Details

sample3.0s

Algorithm

intervals

Results

2.6s	127×	body	10240	exit
145.0ms	257×	body	80	valid
127.0ms	47×	body	1280	nan
69.0ms	41×	body	640	nan
26.0ms	25×	body	320	nan
5.0ms	7×	body	160	nan
3.0ms	8×	body	80	nan

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
3	4020
2	623
1	155
0	60

prune74.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize210.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(sqrt (* 2 PI))

rewrite13.6s

Algorithm

rewrite-expression-head

Rules

217×	`frac-add`
201×	`*-un-lft-identity`
121×	`add-log-exp`
114×	`distribute-lft-out`
94×	`sum-log`
56×	`flip3-+` `flip-+`
32×	`times-frac`
16×	`distribute-lft-out--`
7×	`pow1`
4×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`+-commutative`
2×	`associate-+l+` `sqrt-pow1`
1×	`associate-+r+` `pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 166

Calls

4 calls:

95.0ms	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
562.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
12.9s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
7.0ms	(sqrt (* 2 PI))

series390.0ms

Counts

4 → 10

Calls

4 calls:

60.0ms	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
112.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
217.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
0.0ms	(sqrt (* 2 PI))

simplify5.4s

Counts

176 → 176

Iterations

Iter	Nodes
done	5002
1	2189
0	583

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize133.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(sqrt PI)

rewrite12.0s

Algorithm

rewrite-expression-head

Rules

217×	`frac-add`
202×	`*-un-lft-identity`
121×	`add-log-exp`
114×	`distribute-lft-out`
94×	`sum-log`
56×	`flip3-+` `flip-+`
32×	`times-frac`
16×	`distribute-lft-out--`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`+-commutative` `sqrt-prod`
2×	`associate-+l+`
1×	`rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 168

Calls

4 calls:

95.0ms	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
566.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
11.3s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0ms	(sqrt PI)

series439.0ms

Counts

4 → 10

Calls

4 calls:

87.0ms	(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
104.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
247.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
0.0ms	(sqrt PI)

simplify5.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5003
1	2155
0	572

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize442.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))))
1.0b	(pow (/ 771.3234287776531 (- 3 z)) 3)
1.0b	(sqrt PI)
1.0b	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) 3)

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
30×	`times-frac`
25×	`unpow-prod-down` `cube-prod`
14×	`pow1`
10×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`pow-unpow` `swap-sqr` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times` `associate-r` `associate-l` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`cube-div` `pow-exp` `sqrt-prod` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `flip3--` `unpow3` `associate-l/` `associate-r/` `div-inv` `flip--` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

223.0ms	(* (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))))
20.0ms	(pow (/ 771.3234287776531 (- 3 z)) 3)
1.0ms	(sqrt PI)
40.0ms	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) 3)

series243.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(* (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))))
98.0ms	(pow (/ 771.3234287776531 (- 3 z)) 3)
0.0ms	(sqrt PI)
74.0ms	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) 3)

simplify2.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5020
2	3883
1	1097
0	305

prune4.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize422.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
1.0b	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
1.0b	(sqrt (* 2 PI))
1.5b	(* (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))))

rewrite20.1s

Algorithm

rewrite-expression-head

Rules

1332×	`*-un-lft-identity`
432×	`times-frac` `distribute-lft-out`
216×	`distribute-lft-out--`
111×	`swap-sqr`
88×	`frac-add`
64×	`flip3-+` `flip-+`
57×	`frac-times`
28×	`pow1`
25×	`associate-r` `associate-l`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`associate-l/` `associate-r/`
10×	`add-cbrt-cube` `add-exp-log`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-pow1`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 313

Calls

4 calls:

8.6s	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
8.4s	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
6.0ms	(sqrt (* 2 PI))
3.1s	(* (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))))

series386.0ms

Counts

4 → 10

Calls

4 calls:

114.0ms	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
120.0ms	(* (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))) (+ (+ 0.9999999999998099 (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))) (/ 676.5203681218851 (- 1 z))))
0.0ms	(sqrt (* 2 PI))
150.0ms	(* (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (/ 9.984369578019572e-06 (- 7 z))))

simplify3.6s

Counts

323 → 323

Iterations

Iter	Nodes
done	5001
1	1310
0	348

prune5.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes590.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify55.0ms

Iterations

Iter	Nodes
done	115
1	115
0	82

end0.0ms

sample1.3m

Algorithm

intervals

Results

1.1m	3824×	body	10240	exit
4.5s	8082×	body	80	valid
4.1s	1443×	body	1280	nan
2.6s	1179×	body	640	nan
1.2s	591×	body	320	nan
300.0ms	309×	body	160	nan
133.0ms	280×	body	80	nan