Details

analyze1.9s

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

sample1.7s

Algorithm

intervals

Results

1.6s	129×	body	5120	exit
86.0ms	256×	body	80	valid
8.0ms	391×	pre	80	true
2.0ms	6×	body	80	invalid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5022	78

prune20.0ms

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

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

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:

4.0ms	(/ PI (sin (* PI z)))
193.0ms	(* (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))))))))
29.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series27.0ms

Counts

4 → 10

Calls

4 calls:

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 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))

simplify40.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	2689

prune464.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	10	110

Merged error: 0.0b

Counts

110 → 10

localize61.0ms

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

rewrite200.0ms

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)))
140.0ms	(/ (+ (+ (/ 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))

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

simplify92.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5346	14381

prune3.2s

Filtered

140 candidates to 268 candidates (-91.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	269	9	278

Merged error: 0b

Counts

278 → 9

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

2061×	`frac-add`
811×	`frac-times`
759×	`associate-*r/`
691×	`flip3-+` `flip-+`
563×	`associate-*l/`
315×	`pow-sub`
252×	`exp-diff`
160×	`*-un-lft-identity`
110×	`distribute-lft-out`
50×	`add-exp-log`
38×	`prod-exp`
35×	`add-cbrt-cube`
29×	`associate-l`
20×	`cbrt-unprod`
16×	`pow1`
13×	`add-sqr-sqrt`
11×	`associate-r`
8×	`add-cube-cbrt` `times-frac`
7×	`pow-prod-down`
6×	`unpow-prod-down` `add-log-exp`
5×	`div-exp` `distribute-lft-out--`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `unswap-sqr`
2×	`sqrt-pow1` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `sub-neg` `pow1/2` `sum-log`

Counts

4 → 740

Calls

4 calls:

212.0ms	(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ (+ (/ 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))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
139.0ms	(* (+ (+ (/ 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))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
27.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series86.0ms

Counts

4 → 10

Calls

4 calls:

53.0ms	(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ (+ (/ 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))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
29.0ms	(* (+ (+ (/ 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))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify702.0ms

Algorithm

egg-herbie

Counts

750 → 750

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5595	160346

prune1.5min

Filtered

704 candidates to 750 candidates (-6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	748	2	750
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	751	8	759

Merged error: 0b

Counts

759 → 8

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(* PI (/ 1 (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 (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

691×	`*-un-lft-identity`
520×	`distribute-lft-out`
207×	`frac-add`
119×	`times-frac`
70×	`flip3-+` `flip-+`
62×	`associate-/l/`
50×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
26×	`exp-sum`
25×	`associate-/l*`
14×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`prod-exp` `associate-/r*` `distribute-lft-out--`
3×	`div-exp` `associate-l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `pow-prod-down` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rec-exp` `frac-2neg` `pow1/2` `1-exp` `associate-r/` `clear-num` `sum-log` `sqrt-prod` `un-div-inv` `-commutative`

Counts

4 → 267

Calls

4 calls:

7.0ms	(* PI (/ 1 (sin (* PI z))))
128.0ms	(/ (+ (+ (/ 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))

series32.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(* PI (/ 1 (sin (* PI z))))
16.0ms	(/ (+ (+ (/ 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)))
10.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5387	14327

prune3.8s

Filtered

143 candidates to 277 candidates (-93.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	277	8	285

Merged error: 0b

Counts

285 → 8

regimes81.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	125	78
1	125	78

end0.0ms

sample44.7s

Algorithm

intervals

Results

41.9s	3678×	body	5120	exit
2.3s	7351×	body	80	valid
152.0ms	11122×	pre	80	true
35.0ms	92×	body	80	invalid

Details

analyze1.9s

sample1.7s

simplify35.0ms

prune20.0ms

localize56.0ms

rewrite232.0ms

series27.0ms

simplify40.0ms

prune464.0ms

localize61.0ms

rewrite200.0ms

series28.0ms

simplify92.0ms

prune3.2s

localize56.0ms

rewrite500.0ms

series86.0ms

simplify702.0ms

prune1.5min

localize56.0ms

rewrite186.0ms

series32.0ms

simplify85.0ms

prune3.8s

regimes81.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample44.7s

Profiling