Details

analyze1.7s (1.1%)

Algorithm

1×

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 (1%)

Algorithm

1×

intervals

Results

1.4s	120×	body	5120	exit
74.0ms	256×	body	80	valid
7.0ms	377×	pre	80	true
0.0ms	1×	body	80	invalid

simplify35.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5022	78

prune17.0ms (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

localize54.0ms (0%)

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))

rewrite225.0ms (0.1%)

Algorithm

1×	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:

185.0ms	(* (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))))))))
30.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
3.0ms	(/ PI (sin (* PI z)))
2.0ms	(sqrt (* PI 2.0))

series29.0ms (0%)

Counts

4 → 10

Calls

4 calls:

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

simplify37.0ms (0%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	2689

prune867.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 0.0b

Counts

110 → 11

localize57.0ms (0%)

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 (0.1%)

Algorithm

1×	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)))))
26.0ms	(+ (/ 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))

series50.0ms (0%)

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (cbrt (exp (- z (+ 7.0 0.5)))) (cbrt (exp (- z (+ 7.0 0.5)))))
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))))) (cbrt (exp (- z (+ 7.0 0.5)))))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify216.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5073	36359

prune9.4s (6.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	254	11	265

Merged error: 0.0b

Counts

265 → 11

localize56.0ms (0%)

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))

rewrite482.0ms (0.3%)

Algorithm

1×	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:

205.0ms	(* (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)))))
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))))) (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))

series89.0ms (0.1%)

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)))))
30.0ms	(* (+ (+ (/ 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))

simplify693.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

750 → 750

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5595	160346

prune1.6min (63%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	747	3	750
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	753	8	761

Merged error: 0b

Counts

761 → 8

localize83.0ms (0.1%)

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

rewrite120.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
78×	`times-frac`
44×	`add-cube-cbrt`
32×	`add-log-exp`
27×	`swap-sqr`
26×	`distribute-lft-out--`
21×	`associate-r` `associate-l`
16×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
14×	`pow1`
12×	`frac-add` `sum-log` `frac-sub` `distribute-lft-out`
8×	`diff-log` `associate-/r/`
6×	`flip3--` `flip3-+` `flip--` `flip-+`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`sub-neg` `sqrt-pow1` `pow-prod-down` `associate--r+`
1×	`pow2` `frac-times` `pow-plus` `pow1/2` `associate-r/` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 162

Calls

4 calls:

45.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
43.0ms	(- (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) 0.9999999999998099))))
22.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
2.0ms	(sqrt (* PI 2.0))

series17.0ms (0%)

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

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4956	4429
1	4956	4429

prune5.4s (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Merged error: 0b

Counts

180 → 8

regimes214.0ms (0.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	129	95
1	129	95

end0.0ms (0%)

sample33.9s (22.6%)

Algorithm

1×

intervals

Results

31.9s	2863×	body	5120	exit
1.6s	5991×	body	80	valid
121.0ms	8907×	pre	80	true
15.0ms	52×	body	80	invalid

Details

analyze1.7s (1.1%)

sample1.5s (1%)

simplify35.0ms (0%)

prune17.0ms (0%)

localize54.0ms (0%)

rewrite225.0ms (0.1%)

series29.0ms (0%)

simplify37.0ms (0%)

prune867.0ms (0.6%)

localize57.0ms (0%)

rewrite201.0ms (0.1%)

series50.0ms (0%)

simplify216.0ms (0.1%)

prune9.4s (6.2%)

localize56.0ms (0%)

rewrite482.0ms (0.3%)

series89.0ms (0.1%)

simplify693.0ms (0.5%)

prune1.6min (63%)

localize83.0ms (0.1%)

rewrite120.0ms (0.1%)

series17.0ms (0%)

simplify69.0ms (0%)

prune5.4s (3.6%)

regimes214.0ms (0.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample33.9s (22.6%)

Profiling