Details

sample2.8s

Algorithm

intervals

Results

2.1s	117×	body	10240	exit
214.0ms	260×	body	80	valid
192.0ms	58×	body	1280	nan
108.0ms	27×	body	640	nan
26.0ms	15×	body	320	nan
13.0ms	12×	body	160	nan
5.0ms	10×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4343
2	635
1	155
0	60

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize164.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
1.0b	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
1.0b	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(sqrt (* 2 PI))

rewrite3.1m

Algorithm

rewrite-expression-head

Rules

229×	`*-un-lft-identity`
162×	`frac-add`
140×	`distribute-lft-out`
138×	`add-log-exp`
109×	`sum-log`
55×	`times-frac`
44×	`flip3-+` `flip-+`
35×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`fma-def`
25×	`unpow-prod-down`
11×	`exp-sum`
10×	`associate-/l*`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `div-inv` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `unsub-neg` `pow-prod-down` `pow-exp` `associate-+l-` `sqrt-prod`

Counts

4 → 247

Calls

4 calls:

1.0m	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
178.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
2.1m	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
11.0ms	(sqrt (* 2 PI))

series589.0ms

Counts

4 → 10

Calls

4 calls:

215.0ms	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
176.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
198.0ms	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
0.0ms	(sqrt (* 2 PI))

simplify4.4s

Counts

257 → 257

Iterations

Iter	Nodes
done	5004
1	2149
0	664

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize205.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
1.0b	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))

rewrite2.2m

Algorithm

rewrite-expression-head

Rules

235×	`*-un-lft-identity`
162×	`frac-add`
146×	`distribute-lft-out`
138×	`add-log-exp`
109×	`sum-log`
50×	`flip3-+` `flip-+`
36×	`cbrt-prod`
30×	`add-sqr-sqrt`
29×	`fma-def`
22×	`add-cube-cbrt`
15×	`times-frac`
14×	`pow1` `swap-sqr`
12×	`cbrt-div`
11×	`distribute-lft-out--`
8×	`associate-r` `associate-l`
6×	`pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `associate-+l+` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `div-inv`

Counts

4 → 235

Calls

4 calls:

41.3s	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
1.5m	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
123.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
7.0ms	(sqrt (* 2 PI))

series436.0ms

Counts

4 → 10

Calls

4 calls:

153.0ms	(+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
172.0ms	(+ (/ -176.6150291621406 (+ (- 2 z) 2)) (+ (+ (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))) (/ 12.507343278686905 (+ -1 (- 6 z)))) (/ 771.3234287776531 (- (- 1 z) -2))) (/ -0.13857109526572012 (- 6 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))))
112.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify2.9s

Counts

245 → 245

Iterations

Iter	Nodes
done	5000
1	2028
0	597

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize158.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))) (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))))
1.0b	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
1.0b	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
144×	`frac-times`
120×	`flip3-+` `flip-+`
112×	`*-un-lft-identity`
80×	`cbrt-prod`
48×	`associate-l/` `associate-r/`
44×	`add-sqr-sqrt`
32×	`swap-sqr` `distribute-lft-out`
28×	`pow1`
24×	`add-cube-cbrt`
20×	`associate-r` `associate-l`
18×	`pow1/3`
16×	`distribute-lft-out--`
12×	`unswap-sqr`
10×	`add-exp-log`
7×	`pow-prod-down`
6×	`pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`sqrt-pow1`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 257

Calls

4 calls:

42.0ms	(* (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))) (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))))
81.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
82.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
4.0ms	(sqrt (* 2 PI))

series347.0ms

Counts

4 → 10

Calls

4 calls:

126.0ms	(* (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))) (cbrt (* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))))
109.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
113.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify1.8s

Counts

267 → 267

Iterations

Iter	Nodes
done	5009
3	3523
2	1330
1	589
0	321

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize133.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* 2 PI))
1.5b	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
1.5b	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
1.5b	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
63×	`cbrt-prod`
45×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`distribute-lft-out`
9×	`distribute-lft-out--`
7×	`pow1`
6×	`associate-/r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 113

Calls

4 calls:

5.0ms	(sqrt (* 2 PI))
303.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
11.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
11.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))

series253.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(sqrt (* 2 PI))
83.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
83.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))
87.0ms	(cbrt (/ -176.6150291621406 (+ (- 2 z) 2)))

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5029
3	2490
2	685
1	290
0	143

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes324.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	81
1	81
0	62

end0.0ms

sample1.1m

Algorithm

intervals

Results

53.1s	3905×	body	10240	exit
4.2s	8086×	body	80	valid
4.1s	1533×	body	1280	nan
2.7s	1234×	body	640	nan
1.3s	632×	body	320	nan
413.0ms	293×	body	80	nan
279.0ms	328×	body	160	nan