Details

sample2.6s

Algorithm

intervals

Results

2.2s	128×	body	10240	exit
182.0ms	48×	body	1280	nan
90.0ms	259×	body	80	valid
60.0ms	45×	body	640	nan
19.0ms	20×	body	320	nan
6.0ms	8×	body	160	nan
5.0ms	15×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (1.2s)

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

prune59.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
1.0b	(+ (+ (+ (+ (/ -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))

rewrite1.1m

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
102×	`frac-add`
76×	`distribute-lft-out`
69×	`add-log-exp`
51×	`sum-log`
44×	`times-frac`
30×	`unpow-prod-down`
28×	`flip3-+` `flip-+`
26×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`exp-sum`
11×	`associate-/l*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`unpow-prod-up` `distribute-rgt-neg-in` `sqr-pow`
4×	`associate-+r-` `associate-/r*`
3×	`exp-diff` `div-exp` `associate-/r/`
2×	`+-commutative` `neg-sub0` `associate-+r+` `sqrt-pow1`
1×	`cbrt-undiv` `pow-to-exp` `associate-+l-` `associate-+l+` `frac-2neg` `pow1/2` `unsub-neg` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 171

Calls

4 calls:

212.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
367.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
1.1m	(+ (+ (+ (+ (/ -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)))))
5.0ms	(sqrt (* PI 2.0))

series647.0ms

Counts

4 → 10

Calls

4 calls:

94.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
266.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
286.0ms	(+ (+ (+ (+ (/ -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))

simplify1.2s

Counts

181 → 181

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	596	13999
1	2003	11864
done	5002	11701

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize188.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
1.0b	(+ (+ (+ (+ (/ -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 (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))) (sqrt (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))))
1.0b	(sqrt (* PI 2.0))

rewrite1.0m

Algorithm

rewrite-expression-head

Rules

387×	`*-un-lft-identity`
314×	`times-frac`
303×	`sqrt-prod`
200×	`add-sqr-sqrt`
163×	`unpow-prod-down`
126×	`add-cube-cbrt`
122×	`distribute-lft-out`
100×	`frac-add`
86×	`swap-sqr`
72×	`exp-sum`
64×	`add-log-exp`
58×	`unpow-prod-up`
52×	`associate-r` `associate-l`
48×	`sum-log`
37×	`distribute-lft-out--`
31×	`sqr-pow`
29×	`sub-neg`
26×	`flip3-+` `flip-+`
25×	`unswap-sqr`
22×	`pow1`
11×	`associate-/l*`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
5×	`associate-+l-` `exp-diff` `associate-/r/` `pow-prod-up` `div-inv`
4×	`sqrt-div` `pow-prod-down` `associate-/r*`
3×	`div-exp` `pow-sqr`
1×	`cbrt-undiv` `+-commutative` `pow2` `frac-times` `pow-to-exp` `associate-+l+` `associate-+r+` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `associate-/l/` `pow-sub`

Counts

4 → 395

Calls

4 calls:

255.0ms	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
59.4s	(+ (+ (+ (+ (/ -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)))))
1.3s	(* (sqrt (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))) (sqrt (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))))
8.0ms	(sqrt (* PI 2.0))

series631.0ms

Counts

4 → 10

Calls

4 calls:

227.0ms	(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
222.0ms	(+ (+ (+ (+ (/ -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)))))
182.0ms	(* (sqrt (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))) (sqrt (/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))))
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

405 → 405

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	808	25473
1	2258	19580
done	5001	19201

prune4.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(+ (+ (+ (+ (/ -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))
1.6b	(exp (- (* (log (+ (- 7.0 z) 0.5)) (- 0.5 z)) (+ (- 7.0 z) 0.5)))

rewrite41.1s

Algorithm

rewrite-expression-head

Rules

102×	`frac-add`
79×	`add-log-exp`
70×	`*-un-lft-identity`
53×	`sum-log`
51×	`distribute-lft-out`
28×	`flip3-+` `flip-+`
7×	`pow1` `exp-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `diff-log` `associate--l+` `add-cbrt-cube` `rem-exp-log`
3×	`sub-neg` `exp-prod`
2×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `sqrt-pow1`
1×	`associate-+l-` `associate-+l+` `pow1/2` `exp-diff` `pow-prod-down` `sqrt-prod` `associate--r-`

Counts

4 → 116

Calls

4 calls:

122.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
40.8s	(+ (+ (+ (+ (/ -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)))))
3.0ms	(sqrt (* PI 2.0))
160.0ms	(exp (- (* (log (+ (- 7.0 z) 0.5)) (- 0.5 z)) (+ (- 7.0 z) 0.5)))

series335.0ms

Counts

4 → 10

Calls

4 calls:

48.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
176.0ms	(+ (+ (+ (+ (/ -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))
110.0ms	(exp (- (* (log (+ (- 7.0 z) 0.5)) (- 0.5 z)) (+ (- 7.0 z) 0.5)))

simplify664.0ms

Counts

126 → 126

Iterations

Useful iterations: done (649.0ms)

Iter	Nodes	Cost
0	507	12024
1	1861	10309
done	5001	10160

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
1.0b	(+ (+ (+ (+ (/ -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)

rewrite41.9s

Algorithm

rewrite-expression-head

Rules

132×	`*-un-lft-identity`
102×	`frac-add`
76×	`distribute-lft-out`
69×	`add-log-exp`
51×	`sum-log`
44×	`times-frac`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt` `flip3-+` `flip-+`
27×	`add-cube-cbrt`
12×	`exp-sum`
11×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `unpow-prod-up` `distribute-rgt-neg-in` `sqr-pow`
4×	`associate-+r-` `associate-/r*`
3×	`exp-diff` `div-exp` `sqrt-prod` `associate-/r/`
2×	`+-commutative` `neg-sub0` `associate-+r+`
1×	`cbrt-undiv` `pow-to-exp` `associate-+l-` `rem-sqrt-square` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `unsub-neg` `pow-exp` `clear-num` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 173

Calls

4 calls:

124.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
240.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
41.6s	(+ (+ (+ (+ (/ -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)

series397.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
166.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
180.0ms	(+ (+ (+ (+ (/ -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)

simplify737.0ms

Counts

183 → 183

Iterations

Useful iterations: done (716.0ms)

Iter	Nodes	Cost
0	588	13907
1	1972	11781
done	5002	11620

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 0.9b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	104
1	82	104
done	82	104

end0.0ms

sample51.1s

Algorithm

intervals

Results

42.0s	3822×	body	10240	exit
3.0s	8087×	body	80	valid
2.5s	1453×	body	1280	nan
2.4s	1209×	body	640	nan
467.0ms	622×	body	320	nan
141.0ms	280×	body	160	nan
85.0ms	276×	body	80	nan
0.0ms	1×	body	160	valid