Details

sample423.0ms

Algorithm

intervals

Results

137.0ms	126×	body	10240	exit
87.0ms	98×	body	1280	valid
57.0ms	91×	body	640	valid
38.0ms	58×	body	1280	nan
24.0ms	46×	body	640	nan
15.0ms	34×	body	320	valid
8.0ms	21×	body	320	nan
5.0ms	19×	body	160	valid
5.0ms	19×	body	160	nan
3.0ms	21×	body	80	valid
0.0ms	4×	body	80	nan

simplify934.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (225.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	442	92
3	2463	89
done	5000	89

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
0.9b	(+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))

rewrite17.4s

Algorithm

rewrite-expression-head

Rules

348×	`frac-add`
118×	`flip3-+` `flip-+`
106×	`associate-*r/`
105×	`associate-/l/`
56×	`associate-+l-`
54×	`pow-sub`
52×	`frac-times`
39×	`*-un-lft-identity`
25×	`add-log-exp`
20×	`add-exp-log` `distribute-lft-out`
15×	`sum-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
11×	`associate-r`
10×	`prod-exp`
9×	`add-cube-cbrt`
7×	`pow1` `unpow-prod-down`
5×	`div-exp`
4×	`times-frac` `associate-l` `associate-/r*` `cbrt-unprod`
3×	`cbrt-undiv` `unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `exp-sum` `pow-exp` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `associate-+l+` `associate-+r+` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `-commutative` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 205

Calls

4 calls:

15.0s	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
2.1s	(+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
311.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))

series1.2s

Counts

4 → 10

Calls

4 calls:

837.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
109.0ms	(+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
295.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify621.0ms

Counts

215 → 215

Iterations

Useful iterations: done (596.0ms)

Iter	Nodes	Cost
0	623	19187
1	2075	17332
done	5001	17313

prune2.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
1.0b	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
1.0b	(sqrt (* PI 2.0))

rewrite1000.0ms

Algorithm

rewrite-expression-head

Rules

144×	`*-un-lft-identity`
55×	`distribute-lft-out`
36×	`times-frac`
25×	`unpow-prod-down`
18×	`add-sqr-sqrt` `cube-prod`
13×	`add-cube-cbrt` `distribute-lft-out--`
11×	`add-exp-log` `associate-r`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-unpow`
5×	`cube-div`
4×	`associate-l` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `prod-exp` `unswap-sqr`
2×	`cube-mult` `pow-pow` `sqrt-pow1` `flip3-+` `unpow3` `sqrt-prod` `flip-+` `rem-cube-cbrt`
1×	`unpow-prod-up` `associate-+l-` `pow1/2` `associate-r/` `pow-prod-down` `frac-add` `-commutative` `cbrt-unprod` `pow-sub`

Counts

4 → 117

Calls

4 calls:

307.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
186.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
500.0ms	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
2.0ms	(sqrt (* PI 2.0))

series477.0ms

Counts

4 → 10

Calls

4 calls:

283.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
107.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
87.0ms	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 2 (371.0ms)

Iter	Nodes	Cost
0	309	3617
1	925	3275
2	3583	2952
done	5001	2952

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize127.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
1.0b	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
1.0b	(sqrt (* PI 2.0))
1.0b	(sqrt (* PI 2.0))

rewrite692.0ms

Algorithm

rewrite-expression-head

Rules

132×	`*-un-lft-identity`
50×	`distribute-lft-out`
36×	`times-frac`
18×	`unpow-prod-down` `cube-prod`
12×	`pow1` `distribute-lft-out--`
10×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`cube-div`
4×	`sqrt-pow1` `add-log-exp`
2×	`cube-mult` `pow-to-exp` `pow-pow` `flip3-+` `pow1/2` `unpow3` `pow-prod-down` `pow-exp` `sqrt-prod` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`frac-add`

Counts

4 → 97

Calls

4 calls:

187.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
497.0ms	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
1.0ms	(sqrt (* PI 2.0))
2.0ms	(sqrt (* PI 2.0))

series198.0ms

Counts

4 → 8

Calls

4 calls:

109.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
88.0ms	(pow (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) 3)
0.0ms	(sqrt (* PI 2.0))
0.0ms	(sqrt (* PI 2.0))

simplify636.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	171	2354
1	489	2118
2	1639	1910
done	5000	1910

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0))) (* z (* (+ (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (- (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))
0.9b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0)))
1.0b	(* (+ (pow 0.9999999999998099 3) (pow (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 3)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
1.0b	(sqrt (* PI 2.0))

rewrite9.3s

Algorithm

rewrite-expression-head

Rules

1979×	`frac-times`
1316×	`associate-*r/`
922×	`flip3-+` `flip-+`
540×	`associate-*l/`
351×	`pow-sub`
165×	`add-exp-log` `flip3--` `frac-sub` `flip--`
133×	`prod-exp`
95×	`*-un-lft-identity`
69×	`add-cbrt-cube`
49×	`cbrt-unprod`
30×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out`
26×	`associate-l`
22×	`add-sqr-sqrt` `times-frac`
19×	`associate-r`
18×	`pow1`
17×	`distribute-lft-out--`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`sub-neg`
8×	`add-cube-cbrt` `cube-prod` `pow-prod-down`
4×	`add-log-exp` `difference-of-squares`
3×	`*-commutative`
2×	`unpow-prod-up` `sqrt-pow1`
1×	`pow1/2` `sqrt-prod` `sum-cubes` `unswap-sqr` `sqr-pow`

Counts

4 → 876

Calls

4 calls:

6.0s	(* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0))) (* z (* (+ (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (- (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))
574.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0)))
2.6s	(* (+ (pow 0.9999999999998099 3) (pow (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 3)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
2.0ms	(sqrt (* PI 2.0))

series1.1s

Counts

4 → 10

Calls

4 calls:

656.0ms	(* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0))) (* z (* (+ (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (- (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))))
227.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (- z 1.0) 4.0)))
198.0ms	(* (+ (pow 0.9999999999998099 3) (pow (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) 3)) (- (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))))
0.0ms	(sqrt (* PI 2.0))

simplify809.0ms

Counts

886 → 886

Iterations

Useful iterations: 0 (239.0ms)

Iter	Nodes	Cost
0	1865	151551
done	5000	151551

prune25.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes434.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	81	527
1	117	527
done	117	527

end0.0ms

sample12.0s

Algorithm

intervals

Results

4.1s	3922×	body	10240	exit
3.1s	3390×	body	1280	valid
1.6s	2516×	body	640	valid
1.0s	1530×	body	1280	nan
703.0ms	1346×	body	640	nan
557.0ms	1237×	body	320	valid
256.0ms	652×	body	320	nan
178.0ms	606×	body	160	valid
79.0ms	314×	body	160	nan
51.0ms	344×	body	80	valid
38.0ms	309×	body	80	nan