Details

sample1.9s

Algorithm

intervals

Results

479.0ms	120×	body	10240	exit
393.0ms	108×	body	1280	valid
222.0ms	84×	body	640	valid
118.0ms	48×	body	1280	nan
62.0ms	31×	body	640	nan
57.0ms	37×	body	320	valid
35.0ms	24×	body	320	nan
20.0ms	21×	body	160	valid
6.0ms	11×	body	80	valid
6.0ms	6×	body	160	nan
5.0ms	11×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	2895
2	462
1	140
0	55

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize155.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (exp (- (- 0.5) (- z -6))) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (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	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite15.3s

Algorithm

rewrite-expression-head

Rules

1300×	`frac-add`
374×	`flip3-+` `flip-+`
332×	`associate-*l/`
329×	`frac-times`
167×	`associate-*r/` `pow-sub`
166×	`exp-diff`
164×	`*-un-lft-identity`
86×	`associate-l`
77×	`add-sqr-sqrt`
68×	`prod-diff`
53×	`exp-sum`
43×	`add-cube-cbrt`
32×	`times-frac`
30×	`distribute-lft-out`
26×	`distribute-lft-out--`
21×	`unpow-prod-up`
20×	`add-exp-log`
16×	`difference-of-squares`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube` `prod-exp`
12×	`pow1`
9×	`add-log-exp`
8×	`fma-def`
7×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`neg-mul-1` `associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `unswap-sqr`
2×	`pow-to-exp` `sub-neg` `sqrt-pow1` `pow-exp` `*-commutative` `sqrt-prod` `associate--r-` `sqr-pow`
1×	`+-commutative` `associate-+l+` `pow1/2`

Counts

4 → 513

Calls

4 calls:

14.8s	(* (exp (- (- 0.5) (- z -6))) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))))
291.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
114.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
10.0ms	(sqrt (* PI 2))

series1.3s

Counts

4 → 10

Calls

4 calls:

816.0ms	(* (exp (- (- 0.5) (- z -6))) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))))
98.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
422.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify9.3s

Counts

523 → 523

Iterations

Iter	Nodes
done	5000
0	1651

prune14.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize204.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

133.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))

series410.0ms

Counts

4 → 6

Calls

4 calls:

409.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1594
1	418
0	162

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize185.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
1.0b	(* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI))
1.0b	(* (sqrt 2) (* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI)))
1.0b	(sqrt PI)

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
32×	`times-frac`
31×	`associate-l`
28×	`add-sqr-sqrt` `distribute-lft-out`
23×	`add-cube-cbrt`
22×	`distribute-neg-in` `exp-sum`
18×	`prod-diff`
12×	`pow1` `distribute-lft-out--`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
10×	`sqrt-prod`
9×	`add-exp-log` `add-log-exp`
8×	`fma-def`
7×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `frac-add` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sum-log`
2×	`neg-sub0` `exp-neg` `sub-neg` `flip3-+` `exp-diff` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

4 → 128

Calls

4 calls:

260.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
42.0ms	(* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI))
58.0ms	(* (sqrt 2) (* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI)))
2.0ms	(sqrt PI)

series881.0ms

Counts

4 → 10

Calls

4 calls:

103.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
281.0ms	(* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI))
496.0ms	(* (sqrt 2) (* (exp (- (* (log (+ z 6.5)) (- 0.5 z)))) (sqrt PI)))
0.0ms	(sqrt PI)

simplify3.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	4360
1	907
0	322

prune2.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize172.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (exp -6) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (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	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite15.1s

Algorithm

rewrite-expression-head

Rules

652×	`frac-add`
188×	`flip3-+` `flip-+`
166×	`associate-l/` `associate-r/`
119×	`*-un-lft-identity`
84×	`pow-sub`
82×	`frac-times`
33×	`associate-l`
32×	`add-sqr-sqrt` `times-frac`
30×	`distribute-lft-out`
21×	`unpow-prod-up`
20×	`add-exp-log`
18×	`prod-diff` `add-cube-cbrt`
16×	`distribute-lft-out--`
15×	`add-cbrt-cube` `prod-exp`
12×	`pow1`
9×	`add-log-exp`
8×	`fma-def`
7×	`cbrt-unprod`
6×	`unpow-prod-down` `difference-of-squares`
5×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `*-commutative` `sqrt-prod` `sqr-pow`
1×	`+-commutative` `associate-+l+` `sub-neg` `pow1/2` `associate--r-`

Counts

4 → 294

Calls

4 calls:

14.7s	(* (exp -6) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))))
228.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
115.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
8.0ms	(sqrt (* PI 2))

series1.4s

Counts

4 → 10

Calls

4 calls:

844.0ms	(* (exp -6) (* (+ (+ (+ (+ (/ -176.6150291621406 (- z -3)) (/ -1259.1392167224028 (+ 1 z))) (+ (/ 771.3234287776531 (+ z 2)) (+ 0.9999999999998099 (/ 676.5203681218851 z)))) (/ 12.507343278686905 (- z -4))) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))) (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))))
119.0ms	(+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (- z -7))) (/ -0.13857109526572012 (+ z 5)))
404.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify5.6s

Counts

304 → 304

Iterations

Iter	Nodes
done	5000
1	4286
0	1115

prune8.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	76
1	76
0	57

end0.0ms

sample47.6s

Algorithm

intervals

Results

16.6s	3945×	body	10240	exit
12.0s	3332×	body	1280	valid
5.4s	2548×	body	640	valid
4.5s	1500×	body	1280	nan
3.8s	1357×	body	640	nan
2.3s	1232×	body	320	valid
1.0s	625×	body	320	nan
681.0ms	622×	body	160	valid
349.0ms	309×	body	160	nan
209.0ms	353×	body	80	valid
115.0ms	282×	body	80	nan