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

sample1.6s

Algorithm

intervals

Results

1.5s	121×	body	5120	exit
82.0ms	256×	body	80	valid
6.0ms	379×	pre	80	true
1.0ms	2×	body	80	invalid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5145	88

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

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(/ (+ 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))))))) (exp (+ (neg z) (+ 7.0 0.5))))
1.0b	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

578×	`*-un-lft-identity`
427×	`distribute-lft-out`
107×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`associate-/l*`
21×	`exp-sum`
8×	`add-cbrt-cube`
7×	`pow1` `add-exp-log` `associate-/r*`
6×	`distribute-rgt-neg-in` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow1/2` `exp-diff` `pow-prod-down` `frac-add` `sum-log` `sqrt-prod` `associate-/r/`

Counts

4 → 179

Calls

4 calls:

4.0ms	(/ PI (sin (* PI z)))
1.0s	(/ (+ 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))))))) (exp (+ (neg z) (+ 7.0 0.5))))
36.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series34.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
24.0ms	(/ (+ 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))))))) (exp (+ (neg z) (+ 7.0 0.5))))
5.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4970	9760
1	4970	9760

prune580.0ms

Filtered

81 candidates to 189 candidates (-133.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	180	9	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Merged error: 0.0b

Counts

191 → 9

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

207×	`frac-add`
70×	`flip3-+` `flip-+`
64×	`*-un-lft-identity`
62×	`associate-*l/` `associate-/l/`
31×	`times-frac`
22×	`distribute-lft-out`
14×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`add-cbrt-cube`
8×	`add-exp-log`
7×	`pow1` `associate-/r*`
6×	`distribute-rgt-neg-in` `add-log-exp`
4×	`associate-/l*`
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 → 145

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
142.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
27.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series30.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
19.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
4.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5246	7768

prune3.4s

Filtered

132 candidates to 155 candidates (-17.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	155	9	164

Merged error: 0b

Counts

164 → 9

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI z)
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

3.0ms	(* PI z)
146.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
33.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series26.0ms

Counts

4 → 10

Calls

4 calls:

2.0ms	(* PI z)
20.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
4.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5152	7467

prune2.8s

Filtered

122 candidates to 146 candidates (-19.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	146	9	155

Merged error: 0b

Counts

155 → 9

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI (/ 1 (sin (* PI z))))
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

207×	`frac-add`
70×	`flip3-+` `flip-+`
65×	`*-un-lft-identity`
62×	`associate-*l/` `associate-/l/`
33×	`times-frac`
22×	`distribute-lft-out`
21×	`add-sqr-sqrt`
15×	`add-exp-log`
14×	`add-cube-cbrt` `add-cbrt-cube`
13×	`associate-r`
9×	`pow1`
6×	`distribute-rgt-neg-in` `add-log-exp`
5×	`prod-exp`
4×	`div-exp` `associate-/r*`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-pow1` `exp-sum` `pow-prod-down` `div-inv`
1×	`+-commutative` `rec-exp` `frac-2neg` `pow1/2` `1-exp` `associate-r/` `clear-num` `sum-log` `sqrt-prod` `un-div-inv` `-commutative` `associate-/l*`

Counts

4 → 154

Calls

4 calls:

7.0ms	(* PI (/ 1 (sin (* PI z))))
148.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
28.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series30.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(* PI (/ 1 (sin (* PI z))))
20.0ms	(/ (* (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 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))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
4.0ms	(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5024	7706

prune3.1s

Filtered

136 candidates to 164 candidates (-20.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	164	9	173

Merged error: 0b

Counts

173 → 9

regimes98.0ms

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	88	90
1	88	90

end0.0ms

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

sample48.7s

Algorithm

intervals

Results

45.6s	3783×	body	5120	exit
2.6s	8000×	body	80	valid
201.0ms	11877×	pre	80	true
32.0ms	94×	body	80	invalid

Details

analyze1.8s

sample1.6s

simplify31.0ms

prune18.0ms

localize57.0ms

rewrite1.1s

series34.0ms

simplify93.0ms

prune580.0ms

localize58.0ms

rewrite190.0ms

series30.0ms

simplify56.0ms

prune3.4s

localize62.0ms

rewrite196.0ms

series26.0ms

simplify58.0ms

prune2.8s

localize64.0ms

rewrite198.0ms

series30.0ms

simplify60.0ms

prune3.1s

regimes98.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze1.8s

sample48.7s

Profiling