Details

sample1.8s

Algorithm

intervals

Results

688.0ms	102×	body	1280	valid
555.0ms	137×	body	10240	exit
182.0ms	56×	body	1280	nan
134.0ms	78×	body	640	valid
69.0ms	41×	body	640	nan
61.0ms	45×	body	320	valid
27.0ms	27×	body	320	nan
20.0ms	23×	body	160	valid
12.0ms	15×	body	160	nan
5.0ms	9×	body	80	valid
3.0ms	7×	body	80	nan

simplify889.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2125
2	412
1	139
0	55

prune78.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize203.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (/ (* (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)))))
0.9b	(/ (* (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))

rewrite16.4s

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:

16.1s	(* (/ (* (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)))))
167.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
139.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))

series1.9s

Counts

4 → 10

Calls

4 calls:

901.0ms	(* (/ (* (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)))))
583.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
426.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify7.7s

Counts

284 → 284

Iterations

Iter	Nodes
1	4671
0	939

prune12.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (sqrt (* PI 2)) (exp 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)))))
0.7b	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
0.9b	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
1.0b	(sqrt (* PI 2))

rewrite30.2s

Algorithm

rewrite-expression-head

Rules

1332×	`frac-add`
504×	`*-un-lft-identity`
456×	`flip3-+` `flip-+`
341×	`frac-times` `associate-*r/`
293×	`times-frac`
231×	`exp-sum`
224×	`add-sqr-sqrt`
219×	`add-cube-cbrt`
189×	`prod-diff`
173×	`distribute-lft-out`
161×	`associate-l`
145×	`unpow-prod-down`
39×	`add-exp-log`
32×	`add-cbrt-cube`
29×	`unpow-prod-up` `associate-r` `distribute-lft-out--` `sqr-pow`
22×	`prod-exp`
21×	`sub-neg`
17×	`div-exp`
14×	`pow1` `associate-/r*`
12×	`cbrt-unprod`
10×	`associate-/l*`
7×	`cbrt-undiv`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `associate-*l/` `pow-exp` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`sqrt-pow1` `exp-diff` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-+l-` `pow-sub` `associate-/l/`

Counts

4 → 854

Calls

4 calls:

16.7s	(* (/ (sqrt (* PI 2)) (exp 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)))))
13.4s	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
113.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
4.0ms	(sqrt (* PI 2))

series1.8s

Counts

4 → 10

Calls

4 calls:

447.0ms	(* (/ (sqrt (* PI 2)) (exp 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)))))
1.1s	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
265.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
0.0ms	(sqrt (* PI 2))

simplify12.4s

Counts

864 → 864

Iterations

Iter	Nodes
1	6927
0	1648

prune39.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize172.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (sqrt (* PI 2)) (exp 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)))))
0.7b	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
0.9b	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
1.0b	(sqrt (* PI 2))

rewrite30.8s

Algorithm

rewrite-expression-head

Rules

1332×	`frac-add`
456×	`flip3-+` `flip-+`
341×	`frac-times` `associate-*r/`
224×	`*-un-lft-identity`
129×	`distribute-lft-out`
73×	`times-frac`
54×	`add-sqr-sqrt`
52×	`associate-l`
49×	`add-cube-cbrt`
39×	`add-exp-log`
35×	`unpow-prod-down`
32×	`add-cbrt-cube`
29×	`associate-r`
22×	`prod-exp`
17×	`div-exp`
14×	`pow1`
12×	`cbrt-unprod`
10×	`associate-/l*`
7×	`cbrt-undiv` `unpow-prod-up` `distribute-lft-out--` `sqr-pow`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `associate-*l/` `pow-exp` `associate-/r/` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`neg-sub0` `exp-neg` `sqrt-pow1` `exp-diff` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-+l-` `pow-sub` `associate-/l/`

Counts

4 → 625

Calls

4 calls:

17.3s	(* (/ (sqrt (* PI 2)) (exp 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)))))
13.4s	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
104.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
4.0ms	(sqrt (* PI 2))

series1.7s

Counts

4 → 10

Calls

4 calls:

438.0ms	(* (/ (sqrt (* PI 2)) (exp 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)))))
984.0ms	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 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))))))
274.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
0.0ms	(sqrt (* PI 2))

simplify10.5s

Counts

635 → 635

Iterations

Iter	Nodes
1	6548
0	1462

prune31.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (sqrt (* PI 2)) (exp 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)))))
0.7b	(* (/ (pow (+ (- z -6) 0.5) (- z 1)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5))) (* (/ (sqrt (* PI 2)) (exp 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)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5)))
1.0b	(sqrt (* PI 2))

rewrite19.5s

Algorithm

rewrite-expression-head

Rules

2360×	`times-frac`
2244×	`*-un-lft-identity`
1332×	`frac-add`
1179×	`add-sqr-sqrt`
1174×	`add-cube-cbrt`
930×	`unpow-prod-down`
693×	`unpow-prod-up`
641×	`associate-l`
567×	`prod-diff`
487×	`distribute-lft-out`
456×	`flip3-+` `flip-+`
341×	`frac-times` `associate-*r/`
186×	`distribute-lft-out--` `sqr-pow`
144×	`add-exp-log`
98×	`div-exp`
67×	`prod-exp`
63×	`sub-neg`
50×	`add-cbrt-cube`
44×	`div-inv`
31×	`associate-/r*`
29×	`associate-r`
28×	`pow-to-exp` `pow-exp`
20×	`associate-/l*`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
14×	`pow1`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `pow-sub` `associate-/l/`

Counts

4 → 1881

Calls

4 calls:

10.7s	(* (/ (sqrt (* PI 2)) (exp 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)))))
8.6s	(* (/ (pow (+ (- z -6) 0.5) (- z 1)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5))) (* (/ (sqrt (* PI 2)) (exp 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))))))
144.0ms	(/ (pow (+ (- z -6) 0.5) (- z 1)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5)))
4.0ms	(sqrt (* PI 2))

series1.5s

Counts

4 → 10

Calls

4 calls:

311.0ms	(* (/ (sqrt (* PI 2)) (exp 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)))))
808.0ms	(* (/ (pow (+ (- z -6) 0.5) (- z 1)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5))) (* (/ (sqrt (* PI 2)) (exp 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))))))
359.0ms	(/ (pow (+ (- z -6) 0.5) (- z 1)) (/ (exp (- -6)) (pow (+ (- z -6) 0.5) 0.5)))
0.0ms	(sqrt (* PI 2))

simplify9.9s

Counts

1891 → 1891

Iterations

Iter	Nodes
1	9843
0	2405

prune1.0m

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes91.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
2	82
1	82
0	61

end0.0ms

sample31.2s

Algorithm

intervals

Results

11.5s	3891×	body	10240	exit
6.9s	3378×	body	1280	valid
3.7s	2489×	body	640	valid
2.7s	1477×	body	1280	nan
2.3s	1243×	body	640	nan
2.2s	1274×	body	320	valid
555.0ms	605×	body	320	nan
397.0ms	269×	body	80	nan
369.0ms	620×	body	160	valid
206.0ms	307×	body	160	nan
105.0ms	314×	body	80	valid