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

sample1.5s

Algorithm

intervals

Results

1.4s	117×	body	5120	exit
74.0ms	256×	body	80	valid
7.0ms	378×	pre	80	true
2.0ms	5×	body	80	invalid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

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

localize56.0ms

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))

rewrite251.0ms

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)))
207.0ms	(* (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))))))))
34.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series31.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ PI (sin (* PI z)))
19.0ms	(* (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

108 → 108

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5148	2689

prune443.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 0.0b

Counts

110 → 14

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
120×	`times-frac`
94×	`add-sqr-sqrt`
54×	`distribute-lft-out--`
38×	`difference-of-squares`
22×	`add-cube-cbrt`
20×	`frac-sub`
12×	`frac-times` `associate-r/` `associate-l/` `associate-/r*`
11×	`associate-/l/`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3--` `flip--` `associate-/l*`
3×	`associate-/r/`
2×	`sub-neg` `sqrt-pow1` `diff-log`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-sub` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 144

Calls

4 calls:

49.0ms	(/ (- (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (* (/ -176.6150291621406 (- 4.0 z)) (/ -176.6150291621406 (- 4.0 z)))) (- (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))
28.0ms	(- (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
20.0ms	(- (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (* (/ -176.6150291621406 (- 4.0 z)) (/ -176.6150291621406 (- 4.0 z))))
2.0ms	(sqrt (* PI 2.0))

series20.0ms

Counts

4 → 10

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5616	5070

prune969.0ms

Filtered

107 candidates to 154 candidates (-43.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	153	15	168

Merged error: 0.0b

Counts

168 → 15

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))

rewrite738.0ms

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:

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)))))
32.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
150.0ms	(* (+ (+ (/ 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))

series93.0ms

Counts

4 → 10

Calls

4 calls:

64.0ms	(* (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)))
24.0ms	(* (+ (+ (/ 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))

simplify721.0ms

Algorithm

egg-herbie

Counts

750 → 750

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5595	160346

prune1.7min

Filtered

704 candidates to 750 candidates (-6.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	747	3	750
Fresh	6	7	13
Picked	1	0	1
Done	0	1	1
Total	754	11	765

Merged error: 0.0b

Counts

765 → 11

localize55.0ms

Local error

Found 4 expressions with local error:

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))
1.0b	(sqrt (* PI 2.0))
1.0b	(+ (/ -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))))))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

128×	`frac-add`
118×	`*-un-lft-identity`
87×	`distribute-lft-out`
66×	`add-log-exp`
49×	`sum-log`
21×	`flip3-+` `flip-+`
16×	`associate-*l/`
12×	`add-sqr-sqrt`
11×	`associate-l`
9×	`add-exp-log` `associate-r`
7×	`pow1` `add-cube-cbrt`
6×	`unpow-prod-down` `add-cbrt-cube`
3×	`prod-exp` `unswap-sqr`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `pow-prod-down` `pow-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 132

Calls

4 calls:

114.0ms	(* (+ (/ 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))
2.0ms	(sqrt (* PI 2.0))
92.0ms	(+ (/ -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)))))))
77.0ms	(+ (/ 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))))))

series56.0ms

Counts

4 → 10

Calls

4 calls:

31.0ms	(* (+ (/ 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))
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))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5850	12953

prune1.3s

Filtered

101 candidates to 142 candidates (-40.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	141	12	153

Merged error: 0b

Counts

153 → 12

regimes116.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	153	102
1	153	102

end0.0ms

sample37.1s

Algorithm

intervals

Results

35.0s	3160×	body	5120	exit
1.8s	6436×	body	80	valid
129.0ms	9665×	pre	80	true
20.0ms	68×	body	80	invalid

Details

analyze1.7s

sample1.5s

simplify34.0ms

prune17.0ms

localize56.0ms

rewrite251.0ms

series31.0ms

simplify38.0ms

prune443.0ms

localize60.0ms

rewrite108.0ms

series20.0ms

simplify55.0ms

prune969.0ms

localize54.0ms

rewrite738.0ms

series93.0ms

simplify721.0ms

prune1.7min

localize55.0ms

rewrite293.0ms

series56.0ms

simplify72.0ms

prune1.3s

regimes116.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample37.1s

Profiling