Details

sample2.7s

Algorithm

intervals

Results

2.3s	146×	body	10240	exit
124.0ms	261×	body	80	valid
86.0ms	47×	body	640	nan
74.0ms	38×	body	1280	nan
26.0ms	28×	body	320	nan
7.0ms	10×	body	160	nan
2.0ms	6×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	3571
2	602
1	148
0	60

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize223.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
1.0b	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
1.0b	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
1.0b	(sqrt (* 2.0 PI))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
45×	`add-log-exp`
30×	`sum-log` `distribute-lft-out`
24×	`frac-add`
16×	`times-frac`
14×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`flip3-+` `flip-+`
7×	`pow1`
6×	`add-cbrt-cube` `sqrt-prod`
5×	`exp-sum` `add-exp-log`
4×	`associate-/r` `associate-/l`
3×	`exp-diff` `associate-/r/` `associate-+l-`
2×	`+-commutative` `associate-+r+` `sqrt-pow1`
1×	`neg-sub0` `cbrt-undiv` `associate-+l+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `div-exp` `unsub-neg` `pow-prod-down` `div-inv`

Counts

4 → 109

Calls

4 calls:

759.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
2.9s	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
197.0ms	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
3.0ms	(sqrt (* 2.0 PI))

series445.0ms

Counts

4 → 10

Calls

4 calls:

100.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
212.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
133.0ms	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
0.0ms	(sqrt (* 2.0 PI))

simplify3.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	4168
1	912
0	320

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize246.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
1.0b	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
1.0b	(/ (/ (sqrt (* 2.0 PI)) (* (cbrt (exp (+ (+ 7.0 (- z)) 0.5))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))
1.0b	(sqrt (* 2.0 PI))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

195×	`cbrt-div` `exp-diff` `associate-+l-`
193×	`times-frac`
123×	`associate-/r/`
109×	`*-un-lft-identity`
96×	`cbrt-prod`
72×	`frac-times`
68×	`add-sqr-sqrt` `add-cube-cbrt`
65×	`neg-sub0` `associate-+r-` `unsub-neg`
45×	`add-log-exp`
30×	`sum-log` `distribute-lft-out`
24×	`exp-sum` `associate-l/` `frac-add` `associate-r/`
23×	`associate-/l*`
13×	`flip3-+` `add-exp-log` `flip-+`
9×	`sqrt-prod` `div-inv`
8×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp`
2×	`+-commutative` `associate-+r+` `sqrt-pow1`
1×	`associate-+l+` `clear-num` `frac-2neg` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 281

Calls

4 calls:

824.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
2.7s	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
429.0ms	(/ (/ (sqrt (* 2.0 PI)) (* (cbrt (exp (+ (+ 7.0 (- z)) 0.5))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))
5.0ms	(sqrt (* 2.0 PI))

series407.0ms

Counts

4 → 10

Calls

4 calls:

90.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
156.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
162.0ms	(/ (/ (sqrt (* 2.0 PI)) (* (cbrt (exp (+ (+ 7.0 (- z)) 0.5))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))) (cbrt (exp (+ (+ 7.0 (- z)) 0.5))))
0.0ms	(sqrt (* 2.0 PI))

simplify3.3s

Counts

291 → 291

Iterations

Iter	Nodes
done	5000
2	4864
1	1272
0	491

prune5.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize298.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
1.0b	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (* (* (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))))
1.0b	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
1.0b	(sqrt (* 2.0 PI))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

948×	`frac-add`
900×	`cbrt-div`
577×	`flip3-+` `flip-+`
528×	`frac-times`
132×	`associate-*l/`
72×	`associate-*r/`
23×	`*-un-lft-identity`
18×	`add-log-exp`
16×	`times-frac`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`sum-log`
7×	`pow1`
6×	`add-cbrt-cube` `sqrt-prod` `distribute-lft-out`
5×	`exp-sum` `add-exp-log`
4×	`associate-/r` `associate-/l`
3×	`exp-diff` `associate-/r/` `associate-+l-`
2×	`+-commutative` `sqrt-pow1`
1×	`neg-sub0` `cbrt-undiv` `associate-+l+` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `div-exp` `unsub-neg` `pow-prod-down` `div-inv`

Counts

4 → 454

Calls

4 calls:

779.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
616.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (* (* (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))))
180.0ms	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
6.0ms	(sqrt (* 2.0 PI))

series491.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))
196.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (* (* (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))) (cbrt (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))))
155.0ms	(/ (sqrt (* 2.0 PI)) (exp (+ (+ 7.0 (- z)) 0.5)))
0.0ms	(sqrt (* 2.0 PI))

simplify6.0s

Counts

464 → 464

Iterations

Iter	Nodes
done	5001
1	4394
0	1731

prune17.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize844.0ms

Local error

Found 4 expressions with local error:

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

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
60×	`times-frac`
47×	`unpow-prod-down` `cube-prod`
45×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`distribute-lft-out`
12×	`distribute-rgt-neg-in`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`pow-unpow`
8×	`associate-/r/`
5×	`flip3-+` `pow-exp` `flip-+` `rem-cube-cbrt`
4×	`cube-div` `div-inv` `add-log-exp`
3×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 164

Calls

4 calls:

473.0ms	(pow (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))) 3)
21.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
34.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
5.0ms	(sqrt (* 2.0 PI))

series272.0ms

Counts

4 → 10

Calls

4 calls:

113.0ms	(pow (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z))))) 3)
66.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
92.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
0.0ms	(sqrt (* 2.0 PI))

simplify2.1s

Counts

174 → 174

Iterations

Iter	Nodes
done	5015
2	2598
1	800
0	224

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes539.0ms

Accuracy

0% (1.0b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify40.0ms

Iterations

Iter	Nodes
done	83
1	83
0	61

end0.0ms

sample1.3m

Algorithm

intervals

Results

1.1m	3907×	body	10240	exit
4.7s	1457×	body	1280	nan
4.3s	8089×	body	80	valid
3.2s	1247×	body	640	nan
779.0ms	645×	body	320	nan
206.0ms	305×	body	160	nan
89.0ms	271×	body	80	nan