Details

sample1.5s

Algorithm

intervals

Results

428.0ms	134×	body	10240	exit
322.0ms	118×	body	1280	valid
194.0ms	71×	body	640	valid
187.0ms	57×	body	1280	nan
125.0ms	50×	body	640	nan
80.0ms	44×	body	320	valid
35.0ms	22×	body	320	nan
15.0ms	18×	body	160	valid
10.0ms	12×	body	160	nan
4.0ms	9×	body	80	valid
2.0ms	5×	body	80	nan

simplify884.0ms

Counts: 1 → 1

prune64.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize139.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
1.0b	(sqrt (* PI 2))
1.0b	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))

rewrite24.7s

Algorithm

rewrite-expression-head

Rules

196×	`*-un-lft-identity`
125×	`distribute-lft-out`
104×	`frac-add`
52×	`flip3-+` `flip-+`
45×	`exp-sum`
42×	`add-sqr-sqrt`
36×	`times-frac` `prod-diff`
34×	`associate-l`
33×	`add-cube-cbrt`
32×	`associate-r`
27×	`add-exp-log`
24×	`frac-times` `associate-*r/`
20×	`add-cbrt-cube`
18×	`associate-/r*`
14×	`prod-exp`
9×	`pow1`
8×	`div-exp`
7×	`unpow-prod-down`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `sub-neg` `associate-*l/` `pow-exp` `associate--l+`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `associate-+l-` `sqrt-prod` `div-inv` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-/l*` `difference-of-squares` `associate-/l/`

Counts

4 → 229

Calls

4 calls:

Slowest

24.3s	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
205.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
162.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
8.0ms	(sqrt (* PI 2))

series1.8s

Counts

4 → 10

Calls

4 calls:

Slowest

845.0ms	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
560.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
425.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify3.6s

Counts: 239 → 239

prune9.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize153.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (exp (- -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
1.0b	(sqrt (* PI 2))
1.0b	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0b	(/ -176.6150291621406 (- z -3))

rewrite24.5s

Algorithm

rewrite-expression-head

Rules

186×	`*-un-lft-identity`
116×	`distribute-lft-out`
104×	`frac-add`
53×	`add-sqr-sqrt`
52×	`flip3-+` `times-frac` `flip-+`
41×	`associate-l`
33×	`add-cube-cbrt`
32×	`associate-r`
25×	`add-exp-log`
24×	`frac-times` `associate-*r/`
22×	`add-cbrt-cube`
12×	`prod-exp`
10×	`div-exp`
9×	`pow1`
7×	`unpow-prod-down`
6×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
5×	`associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `associate-/l*`
2×	`pow-to-exp` `sqrt-pow1` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `sqrt-prod` `sqr-pow`
1×	`neg-sub0` `distribute-rgt-in` `exp-neg` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `flip3--` `pow1/2` `exp-diff` `associate-+l-` `flip--` `pow-sub`

Counts

4 → 221

Calls

4 calls:

Slowest

24.3s	(* (/ (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (exp (- -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
155.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
8.0ms	(/ -176.6150291621406 (- z -3))
6.0ms	(sqrt (* PI 2))

series1.6s

Counts

4 → 10

Calls

4 calls:

Slowest

1.2s	(* (/ (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (exp (- -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
383.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
27.0ms	(/ -176.6150291621406 (- z -3))
0.0ms	(sqrt (* PI 2))

simplify3.5s

Counts: 231 → 231

prune8.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize231.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (* (log 6.5) (sqrt 2)) (exp (+ 0.5 6)))))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (sqrt 2) (exp (+ 0.5 6)))))
1.0b	(/ (sqrt 2) (exp (+ 0.5 6)))
1.0b	(sqrt PI)

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

238×	`add-exp-log`
156×	`prod-exp`
91×	`pow-exp`
79×	`div-exp`
68×	`unpow-prod-down`
66×	`times-frac`
58×	`associate-l`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
29×	`add-cbrt-cube`
28×	`pow-to-exp`
21×	`rec-exp` `1-exp`
18×	`sqrt-prod`
13×	`cbrt-unprod`
8×	`sqr-pow`
7×	`exp-sum`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`associate-r` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 240

Calls

4 calls:

Slowest

171.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (* (log 6.5) (sqrt 2)) (exp (+ 0.5 6)))))
135.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (sqrt 2) (exp (+ 0.5 6)))))
17.0ms	(/ (sqrt 2) (exp (+ 0.5 6)))
1.0ms	(sqrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (* (log 6.5) (sqrt 2)) (exp (+ 0.5 6)))))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* (sqrt PI) (/ (sqrt 2) (exp (+ 0.5 6)))))
0.0ms	(/ (sqrt 2) (exp (+ 0.5 6)))
0.0ms	(sqrt PI)

simplify2.2s

Counts: 244 → 244

prune13.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize186.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) (exp (- -6)))
1.0b	(sqrt (* PI 2))
1.0b	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.5b	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))

rewrite31.9s

Algorithm

rewrite-expression-head

Rules

208×	`frac-add`
157×	`*-un-lft-identity`
116×	`distribute-lft-out`
104×	`flip3-+` `flip-+`
49×	`associate-/l/`
48×	`frac-times` `associate-*r/`
34×	`add-exp-log`
32×	`associate-r`
29×	`add-cbrt-cube`
21×	`add-sqr-sqrt`
19×	`associate-l` `prod-exp`
14×	`div-exp`
12×	`add-cube-cbrt`
9×	`pow1` `cbrt-unprod`
8×	`cbrt-undiv`
7×	`unpow-prod-down` `times-frac`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-/r` `associate-l/` `pow-exp`
2×	`sqrt-pow1` `pow-prod-down` `associate-/r/` `*-commutative` `sqrt-prod` `div-inv` `distribute-lft-out--` `sqr-pow`
1×	`neg-sub0` `distribute-rgt-in` `exp-neg` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `exp-diff` `exp-sum` `associate-+l-` `associate-/l*` `pow-sub` `difference-of-squares`

Counts

4 → 237

Calls

4 calls:

Slowest

24.2s	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
7.6s	(/ (* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) (exp (- -6)))
143.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))

series2.3s

Counts

4 → 10

Calls

4 calls:

Slowest

1.1s	(/ (* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) (exp (- -6)))
844.0ms	(* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099)))
379.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify3.6s

Counts: 247 → 247

prune11.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch26.0ms

end0.0ms

sample48.9s

Algorithm

intervals

Results

16.5s	3920×	body	10240	exit
11.5s	3437×	body	1280	valid
6.3s	2477×	body	640	valid
5.1s	1557×	body	1280	nan
3.5s	1292×	body	640	nan
2.2s	1201×	body	320	valid
1.3s	620×	body	320	nan
791.0ms	309×	body	160	nan
760.0ms	651×	body	160	valid
195.0ms	285×	body	80	nan
143.0ms	332×	body	80	valid