Details

sample1.3s

Algorithm

intervals

Results

462.0ms	114×	body	10240	exit
294.0ms	103×	body	1280	valid
174.0ms	83×	body	640	valid
100.0ms	34×	body	1280	nan
83.0ms	49×	body	640	nan
57.0ms	18×	body	160	nan
53.0ms	37×	body	320	valid
24.0ms	18×	body	320	nan
18.0ms	21×	body	160	valid
7.0ms	15×	body	80	valid
6.0ms	14×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
3	2125
2	412
1	139
0	55

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize135.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
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))

rewrite17.5s

Algorithm

rewrite-expression-head

Rules

444×	`frac-add`
157×	`*-un-lft-identity`
152×	`flip3-+` `flip-+`
117×	`distribute-lft-out`
68×	`frac-times` `associate-*r/`
32×	`associate-r`
27×	`add-exp-log`
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 → 274

Calls

4 calls:

17.2s	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
131.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
160.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
7.0ms	(sqrt (* PI 2))

series1.9s

Counts

4 → 10

Calls

4 calls:

887.0ms	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
581.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
418.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify7.5s

Counts

284 → 284

Iterations

Iter	Nodes
1	4671
0	939

prune11.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize181.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ z 6.5))
0.4b	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.0b	(* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI))
1.0b	(sqrt PI)

rewrite13.2s

Algorithm

rewrite-expression-head

Rules

444×	`frac-add`
153×	`*-un-lft-identity`
152×	`flip3-+` `flip-+`
116×	`distribute-lft-out`
71×	`associate-*l/`
68×	`frac-times` `associate-*r/`
34×	`associate-r`
27×	`add-cbrt-cube`
21×	`add-exp-log`
16×	`add-sqr-sqrt`
12×	`pow1` `prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
9×	`associate-l`
7×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `exp-prod` `times-frac` `div-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
2×	`exp-sum` `*-commutative` `unswap-sqr` `rem-exp-log`
1×	`distribute-rgt-in` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 257

Calls

4 calls:

20.0ms	(exp (+ z 6.5))
13.0s	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
114.0ms	(* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI))
1.0ms	(sqrt PI)

series1.6s

Counts

4 → 10

Calls

4 calls:

25.0ms	(exp (+ z 6.5))
975.0ms	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
589.0ms	(* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt PI))
0.0ms	(sqrt PI)

simplify6.8s

Counts

267 → 267

Iterations

Iter	Nodes
1	4380
0	881

prune14.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize195.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ z 6.5))
0.4b	(* (* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite14.8s

Algorithm

rewrite-expression-head

Rules

444×	`frac-add`
152×	`flip3-+` `flip-+`
150×	`*-un-lft-identity`
139×	`associate-*l/`
116×	`distribute-lft-out`
68×	`frac-times` `associate-*r/`
28×	`associate-r`
24×	`add-cbrt-cube`
21×	`add-exp-log`
15×	`pow1`
13×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`add-log-exp`
6×	`pow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `rem-exp-log`
1×	`distribute-rgt-in` `sum-log` `distribute-lft-in` `associate-l` `exp-sum` `*-commutative`

Counts

4 → 241

Calls

4 calls:

10.0ms	(exp (+ z 6.5))
14.8s	(* (* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series1.0s

Counts

4 → 8

Calls

4 calls:

20.0ms	(exp (+ z 6.5))
997.0ms	(* (* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify5.3s

Counts

249 → 249

Iterations

Iter	Nodes
1	4277
0	847

prune13.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize174.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
0.3b	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite30.2s

Algorithm

rewrite-expression-head

Rules

666×	`frac-add`
272×	`associate-*r/`
228×	`flip3-+` `flip-+`
150×	`*-un-lft-identity`
115×	`distribute-lft-out`
70×	`associate-*l/`
68×	`frac-times`
38×	`add-cbrt-cube`
32×	`add-exp-log`
29×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
20×	`pow1`
18×	`add-sqr-sqrt` `sqrt-prod`
10×	`associate-l` `add-cube-cbrt`
9×	`pow-prod-down`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`

Counts

4 → 330

Calls

4 calls:

17.1s	(* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
13.0s	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series1.2s

Counts

4 → 8

Calls

4 calls:

293.0ms	(* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
928.0ms	(* (* (/ (* (sqrt 2) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (exp (+ z 6.5))) (sqrt (sqrt PI))) (* (sqrt (sqrt PI)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify5.4s

Counts

338 → 338

Iterations

Iter	Nodes
1	4478
0	941

prune18.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch0.0ms

simplify19.0ms

Iterations

Iter	Nodes
3	88
2	88
1	82
0	59

end0.0ms

sample50.4s

Algorithm

intervals

Results

16.7s	3841×	body	10240	exit
13.0s	3437×	body	1280	valid
6.8s	2408×	body	640	valid
4.4s	1473×	body	1280	nan
3.8s	1206×	body	640	nan
2.5s	1253×	body	320	valid
1.2s	650×	body	320	nan
743.0ms	621×	body	160	valid
347.0ms	313×	body	160	nan
194.0ms	373×	body	80	valid
137.0ms	303×	body	80	nan