Details

analyze1.7s

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

sample1.3s

Algorithm

intervals

Results

1.1s	96×	body	5120	exit
81.0ms	256×	body	80	valid
6.0ms	353×	pre	80	true
0.0ms	1×	body	80	invalid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5022	78

prune17.0ms

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	(* (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))

rewrite241.0ms

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)))
198.0ms	(* (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))))))))
32.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series29.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
18.0ms	(* (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))

simplify39.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5148	2689

prune427.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Merged error: 0.0b

Counts

110 → 10

localize60.0ms

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

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

690×	`*-un-lft-identity`
520×	`distribute-lft-out`
207×	`frac-add`
117×	`times-frac`
70×	`flip3-+` `flip-+`
62×	`associate-/l/`
43×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`associate-/l*`
26×	`exp-sum`
8×	`add-cbrt-cube`
7×	`pow1` `add-exp-log` `associate-/r*`
6×	`add-log-exp`
4×	`distribute-lft-out--`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod`

Counts

4 → 258

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
143.0ms	(/ (+ (+ (/ 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)))
27.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series28.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
17.0ms	(/ (+ (+ (/ 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)))
5.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5346	14381

prune3.4s

Filtered

140 candidates to 268 candidates (-91.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	262	6	268
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	267	11	278

Merged error: 0b

Counts

278 → 11

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

690×	`*-un-lft-identity`
520×	`distribute-lft-out`
207×	`frac-add`
117×	`times-frac`
70×	`flip3-+` `flip-+`
62×	`associate-/l/`
43×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`associate-/l*`
26×	`exp-sum`
8×	`add-cbrt-cube`
7×	`pow1` `add-exp-log` `associate-/r*`
6×	`add-log-exp`
4×	`distribute-lft-out--`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod`

Counts

4 → 258

Calls

4 calls:

4.0ms	(/ (sin (* PI z)) PI)
141.0ms	(/ (+ (+ (/ 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)))
26.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series27.0ms

Counts

4 → 10

Calls

4 calls:

5.0ms	(/ (sin (* PI z)) PI)
17.0ms	(/ (+ (+ (/ 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)))
5.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5281	14305

prune3.8s

Filtered

139 candidates to 268 candidates (-92.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Merged error: 0b

Counts

279 → 11

localize60.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt PI) (cbrt PI))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt PI) (cbrt PI))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (cbrt PI) (cbrt PI))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4969	648
1	4969	648

prune254.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	77	11	88

Merged error: 0b

Counts

88 → 11

regimes115.0ms

Accuracy

0% (0.3b 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

sample48.0s

Algorithm

intervals

Results

45.0s	3759×	body	5120	exit
2.5s	8000×	body	80	valid
203.0ms	11839×	pre	80	true
26.0ms	80×	body	80	invalid

Details

analyze1.7s

sample1.3s

simplify36.0ms

prune17.0ms

localize57.0ms

rewrite241.0ms

series29.0ms

simplify39.0ms

prune427.0ms

localize60.0ms

rewrite206.0ms

series28.0ms

simplify94.0ms

prune3.4s

localize56.0ms

rewrite203.0ms

series27.0ms

simplify94.0ms

prune3.8s

localize60.0ms

rewrite16.0ms

series0.0ms

simplify52.0ms

prune254.0ms

regimes115.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample48.0s

Profiling