Details

sample1.5s

Algorithm

intervals

Results

1.3s	119×	body	10240	exit
46.0ms	257×	body	80	valid
39.0ms	39×	body	1280	nan
21.0ms	30×	body	640	nan
9.0ms	18×	body	320	nan
4.0ms	11×	body	160	nan
1.0ms	7×	body	80	nan

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (520.0ms)

Iter	Nodes	Cost
0	60	123
1	148	123
2	609	121
3	3846	88
done	5001	88

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.0b	(sqrt (* PI 2.0))

rewrite1.5m

Algorithm

rewrite-expression-head

Rules

140×	`frac-add`
92×	`*-un-lft-identity` `add-log-exp`
70×	`sum-log` `distribute-lft-out`
32×	`flip3-+` `flip-+`
7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
3×	`+-commutative` `associate-+r+`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 118

Calls

4 calls:

379.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
122.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.5m	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
4.0ms	(sqrt (* PI 2.0))

series344.0ms

Counts

4 → 10

Calls

4 calls:

83.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
55.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
206.0ms	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
0.0ms	(sqrt (* PI 2.0))

simplify823.0ms

Counts

128 → 128

Iterations

Useful iterations: done (802.0ms)

Iter	Nodes	Cost
0	605	16021
1	2321	13557
done	5000	13431

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.0b	(sqrt PI)

rewrite1.5m

Algorithm

rewrite-expression-head

Rules

140×	`frac-add`
93×	`*-un-lft-identity`
92×	`add-log-exp`
70×	`sum-log` `distribute-lft-out`
32×	`flip3-+` `flip-+`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `add-cbrt-cube`
3×	`+-commutative` `associate-+r+` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 120

Calls

4 calls:

362.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
117.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.5m	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.0ms	(sqrt PI)

series319.0ms

Counts

4 → 10

Calls

4 calls:

75.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
47.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
196.0ms	(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
0.0ms	(sqrt PI)

simplify767.0ms

Counts

130 → 130

Iterations

Useful iterations: done (749.0ms)

Iter	Nodes	Cost
0	596	15929
1	2284	13473
done	5002	13349

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(* (* (- 4.0 z) (* (+ (* (/ -1259.1392167224028 (- 2.0 z)) (- (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (* (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (- 5.0 z))) (- (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))
1.0b	(sqrt PI)

rewrite24.8s

Algorithm

rewrite-expression-head

Rules

101524×	`frac-add`
97246×	`frac-times`
36112×	`flip3-+` `flip-+`
30483×	`flip3--` `flip--`
28107×	`frac-sub`
27347×	`associate-*r/`
22594×	`associate-*l/`
38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
14×	`pow1` `add-log-exp`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac` `associate-r`
9×	`distribute-lft-out--`
6×	`add-cube-cbrt` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
4×	`difference-of-squares`
3×	`sqrt-prod`
2×	`+-commutative` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 29564

Calls

4 calls:

117.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
128.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
15.2s	(* (* (- 4.0 z) (* (+ (* (/ -1259.1392167224028 (- 2.0 z)) (- (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (* (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (- 5.0 z))) (- (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))
1.0ms	(sqrt PI)

series587.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
48.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
488.0ms	(* (* (- 4.0 z) (* (+ (* (/ -1259.1392167224028 (- 2.0 z)) (- (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (* (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))))) (- 5.0 z))) (- (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))
0.0ms	(sqrt PI)

simplify48.0s

Counts

29574 → 29574

Iterations

Useful iterations: 0 (14.0s)

Iter	Nodes	Cost
0	67895	11875063
done	67895	11875063

Details

sample1.5s

simplify1.6s

prune31.0ms

localize56.0ms

rewrite1.5m

series344.0ms

simplify823.0ms

prune1.4s

localize57.0ms

rewrite1.5m

series319.0ms

simplify767.0ms

prune1.3s

localize99.0ms

rewrite24.8s

series587.0ms

simplify48.0s

prune5.6m