161 → 15

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin (* PI z)) PI)
0.9b	(/ (* (+ (+ (/ 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))

rewrite173.0ms

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:

4.0ms	(/ (sin (* PI z)) PI)
129.0ms	(/ (* (+ (+ (/ 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)))
24.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series28.0ms

Counts

4 → 10

Calls

4 calls:

5.0ms	(/ (sin (* PI z)) PI)
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 (19.0ms)

Iter	Nodes	Cost
0	5455	6764

prune3.7s

Filtered

131 candidates to 150 candidates (-14.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	151	14	165

Merged error: 0.0b

Counts

165 → 14

localize58.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* (+ (/ 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	(sqrt (* PI 2.0))
1.1b	(+ (/ -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))))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

113.0ms	(/ (* (+ (/ 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)))
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)))))))
75.0ms	(+ (/ 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))))))

series44.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(/ (* (+ (/ 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)))
0.0ms	(sqrt (* PI 2.0))
13.0ms	(+ (/ -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))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5284	9552

prune1.4s

Filtered

100 candidates to 130 candidates (-30.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Merged error: 0.0b

Counts

144 → 13

regimes149.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	79
1	102	79

end0.0ms

sample52.4s

Algorithm

intervals

Results

49.3s	4094×	body	5120	exit
2.5s	8000×	body	80	valid
218.0ms	12172×	pre	80	true
26.0ms	78×	body	80	invalid

Details

analyze1.8s

sample1.9s

simplify32.0ms

prune18.0ms

localize55.0ms

rewrite209.0ms

series31.0ms

simplify36.0ms

prune459.0ms

localize53.0ms

rewrite167.0ms

series30.0ms

simplify56.0ms

prune3.4s

localize60.0ms

rewrite173.0ms

series28.0ms

simplify51.0ms

prune3.7s

localize58.0ms

rewrite292.0ms

series44.0ms

simplify70.0ms

prune1.4s

regimes149.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample52.4s

Profiling