Details

sample903.0ms

Algorithm

intervals

Results

283.0ms	116×	body	10240	exit
212.0ms	107×	body	1280	valid
170.0ms	87×	body	640	valid
51.0ms	43×	body	1280	nan
47.0ms	47×	body	640	nan
28.0ms	36×	body	320	valid
17.0ms	26×	body	320	nan
10.0ms	20×	body	160	valid
8.0ms	18×	body	160	nan
2.0ms	9×	body	80	nan
2.0ms	8×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	2879
2	449
1	133
0	55

prune49.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize170.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- z (- (- 1.0 0.5) 7.0)))
1.0b	(/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))
1.0b	(sqrt (* PI 2.0))
1.5b	(* (* (sqrt (* PI 2.0)) (/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

737×	`*-un-lft-identity`
364×	`frac-add`
331×	`add-sqr-sqrt`
294×	`exp-sum`
288×	`times-frac`
252×	`prod-diff`
207×	`distribute-lft-out--`
195×	`add-cube-cbrt`
175×	`unpow-prod-down`
156×	`distribute-lft-out`
93×	`associate-*r/`
82×	`flip3-+` `flip-+`
68×	`difference-of-squares`
46×	`frac-times`
25×	`unpow-prod-up` `sqr-pow`
24×	`associate-/r*`
20×	`associate-r`
19×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`sub-neg` `associate--r-` `add-log-exp`
12×	`pow1` `associate-/l*`
9×	`prod-exp`
7×	`exp-prod`
6×	`diff-log` `div-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `rem-exp-log`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `exp-diff` `pow-exp`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-l` `associate-l/` `associate-/r/` `-commutative` `associate-+l-` `sqrt-prod` `div-inv` `pow-sub` `associate-/l/`

Counts

4 → 533

Calls

4 calls:

265.0ms	(exp (- z (- (- 1.0 0.5) 7.0)))
885.0ms	(/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))
7.0ms	(sqrt (* PI 2.0))
1.1m	(* (* (sqrt (* PI 2.0)) (/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))

series1.2s

Counts

4 → 10

Calls

4 calls:

22.0ms	(exp (- z (- (- 1.0 0.5) 7.0)))
264.0ms	(/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))
0.0ms	(sqrt (* PI 2.0))
909.0ms	(* (* (sqrt (* PI 2.0)) (/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))

simplify2.0s

Counts

543 → 543

Iterations

Iter	Nodes
done	5000
1	4648
0	1223

prune9.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize278.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (sqrt 2.0) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI)))
1.2b	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
49×	`add-exp-log`
42×	`sqrt-prod`
26×	`prod-exp`
20×	`add-cbrt-cube`
13×	`pow-exp`
12×	`div-exp` `associate-/l*`
10×	`associate-/r*`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `associate-l`
4×	`expm1-log1p-u` `pow-to-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `pow-prod-down` `associate-/r/` `*-commutative`

Counts

4 → 163

Calls

4 calls:

1.0ms	(sqrt PI)
11.0ms	(/ (sqrt 2.0) (exp 6.5))
50.0ms	(* (sqrt 2.0) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI)))
14.0ms	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

series526.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (sqrt 2.0) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI)))
526.0ms	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

simplify1.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	2843
1	706
0	293

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize252.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.2b	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-sqr-sqrt`
162×	`times-frac`
156×	`unpow-prod-down`
103×	`*-un-lft-identity`
87×	`associate-l`
85×	`add-cube-cbrt`
80×	`add-exp-log`
60×	`sqrt-prod`
54×	`unswap-sqr`
39×	`pow-exp`
37×	`prod-exp`
30×	`sqr-pow`
23×	`div-exp`
19×	`add-cbrt-cube`
18×	`associate-r`
12×	`pow-to-exp`
11×	`div-inv`
9×	`rec-exp` `1-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow1` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`clear-num` `frac-2neg` `associate-/r/`

Counts

4 → 302

Calls

4 calls:

44.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
39.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
40.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
13.0ms	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

series413.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
413.0ms	(/ (sqrt 2.0) (/ (exp 6.5) (* z (log 6.5))))

simplify1.0s

Counts

308 → 308

Iterations

Iter	Nodes
done	5002
2	2921
1	753
0	322

prune4.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize233.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0))))
1.0b	(* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))
1.4b	(/ (* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))) (exp (- z (- (- 1.0 0.5) 7.0))))

rewrite1.1m

Algorithm

rewrite-expression-head

Rules

848×	`frac-add`
235×	`associate-*l/`
212×	`flip3-+` `flip-+`
177×	`*-un-lft-identity`
119×	`associate-+r-` `pow-sub`
117×	`associate-/l/`
116×	`frac-times`
94×	`distribute-lft-out`
45×	`add-sqr-sqrt`
42×	`exp-sum`
36×	`prod-diff`
34×	`associate-l`
30×	`add-exp-log`
28×	`add-cube-cbrt`
24×	`associate-/r*` `times-frac`
20×	`add-cbrt-cube` `distribute-lft-out--`
17×	`prod-exp`
9×	`pow1`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`difference-of-squares`
5×	`div-exp` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-exp` `unswap-sqr`
2×	`sub-neg` `sqrt-pow1` `pow-prod-down` `associate-r/` `-commutative` `sqrt-prod` `associate--r-` `sqr-pow`
1×	`unpow-prod-up` `clear-num` `frac-2neg` `pow1/2` `exp-diff` `associate-/r/` `div-inv` `associate-/l*`

Counts

4 → 391

Calls

4 calls:

45.2s	(* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0))))
348.0ms	(* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))
4.0ms	(sqrt (* PI 2.0))
19.6s	(/ (* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))) (exp (- z (- (- 1.0 0.5) 7.0))))

series1.4s

Counts

4 → 10

Calls

4 calls:

483.0ms	(* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0))))
270.0ms	(* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))
623.0ms	(/ (* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))) (exp (- z (- (- 1.0 0.5) 7.0))))

simplify969.0ms

Counts

401 → 401

Iterations

Iter	Nodes
done	5001
1	4220
0	1105

prune8.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	74
1	74
0	55

end0.0ms

sample23.3s

Algorithm

intervals

Results

8.7s	3944×	body	10240	exit
5.8s	3417×	body	1280	valid
2.5s	2467×	body	640	valid
1.9s	1491×	body	1280	nan
1.7s	1230×	body	320	valid
1.1s	1318×	body	640	nan
424.0ms	642×	body	320	nan
395.0ms	638×	body	160	valid
178.0ms	325×	body	160	nan
93.0ms	347×	body	80	valid
79.0ms	321×	body	80	nan