Details

sample1.5s

Algorithm

intervals

Results

583.0ms	126×	body	10240	exit
324.0ms	110×	body	1280	valid
202.0ms	84×	body	640	valid
142.0ms	44×	body	1280	nan
64.0ms	35×	body	640	nan
58.0ms	34×	body	320	valid
20.0ms	12×	body	320	nan
14.0ms	18×	body	160	valid
8.0ms	12×	body	80	valid
7.0ms	9×	body	160	nan
5.0ms	10×	body	80	nan

simplify1.3s

Counts: 1 → 1

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize152.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (/ (* (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)))

rewrite24.2s

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

23.9s	(* (/ (* (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)))
146.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
146.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
8.0ms	(sqrt (* PI 2))

series1.9s

Counts

4 → 10

Calls

4 calls:

Slowest

847.0ms	(* (/ (* (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)))
634.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
461.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify3.9s

Counts: 286 → 239

prune9.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize191.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (+ (+ (+ (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))) (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2)))) 0.9999999999998099) (+ (+ (/ 12.507343278686905 (+ 4 z)) (/ -0.13857109526572012 (+ 6 (- z 1)))) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ 6 z))))) (/ (sqrt (* PI 2)) (exp 6)))
1.0b	(/ (sqrt (* PI 2)) (exp 6))
1.0b	(sqrt (* PI 2))
1.0b	(/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp (+ z 0.5)))

rewrite18.3s

Algorithm

rewrite-expression-head

Rules

242×	`*-un-lft-identity`
148×	`distribute-lft-out`
104×	`frac-add`
69×	`times-frac`
59×	`add-sqr-sqrt`
52×	`flip3-+` `flip-+`
44×	`add-cube-cbrt`
33×	`associate-l`
30×	`unpow-prod-down`
24×	`frac-times` `associate-*l/`
16×	`associate-r`
15×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`exp-sum`
11×	`add-exp-log`
10×	`distribute-lft-out--`
9×	`pow1`
8×	`sqrt-prod`
7×	`associate-/r*`
5×	`unpow-prod-up` `div-exp` `difference-of-squares` `sqr-pow`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow-prod-down` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `pow1/2` `pow-exp` `associate-r/` `-commutative` `associate-+l-` `pow-sub` `associate-/l/`

Counts

4 → 241

Calls

4 calls:

Slowest

18.1s	(* (+ (+ (+ (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))) (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2)))) 0.9999999999998099) (+ (+ (/ 12.507343278686905 (+ 4 z)) (/ -0.13857109526572012 (+ 6 (- z 1)))) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ 6 z))))) (/ (sqrt (* PI 2)) (exp 6)))
147.0ms	(/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp (+ z 0.5)))
16.0ms	(/ (sqrt (* PI 2)) (exp 6))
8.0ms	(sqrt (* PI 2))

series717.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

459.0ms	(* (+ (+ (+ (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))) (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2)))) 0.9999999999998099) (+ (+ (/ 12.507343278686905 (+ 4 z)) (/ -0.13857109526572012 (+ 6 (- z 1)))) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ 6 z))))) (/ (sqrt (* PI 2)) (exp 6)))
258.0ms	(/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp (+ z 0.5)))
0.0ms	(/ (sqrt (* PI 2)) (exp 6))
0.0ms	(sqrt (* PI 2))

simplify4.1s

Counts: 332 → 249

prune9.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize154.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (/ (sqrt (* PI 2)) (exp (- 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	(/ (sqrt (* PI 2)) (exp (- 0.5 -6)))
0.4b	(* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp z)) (* (/ (sqrt (* PI 2)) (exp (- 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))))

rewrite41.7s

Algorithm

rewrite-expression-head

Rules

312×	`frac-add`
271×	`*-un-lft-identity`
156×	`flip3-+` `flip-+`
146×	`times-frac`
127×	`add-sqr-sqrt`
121×	`frac-times` `associate-*r/`
118×	`distribute-lft-out`
116×	`add-cube-cbrt`
99×	`exp-sum`
98×	`associate-l`
81×	`prod-diff`
38×	`add-exp-log`
32×	`add-cbrt-cube`
30×	`sqrt-prod`
29×	`associate-r`
22×	`prod-exp`
18×	`unpow-prod-down`
15×	`div-exp`
14×	`pow1` `associate-/r*`
12×	`cbrt-unprod`
9×	`sub-neg`
7×	`cbrt-undiv`
6×	`distribute-lft-out--`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `associate-l/` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-up` `pow-exp` `div-inv` `difference-of-squares` `sqr-pow`
2×	`sqrt-pow1` `exp-diff` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2`

Counts

4 → 434

Calls

4 calls:

Slowest

23.8s	(* (/ (sqrt (* PI 2)) (exp (- 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)))
17.9s	(* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp z)) (* (/ (sqrt (* PI 2)) (exp (- 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))))
26.0ms	(/ (sqrt (* PI 2)) (exp (- 0.5 -6)))
4.0ms	(sqrt (* PI 2))

series1.2s

Counts

4 → 8

Calls

4 calls:

Slowest

811.0ms	(* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (exp z)) (* (/ (sqrt (* PI 2)) (exp (- 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))))
420.0ms	(* (/ (sqrt (* PI 2)) (exp (- 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)))
0.0ms	(sqrt (* PI 2))
0.0ms	(/ (sqrt (* PI 2)) (exp (- 0.5 -6)))

simplify7.4s

Counts: 578 → 442

prune18.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2) (exp 6))
1.0b	(* (/ (sqrt 2) (exp 6)) (sqrt PI))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity` `add-cube-cbrt`
35×	`sqrt-prod`
22×	`associate-l`
11×	`add-cbrt-cube`
9×	`add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 125

Calls

4 calls:

Slowest

34.0ms	(* (/ (sqrt 2) (exp 6)) (sqrt PI))
6.0ms	(/ (sqrt 2) (exp 6))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(/ (sqrt 2) (exp 6))
0.0ms	(* (/ (sqrt 2) (exp 6)) (sqrt PI))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify517.0ms

Counts: 155 → 129

prune3.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch12.0ms

end0.0ms

sample46.0s

Algorithm

intervals

Results

17.3s	3917×	body	10240	exit
11.1s	3410×	body	1280	valid
6.2s	2522×	body	640	valid
4.3s	1565×	body	1280	nan
2.4s	1231×	body	640	nan
2.2s	1231×	body	320	valid
915.0ms	598×	body	320	nan
572.0ms	590×	body	160	valid
376.0ms	309×	body	160	nan
223.0ms	336×	body	80	valid
120.0ms	301×	body	80	nan