Details

sample2.0s

Algorithm

intervals

Results

1.7s	142×	body	5120	exit
124.0ms	59×	body	1280	nan
80.0ms	258×	body	80	valid
57.0ms	41×	body	640	nan
21.0ms	22×	body	320	nan
5.0ms	9×	body	160	nan
2.0ms	6×	body	80	nan

simplify35.0ms

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

localize53.0ms

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))

rewrite237.0ms

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`
5×	`associate-l`
4×	`distribute-lft-out--`
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 → 99

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
196.0ms	(* (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))))))))
31.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series29.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ 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))))))))
5.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5148	2743

prune551.0ms

Filtered

72 candidates to 109 candidates (-51.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	12	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 0.0b

Counts

111 → 13

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
24×	`times-frac`
15×	`distribute-lft-out`
12×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
3×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 62

Calls

4 calls:

26.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
27.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
31.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series15.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
7.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5022	979

prune404.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Merged error: 0.0b

Counts

85 → 12

localize54.0ms

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

rewrite529.0ms

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`
12×	`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×	`unpow-prod-up` `sqrt-pow1` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`+-commutative` `sub-neg` `pow1/2` `sum-log`

Counts

4 → 741

Calls

4 calls:

225.0ms	(* (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)))))
26.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 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))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
2.0ms	(sqrt (* PI 2.0))

series84.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (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)))))
5.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
23.0ms	(* (+ (+ (/ 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)))
0.0ms	(sqrt (* PI 2.0))

simplify907.0ms

Algorithm

egg-herbie

Counts

751 → 751

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5595	160403

prune1.5min

Filtered

704 candidates to 751 candidates (-6.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	746	5	751
Fresh	7	3	10
Picked	0	1	1
Done	0	1	1
Total	753	10	763

Merged error: 0b

Counts

763 → 10

localize80.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099)))
1.0b	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
1.0b	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
1.0b	(sqrt (* PI 2.0))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity` `add-log-exp`
19×	`add-sqr-sqrt`
18×	`sum-log` `distribute-lft-out`
16×	`frac-sub`
14×	`frac-add`
12×	`diff-log` `distribute-lft-out--`
8×	`flip3-+` `flip-+`
7×	`pow1`
6×	`difference-of-squares`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `times-frac` `flip--` `associate--r+`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

56.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099)))
49.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
47.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
6.0ms	(sqrt (* PI 2.0))

series22.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099)))
7.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
7.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
0.0ms	(sqrt (* PI 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5034	4404

prune1.3s

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	103	10	113

Merged error: 0b

Counts

113 → 10

regimes251.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	129	105
1	129	105

end0.0ms

sample51.7s

Algorithm

intervals

Results

43.9s	3909×	body	5120	exit
2.7s	1499×	body	1280	nan
2.3s	8092×	body	80	valid
1.6s	1259×	body	640	nan
602.0ms	652×	body	320	nan
171.0ms	290×	body	160	nan
87.0ms	307×	body	80	nan

Details

sample2.0s

simplify35.0ms

prune17.0ms

localize53.0ms

rewrite237.0ms

series29.0ms

simplify38.0ms

prune551.0ms

localize57.0ms

rewrite89.0ms

series15.0ms

simplify52.0ms

prune404.0ms

localize54.0ms

rewrite529.0ms

series84.0ms

simplify907.0ms

prune1.5min

localize80.0ms

rewrite163.0ms

series22.0ms

simplify46.0ms

prune1.3s

regimes251.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample51.7s

end1.2s

Profiling