Details

sample2.1s

Algorithm

intervals

Results

567.0ms	140×	body	10240	exit
413.0ms	111×	body	1280	valid
220.0ms	83×	body	640	valid
189.0ms	57×	body	1280	nan
85.0ms	43×	body	640	nan
45.0ms	32×	body	320	valid
24.0ms	17×	body	320	nan
19.0ms	20×	body	160	valid
9.0ms	10×	body	160	nan
7.0ms	15×	body	80	valid
5.0ms	10×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2007
3	2007
2	420
1	140
0	55

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize185.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
1.0b	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
1.0b	(sqrt (* PI 2))

rewrite16.4s

Algorithm

rewrite-expression-head

Rules

656×	`*-un-lft-identity`
479×	`distribute-lft-out`
216×	`frac-add`
116×	`times-frac`
58×	`associate-/l/`
55×	`flip3-+` `flip-+`
41×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
24×	`exp-sum`
23×	`associate-/l*`
10×	`associate-l` `add-exp-log`
9×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down`
5×	`distribute-lft-out--`
4×	`associate-/r` `associate-r*` `insert-posit16`
3×	`sum-log` `prod-exp` `unswap-sqr`
2×	`sqrt-pow1` `associate-+l-` `sqrt-prod` `sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `unpow-prod-up` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `associate-/r/` `-commutative` `cbrt-unprod` `div-inv` `pow-sub`

Counts

4 → 261

Calls

4 calls:

162.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
187.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
16.1s	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
5.0ms	(sqrt (* PI 2))

series773.0ms

Counts

4 → 10

Calls

4 calls:

85.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
424.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
264.0ms	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
0.0ms	(sqrt (* PI 2))

simplify2.6s

Counts

271 → 271

Iterations

Iter	Nodes
done	2005
2	2005
1	1613
0	482

prune9.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize219.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
1.0b	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
1.0b	(sqrt (* PI 2))
4.4b	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

rewrite15.8s

Algorithm

rewrite-expression-head

Rules

661×	`*-un-lft-identity`
481×	`distribute-lft-out`
216×	`frac-add`
116×	`times-frac`
58×	`associate-/l/`
56×	`flip3-+` `flip-+`
36×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`exp-sum`
23×	`associate-/l*`
14×	`log-prod`
11×	`associate-+r+`
10×	`add-log-exp`
7×	`pow1`
6×	`add-cbrt-cube` `distribute-lft-out--`
5×	`distribute-rgt-in` `distribute-lft-in` `add-exp-log`
4×	`associate-+l+` `associate-/r*` `sum-log` `insert-posit16`
2×	`+-commutative` `sqrt-pow1` `sqrt-prod`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `associate-/r/` `associate-+l-` `div-inv`

Counts

4 → 256

Calls

4 calls:

131.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
15.5s	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
6.0ms	(sqrt (* PI 2))
75.0ms	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

series633.0ms

Counts

4 → 10

Calls

4 calls:

133.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
220.0ms	(/ (+ (+ (/ 1.5056327351493116e-07 (- z -7)) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (/ -1259.1392167224028 (+ z 1)))) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))) (exp (+ (- z -6) 0.5)))
0.0ms	(sqrt (* PI 2))
279.0ms	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

simplify2.2s

Counts

266 → 266

Iterations

Iter	Nodes
done	2002
2	2002
1	1562
0	475

prune11.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize165.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))
0.9b	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
1.0b	(sqrt (* PI 2))
4.4b	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

251×	`*-un-lft-identity`
101×	`distribute-lft-out`
88×	`times-frac`
22×	`distribute-lft-out--`
19×	`add-log-exp`
14×	`log-prod`
13×	`frac-add`
11×	`associate-+r+`
10×	`sum-log`
7×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
6×	`flip3-+` `flip-+`
5×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`+-commutative`
2×	`sqrt-pow1` `sqrt-prod`
1×	`pow1/2` `pow-prod-down`

Counts

4 → 104

Calls

4 calls:

856.0ms	(+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))
133.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
5.0ms	(sqrt (* PI 2))
73.0ms	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

series458.0ms

Counts

4 → 10

Calls

4 calls:

132.0ms	(+ (+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5)))) (/ 9.984369578019572e-06 (- z -6)))
90.0ms	(+ (/ 12.507343278686905 (+ z 4)) (+ (/ -176.6150291621406 (+ z 3)) (/ -0.13857109526572012 (- z -5))))
0.0ms	(sqrt (* PI 2))
235.0ms	(+ (log (sqrt (* PI 2))) (* (- z (- 1 0.5)) (log (+ 0.5 (- z -6)))))

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
2	2000
1	745
0	280

prune4.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize219.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(* (sqrt (* PI 2)) (sqrt (* PI 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`pow1`
34×	`sqrt-pow1`
23×	`pow-prod-down`
13×	`pow1/2`
10×	`add-sqr-sqrt` `pow-prod-up`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-cbrt-cube` `add-exp-log` `pow-sqr`
4×	`swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

5.0ms	(sqrt (* PI 2))
3.0ms	(sqrt (* PI 2))
3.0ms	(sqrt (* PI 2))
22.0ms	(* (sqrt (* PI 2)) (sqrt (* PI 2)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(* (sqrt (* PI 2)) (sqrt (* PI 2)))

simplify1.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	2001
4	2001
3	1361
2	323
1	137
0	59

prune3.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify33.0ms

Iterations

Iter	Nodes
done	78
1	78
0	58

end0.0ms

sample51.2s

Algorithm

intervals

Results

18.9s	3805×	body	10240	exit
11.8s	3434×	body	1280	valid
6.8s	2446×	body	640	valid
5.3s	1560×	body	1280	nan
2.7s	1220×	body	640	nan
2.6s	1234×	body	320	valid
1.1s	660×	body	320	nan
678.0ms	633×	body	160	valid
413.0ms	344×	body	160	nan
189.0ms	345×	body	80	valid
136.0ms	313×	body	80	nan