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

sample1.9s

Algorithm

intervals

Results

1.8s	145×	body	5120	exit
82.0ms	256×	body	80	valid
8.0ms	403×	pre	80	true
1.0ms	2×	body	80	invalid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5022	78

prune16.0ms

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: 1.5b

Counts

2 → 2

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 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))

rewrite227.0ms

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)))
191.0ms	(* (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))))))))
26.0ms	(+ (/ 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))

simplify37.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	2689

prune473.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 0.3b

Counts

110 → 13

localize58.0ms

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

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

413×	`frac-add`
162×	`*-un-lft-identity`
139×	`flip3-+` `flip-+`
108×	`distribute-lft-out`
67×	`cbrt-div` `exp-diff`
63×	`frac-times` `associate-*l/`
32×	`associate-l`
27×	`add-sqr-sqrt`
25×	`cbrt-prod`
16×	`pow1`
15×	`add-cube-cbrt`
14×	`associate-r`
8×	`add-exp-log` `times-frac`
7×	`swap-sqr`
6×	`pow1/3` `add-log-exp` `unswap-sqr`
5×	`sub-neg` `exp-sum` `add-cbrt-cube`
4×	`pow-prod-down` `distribute-lft-out--`
2×	`sqrt-pow1` `associate-r/` `prod-exp` `pow-sqr` `-commutative` `pow-prod-up` `cbrt-unprod`
1×	`+-commutative` `pow2` `pow-plus` `pow1/2` `sum-log` `sqrt-prod`

Counts

4 → 244

Calls

4 calls:

132.0ms	(* (+ (+ (/ 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))))) (cbrt (exp (- z (+ 7.0 0.5)))))
30.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
15.0ms	(* (cbrt (exp (- z (+ 7.0 0.5)))) (cbrt (exp (- z (+ 7.0 0.5)))))
2.0ms	(sqrt (* PI 2.0))

series55.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(* (+ (+ (/ 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))))) (cbrt (exp (- z (+ 7.0 0.5)))))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
30.0ms	(* (cbrt (exp (- z (+ 7.0 0.5)))) (cbrt (exp (- z (+ 7.0 0.5)))))
0.0ms	(sqrt (* PI 2.0))

simplify211.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5073	36359

prune8.9s

Filtered

207 candidates to 254 candidates (-22.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	254	13	267

Merged error: 0.3b

Counts

267 → 13

localize56.0ms

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))) (+ (+ (/ 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))

rewrite486.0ms

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:

208.0ms	(* (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)))))
134.0ms	(* (+ (+ (/ 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)))
25.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series86.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (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)))))
22.0ms	(* (+ (+ (/ 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)))
13.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify694.0ms

Algorithm

egg-herbie

Counts

750 → 750

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5595	160346

prune1.3min

Filtered

704 candidates to 750 candidates (-6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	744	6	750
Fresh	10	1	11
Picked	1	0	1
Done	0	1	1
Total	755	8	763

Merged error: 0.0b

Counts

763 → 8

localize110.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0b	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0b	(sqrt (* PI 2.0))
1.6b	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

199×	`*-un-lft-identity`
187×	`add-sqr-sqrt`
182×	`times-frac`
103×	`add-cube-cbrt`
54×	`swap-sqr`
42×	`associate-r` `associate-l` `distribute-lft-out--`
31×	`add-exp-log` `add-cbrt-cube`
30×	`difference-of-squares`
22×	`pow1`
21×	`unpow-prod-down` `cube-prod`
20×	`associate-/r/`
10×	`flip3--` `flip--` `div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `pow-prod-down`
2×	`pow2` `frac-times` `sqrt-pow1` `pow-plus` `associate-r/` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `pow1/2` `unpow3` `sqrt-prod` `sqr-pow`

Counts

4 → 267

Calls

4 calls:

18.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
18.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
2.0ms	(sqrt (* PI 2.0))
8.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

series8.0ms

Counts

4 → 10

Calls

4 calls:

3.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
2.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
0.0ms	(sqrt (* PI 2.0))
3.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5120	3571

prune7.9s

Filtered

159 candidates to 277 candidates (-74.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	277	8	285

Merged error: 0.0b

Counts

285 → 8

regimes189.0ms

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	280	343
1	280	343

end0.0ms

sample46.1s

Algorithm

intervals

Results

43.3s	3821×	body	5120	exit
2.4s	7831×	body	80	valid
155.0ms	11741×	pre	80	true
30.0ms	88×	body	80	invalid

Details

analyze1.8s

sample1.9s

simplify35.0ms

prune16.0ms

localize57.0ms

rewrite227.0ms

series29.0ms

simplify37.0ms

prune473.0ms

localize58.0ms

rewrite201.0ms

series55.0ms

simplify211.0ms

prune8.9s

localize56.0ms

rewrite486.0ms

series86.0ms

simplify694.0ms

prune1.3min

localize110.0ms

rewrite62.0ms

series8.0ms

simplify74.0ms

prune7.9s

regimes189.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample46.1s

Profiling