Details

sample1.5s

Algorithm

intervals

Results

585.0ms	129×	body	10240	exit
379.0ms	115×	body	1280	valid
160.0ms	83×	body	640	valid
104.0ms	43×	body	1280	nan
83.0ms	43×	body	640	nan
43.0ms	34×	body	320	valid
27.0ms	22×	body	320	nan
16.0ms	19×	body	160	valid
13.0ms	14×	body	160	nan
4.0ms	9×	body	80	valid
3.0ms	8×	body	80	nan

simplify968.0ms

Counts: 1 → 1

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize164.0ms

Local error

Found 4 expressions with local error:

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)))
0.6b	(* (/ (* (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)))

rewrite23.6s

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

23.3s	(* (/ (* (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)))
180.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
161.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
4.0ms	(sqrt (* PI 2))

series1.7s

Counts

4 → 10

Calls

4 calls:

Slowest

868.0ms	(* (/ (* (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)))
514.0ms	(/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6)))
350.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify4.1s

Counts: 239 → 239

prune8.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize161.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.6b	(* (* (/ (* (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)))
0.0b	(+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1)))

rewrite18.8s

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
128×	`distribute-lft-out`
105×	`frac-add`
54×	`flip3-+` `flip-+`
32×	`associate-r`
27×	`associate-*l/`
24×	`frac-times` `associate-*r/`
23×	`add-sqr-sqrt` `add-exp-log`
20×	`times-frac` `add-cbrt-cube`
18×	`fma-def`
17×	`prod-exp`
16×	`add-cube-cbrt`
12×	`pow1` `associate-l`
9×	`cbrt-unprod`
7×	`unpow-prod-down`
6×	`add-log-exp`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`unswap-sqr`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `pow-exp` `associate-/r/` `*-commutative` `sqrt-prod` `distribute-lft-out--` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `+-commutative` `sum-log` `distribute-lft-in` `pow1/2` `associate-+l-` `div-inv` `pow-sub` `difference-of-squares`

Counts

4 → 189

Calls

4 calls:

Slowest

18.5s	(* (* (/ (* (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)))
225.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
58.0ms	(+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1)))
5.0ms	(sqrt (* PI 2))

series1.6s

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))) (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)))
380.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
66.0ms	(+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1)))
0.0ms	(sqrt (* PI 2))

simplify4.8s

Counts: 199 → 199

prune7.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize175.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (exp (- (+ z 0.5) -6)))))
0.6b	(* (* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (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)))
0.0b	(exp (- (+ z 0.5) -6))

rewrite19.5s

Algorithm

rewrite-expression-head

Rules

559×	`*-un-lft-identity`
347×	`times-frac`
325×	`add-sqr-sqrt`
308×	`sqrt-prod`
240×	`exp-sum`
237×	`associate-l`
213×	`add-cube-cbrt`
208×	`frac-add`
192×	`prod-diff`
185×	`distribute-lft-out`
132×	`unpow-prod-down`
117×	`associate-r`
104×	`flip3-+` `flip-+`
98×	`frac-times`
62×	`add-exp-log`
50×	`associate-*r/`
44×	`distribute-lft-out--`
34×	`add-cbrt-cube`
29×	`associate-*l/`
27×	`sqr-pow`
25×	`prod-exp`
22×	`difference-of-squares`
21×	`unpow-prod-up` `unswap-sqr`
20×	`div-exp`
16×	`sub-neg` `associate--l+`
14×	`pow1`
13×	`cbrt-unprod`
10×	`add-log-exp`
8×	`cbrt-undiv`
6×	`exp-prod`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `insert-posit16` `log1p-expm1-u`
3×	`exp-diff` `rem-exp-log`
2×	`sqrt-pow1` `sqrt-div` `diff-log` `associate-/r/` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `sum-log` `distribute-lft-in` `pow1/2`

Counts

4 → 579

Calls

4 calls:

Slowest

18.7s	(* (* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (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 (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (exp (- (+ z 0.5) -6)))))
89.0ms	(exp (- (+ z 0.5) -6))
7.0ms	(sqrt (* PI 2))

series1.4s

Counts

4 → 10

Calls

4 calls:

Slowest

912.0ms	(* (* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (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)))
520.0ms	(* (/ (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (exp (- (+ z 0.5) -6)))) (/ (sqrt (* PI 2)) (sqrt (exp (- (+ z 0.5) -6)))))
12.0ms	(exp (- (+ z 0.5) -6))
0.0ms	(sqrt (* PI 2))

simplify6.9s

Counts: 589 → 589

prune23.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize210.0ms

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	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`pow1`
12×	`*-un-lft-identity`
11×	`associate-l`
9×	`add-exp-log`
7×	`unpow-prod-down` `add-cube-cbrt`
6×	`sqrt-pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `pow-prod-down` `prod-exp` `unswap-sqr`
2×	`distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-up` `associate-l/` `pow-exp` `-commutative` `associate-+l-` `cbrt-unprod` `distribute-lft-out` `pow-sub` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

Slowest

189.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))

series289.0ms

Counts

4 → 6

Calls

4 calls:

Slowest

289.0ms	(* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify2.8s

Counts: 82 → 82

prune3.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes130.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch14.0ms

end0.0ms

sample47.6s

Algorithm

intervals

Results

17.3s	3994×	body	10240	exit
10.6s	3324×	body	1280	valid
6.4s	2516×	body	640	valid
5.3s	1482×	body	1280	nan
2.5s	1259×	body	640	nan
2.3s	1262×	body	320	valid
1.1s	638×	body	160	valid
892.0ms	598×	body	320	nan
354.0ms	320×	body	160	nan
215.0ms	366×	body	80	valid
118.0ms	294×	body	80	nan