Details

sample905.0ms

Algorithm

intervals

Results

292.0ms	102×	body	1280	valid
219.0ms	108×	body	10240	exit
94.0ms	81×	body	640	valid
62.0ms	49×	body	1280	nan
55.0ms	27×	body	320	nan
41.0ms	41×	body	320	valid
37.0ms	35×	body	640	nan
12.0ms	24×	body	160	valid
5.0ms	9×	body	160	nan
3.0ms	11×	body	80	valid
2.0ms	7×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5019
3	2301
2	420
1	140
0	55

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize159.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6))))
1.0b	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
1.0b	(sqrt (* PI 2))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
33×	`distribute-lft-out`
28×	`times-frac`
15×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-l`
11×	`add-cbrt-cube`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`unpow-prod-down` `prod-exp`
4×	`associate-/r` `div-exp` `associate-r*` `frac-add` `insert-posit16`
3×	`unpow-prod-up` `sum-log` `unswap-sqr`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `flip3-+` `exp-sum` `associate-*l/` `pow-exp` `sqrt-prod` `cbrt-unprod` `flip-+` `pow-sub` `sqr-pow`
1×	`+-commutative` `associate-+l+` `clear-num` `associate-+r-` `sub-neg` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `associate-/r/` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `associate--r-` `associate-/l/`

Counts

4 → 100

Calls

4 calls:

115.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
95.0ms	(/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6))))
205.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
5.0ms	(sqrt (* PI 2))

series1.0s

Counts

4 → 10

Calls

4 calls:

434.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
508.0ms	(/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6))))
103.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
0.0ms	(sqrt (* PI 2))

simplify3.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5034
2	3368
1	888
0	310

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize154.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
1.0b	(sqrt (* PI 2))

rewrite16.1s

Algorithm

rewrite-expression-head

Rules

556×	`frac-add`
216×	`*-un-lft-identity`
170×	`flip3-+` `flip-+`
147×	`distribute-lft-out`
75×	`associate-*l/`
72×	`frac-times` `associate-*r/`
31×	`associate-r`
24×	`times-frac`
23×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`prod-exp`
13×	`add-sqr-sqrt` `associate-l`
12×	`pow1`
9×	`cbrt-unprod` `add-log-exp`
8×	`add-cube-cbrt`
6×	`unpow-prod-down`
4×	`div-exp` `pow-prod-down` `insert-posit16`
3×	`unpow-prod-up` `sum-log` `unswap-sqr`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `pow-exp` `*-commutative` `sqrt-prod` `sqr-pow`
1×	`distribute-rgt-in` `+-commutative` `associate-+l+` `sub-neg` `distribute-lft-in` `pow1/2` `distribute-lft-out--` `associate--r-` `pow-sub`

Counts

4 → 268

Calls

4 calls:

15.8s	(* (* (/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
80.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
197.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
5.0ms	(sqrt (* PI 2))

series1.6s

Counts

4 → 10

Calls

4 calls:

1.0s	(* (* (/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
451.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
123.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
0.0ms	(sqrt (* PI 2))

simplify11.8s

Counts

278 → 278

Iterations

Iter	Nodes
done	5002
1	4914
0	1030

prune6.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize161.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
1.0b	(* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI))
1.0b	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
1.0b	(sqrt PI)

rewrite15.9s

Algorithm

rewrite-expression-head

Rules

556×	`frac-add`
211×	`*-un-lft-identity`
170×	`flip3-+` `flip-+`
145×	`distribute-lft-out`
75×	`associate-*l/`
73×	`associate-*r/`
72×	`frac-times`
34×	`add-exp-log`
33×	`associate-r`
29×	`add-cbrt-cube`
27×	`prod-exp`
24×	`times-frac`
15×	`cbrt-unprod`
12×	`pow1`
9×	`add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt`
6×	`sqrt-prod`
5×	`div-exp`
4×	`pow-prod-down` `insert-posit16`
3×	`cbrt-undiv` `sum-log`
2×	`pow-to-exp` `associate-l` `pow-exp` `*-commutative`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `associate-+l+` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-sub`

Counts

4 → 263

Calls

4 calls:

15.6s	(* (* (/ (* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
45.0ms	(* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI))
208.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
1.0ms	(sqrt PI)

series1.5s

Counts

4 → 10

Calls

4 calls:

1.1s	(* (* (/ (* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
365.0ms	(* (* (sqrt 2) (pow (+ z 6.5) (- z 0.5))) (sqrt PI))
97.0ms	(+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))
0.0ms	(sqrt PI)

simplify10.6s

Counts

273 → 273

Iterations

Iter	Nodes
done	5001
1	4933
0	1025

prune6.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize166.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (+ (/ -176.6150291621406 (+ 3 z)) (+ (/ 12.507343278686905 (+ z 4)) (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ 1 z)) (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z))))) (exp -6))
1.0b	(+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z)))
1.0b	(* (pow (+ 0.5 (+ z 6)) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite40.4s

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
93×	`distribute-lft-out`
85×	`frac-add`
33×	`associate-*l/`
31×	`associate-l`
29×	`flip3-+` `flip-+`
16×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac` `add-cbrt-cube`
7×	`associate-r`
6×	`unpow-prod-down` `add-log-exp`
4×	`prod-exp` `insert-posit16` `unswap-sqr`
2×	`sqrt-pow1` `pow-prod-down` `*-commutative` `sqrt-prod` `cbrt-unprod` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-up` `+-commutative` `sum-log` `pow1/2` `pow-exp` `associate-+l-` `pow-sub`

Counts

4 → 130

Calls

4 calls:

40.2s	(* (+ (+ (/ -176.6150291621406 (+ 3 z)) (+ (/ 12.507343278686905 (+ z 4)) (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ 1 z)) (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z))))) (exp -6))
46.0ms	(+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z)))
140.0ms	(* (pow (+ 0.5 (+ z 6)) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
3.0ms	(sqrt (* PI 2))

series718.0ms

Counts

4 → 10

Calls

4 calls:

216.0ms	(* (+ (+ (/ -176.6150291621406 (+ 3 z)) (+ (/ 12.507343278686905 (+ z 4)) (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (+ 1 z)) (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z))))) (exp -6))
70.0ms	(+ (/ 1.5056327351493116e-07 (+ z 7)) (/ -0.13857109526572012 (+ 5 z)))
432.0ms	(* (pow (+ 0.5 (+ z 6)) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify4.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
1	1538
0	458

prune2.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.5b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 0.8b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	80
1	80
0	57

end0.0ms

sample35.4s

Algorithm

intervals

Results

13.2s	3806×	body	10240	exit
9.5s	3352×	body	1280	valid
3.8s	2466×	body	640	valid
2.8s	1258×	body	640	nan
2.7s	1560×	body	1280	nan
1.4s	1275×	body	320	valid
585.0ms	633×	body	320	nan
406.0ms	620×	body	160	valid
253.0ms	342×	body	160	nan
122.0ms	301×	body	80	nan
105.0ms	384×	body	80	valid