Details

sample1.5s

Algorithm

intervals

Results

456.0ms	127×	body	10240	exit
291.0ms	108×	body	1280	valid
264.0ms	84×	body	640	valid
157.0ms	55×	body	1280	nan
120.0ms	49×	body	640	nan
67.0ms	31×	body	320	nan
47.0ms	37×	body	320	valid
23.0ms	25×	body	160	valid
5.0ms	7×	body	160	nan
2.0ms	7×	body	80	nan
2.0ms	5×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
3	2001
2	422
1	140
0	55

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize111.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
1.0b	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
1.0b	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite2.4m

Algorithm

rewrite-expression-head

Rules

276×	`frac-add`
94×	`*-un-lft-identity`
65×	`distribute-lft-out`
62×	`flip3-+` `flip-+`
38×	`frac-times` `associate-*r/`
27×	`add-exp-log`
21×	`associate-r`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt` `associate-l`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
6×	`unpow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `associate-+l-` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `exp-sum` `associate-*l/` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `sqrt-prod` `div-inv` `pow-sub` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-/l*` `distribute-lft-out--` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

2.4m	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
127.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
171.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))

series1.3s

Counts

4 → 10

Calls

4 calls:

616.0ms	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
408.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
281.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify2.9s

Counts

213 → 213

Iterations

Iter	Nodes
done	2000
1	2000
0	797

prune7.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize170.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))
0.7b	(* (* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
1.0b	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5)))))
1.0b	(sqrt (* PI 2))

rewrite1.3m

Algorithm

rewrite-expression-head

Rules

552×	`frac-add`
186×	`*-un-lft-identity`
158×	`times-frac`
154×	`frac-times`
142×	`add-sqr-sqrt`
124×	`flip3-+` `flip-+`
108×	`sqrt-prod`
78×	`associate-*r/`
77×	`distribute-lft-out`
76×	`associate-l`
74×	`add-cube-cbrt`
64×	`add-exp-log`
50×	`associate-r`
43×	`associate-*l/`
41×	`unpow-prod-down`
36×	`add-cbrt-cube`
25×	`prod-exp`
21×	`div-exp` `unswap-sqr`
19×	`exp-sum`
14×	`pow1`
13×	`cbrt-unprod` `sqr-pow`
9×	`cbrt-undiv`
7×	`unpow-prod-up` `associate-/r*` `distribute-lft-out--`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`exp-diff` `sqrt-div` `associate-/r/` `associate-+l-` `div-inv`
2×	`sqrt-pow1` `*-commutative`
1×	`distribute-rgt-in` `sqrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2`

Counts

4 → 428

Calls

4 calls:

60.0ms	(/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))
1.3m	(* (* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
561.0ms	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5)))))
6.0ms	(sqrt (* PI 2))

series1.0s

Counts

4 → 10

Calls

4 calls:

101.0ms	(/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))
565.0ms	(* (* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
374.0ms	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5)))))
0.0ms	(sqrt (* PI 2))

simplify2.7s

Counts

438 → 438

Iterations

Iter	Nodes
done	2002
1	2002
0	1056

prune11.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
0.7b	(/ (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))) (* (sqrt (exp (+ (- z -6) 0.5))) (sqrt (exp (+ (- z -6) 0.5)))))
1.0b	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite2.1m

Algorithm

rewrite-expression-head

Rules

552×	`frac-add`
124×	`flip3-+` `flip-+`
90×	`*-un-lft-identity`
83×	`associate-+l-`
82×	`associate-*l/`
79×	`pow-sub`
77×	`frac-times` `associate-*r/` `associate-/l/`
65×	`distribute-lft-out`
56×	`add-exp-log`
32×	`add-cbrt-cube`
29×	`prod-exp`
21×	`associate-r`
13×	`add-sqr-sqrt` `cbrt-unprod`
11×	`associate-l`
10×	`div-exp`
9×	`pow1`
8×	`add-cube-cbrt`
6×	`cbrt-undiv` `unpow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `exp-diff` `sqrt-div` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/` `unswap-sqr`
2×	`sqrt-pow1` `pow-prod-down` `*-commutative` `sqrt-prod` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `times-frac` `pow1/2` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 274

Calls

4 calls:

1.3m	(* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
47.7s	(/ (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))) (* (sqrt (exp (+ (- z -6) 0.5))) (sqrt (exp (+ (- z -6) 0.5)))))
116.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))

series1.3s

Counts

4 → 10

Calls

4 calls:

434.0ms	(* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
570.0ms	(/ (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))) (* (sqrt (exp (+ (- z -6) 0.5))) (sqrt (exp (+ (- z -6) 0.5)))))
264.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify2.2s

Counts

284 → 284

Iterations

Iter	Nodes
done	2001
1	2001
0	886

prune8.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize133.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(* (sqrt 2) (log 6.5))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`log-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
8.0ms	(* (sqrt 2) (log 6.5))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(* (sqrt 2) (log 6.5))

simplify778.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	2005
3	2005
2	695
1	251
0	117

prune2.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	78
1	78
0	57

end0.0ms

sample30.0s

Algorithm

intervals

Results

11.4s	3935×	body	10240	exit
6.3s	3277×	body	1280	valid
4.1s	2566×	body	640	valid
2.7s	1481×	body	1280	nan
2.1s	1318×	body	640	nan
1.5s	1249×	body	320	valid
731.0ms	668×	body	160	valid
597.0ms	632×	body	320	nan
169.0ms	327×	body	160	nan
90.0ms	335×	body	80	valid
86.0ms	329×	body	80	nan