Details

sample2.8s

Algorithm

intervals

Results

2.3s	134×	body	10240	exit
164.0ms	65×	body	1280	nan
104.0ms	261×	body	80	valid
53.0ms	40×	body	640	nan
19.0ms	22×	body	320	nan
7.0ms	10×	body	160	nan
2.0ms	6×	body	80	nan

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (1.1s)

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

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize99.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(sqrt (* PI 2.0))
1.0b	(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -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))))))))

rewrite4.2m

Algorithm

rewrite-expression-head

Rules

530×	`frac-add`
137×	`frac-times` `associate-*r/`
123×	`*-un-lft-identity`
110×	`flip3-+` `flip-+`
88×	`times-frac`
54×	`unpow-prod-down`
51×	`associate-l`
48×	`distribute-lft-out`
46×	`add-sqr-sqrt` `add-cube-cbrt`
39×	`add-exp-log`
27×	`add-cbrt-cube`
23×	`exp-sum`
20×	`prod-exp`
16×	`div-exp`
12×	`pow1`
11×	`associate-/l*`
10×	`cbrt-unprod`
9×	`unpow-prod-up` `distribute-rgt-neg-in` `add-log-exp` `sqr-pow`
8×	`associate-+r-`
6×	`cbrt-undiv` `exp-diff` `associate-/r/`
4×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `pow-exp` `associate-/r*`
3×	`neg-sub0` `associate-*l/` `sum-log`
2×	`sqrt-pow1` `unsub-neg` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r+` `frac-2neg` `pow1/2` `associate-r` `clear-num` `sqrt-prod` `*-commutative` `associate-/l/` `pow-sub`

Counts

4 → 328

Calls

4 calls:

247.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
129.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
3.0ms	(sqrt (* PI 2.0))
4.2m	(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -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))))))))

series743.0ms

Counts

4 → 10

Calls

4 calls:

160.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
51.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* PI 2.0))
531.0ms	(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -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))))))))

simplify1.4s

Counts

338 → 338

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	1128	58786
1	4379	50055
done	5000	49015

prune5.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))))
1.0b	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(sqrt (* PI 2.0))

rewrite13.1s

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
102×	`frac-add`
69×	`add-log-exp`
61×	`distribute-lft-out`
51×	`sum-log`
44×	`times-frac`
28×	`flip3-+` `flip-+`
26×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`unpow-prod-down`
12×	`exp-sum`
11×	`associate-/l*`
10×	`unpow-prod-up`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `distribute-lft-out--` `sqr-pow`
4×	`associate-/r*`
3×	`div-exp`
2×	`+-commutative` `associate-+r+` `sqrt-pow1`
1×	`cbrt-undiv` `pow-to-exp` `associate-+l-` `associate-+l+` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `associate-/r/` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 169

Calls

4 calls:

12.7s	(+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))))
201.0ms	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
131.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
4.0ms	(sqrt (* PI 2.0))

series399.0ms

Counts

4 → 10

Calls

4 calls:

184.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))))
165.0ms	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
50.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* PI 2.0))

simplify606.0ms

Counts

179 → 179

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	588	12681
1	1828	11681
done	5002	11518

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize422.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
1.0b	(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))
1.0b	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
1.0b	(sqrt (* PI 2.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

7434×	`frac-add`
3624×	`associate-*l/`
3368×	`frac-times`
2501×	`cube-div`
2399×	`flip3-+` `flip-+`
1248×	`associate-*r/`
1200×	`frac-sub`
1030×	`flip3--` `flip--`
48×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow-unpow` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`associate-+r+` `associate-/r/`
3×	`pow-exp` `rem-cube-cbrt`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `sqrt-pow1` `unpow3` `div-inv` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow1/2` `div-exp` `pow-prod-down` `sum-log` `sqrt-prod`

Counts

4 → 2199

Calls

4 calls:

221.0ms	(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
174.0ms	(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))
15.0ms	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
4.0ms	(sqrt (* PI 2.0))

series779.0ms

Counts

4 → 10

Calls

4 calls:

75.0ms	(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
656.0ms	(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))
48.0ms	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
0.0ms	(sqrt (* PI 2.0))

simplify4.0s

Counts

2209 → 2209

Iterations

Useful iterations: 0 (1.1s)

Iter	Nodes	Cost
0	7896	829237
done	7896	829237

prune1.6m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize318.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* (/ 771.3234287776531 (+ (- z) 3.0)) (/ 771.3234287776531 (+ (- z) 3.0))) (* (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
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	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))

rewrite510.0ms

Algorithm

rewrite-expression-head

Rules

30×	`frac-sub`
21×	`flip3-+` `flip-+` `add-log-exp`
20×	`frac-times`
19×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-r/` `associate-l/`
7×	`diff-log` `difference-of-squares`
6×	`distribute-lft-out--`
5×	`associate--r+`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `add-cbrt-cube` `flip--`
3×	`times-frac` `sum-log` `distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 99

Calls

4 calls:

36.0ms	(- (* (/ 771.3234287776531 (+ (- z) 3.0)) (/ 771.3234287776531 (+ (- z) 3.0))) (* (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
155.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
157.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
156.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* (/ 771.3234287776531 (+ (- z) 3.0)) (/ 771.3234287776531 (+ (- z) 3.0))) (* (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
59.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
59.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
56.0ms	(- (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))

simplify941.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (310.0ms)

Iter	Nodes	Cost
0	211	4575
1	640	4235
2	2826	3823
done	5000	3823

prune4.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.1b

regimes583.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	79
1	73	79
done	73	79

end0.0ms

sample52.9s

Algorithm

intervals

Results

44.9s	3969×	body	10240	exit
2.6s	8098×	body	80	valid
2.5s	1473×	body	1280	nan
1.5s	1153×	body	640	nan
762.0ms	656×	body	320	nan
161.0ms	328×	body	160	nan
87.0ms	281×	body	80	nan
0.0ms	1×	body	160	valid