Details

sample3.1s

Algorithm

intervals

Results

2.0s	111×	body	10240	exit
581.0ms	258×	body	80	valid
180.0ms	43×	body	1280	nan
136.0ms	41×	body	640	nan
20.0ms	12×	body	320	nan
9.0ms	13×	body	80	nan
8.0ms	7×	body	160	nan

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4112
2	625
1	155
0	60

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize161.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0s

Algorithm

rewrite-expression-head

Rules

281×	`*-un-lft-identity`
141×	`distribute-lft-out`
110×	`add-log-exp`
103×	`frac-add`
87×	`times-frac`
85×	`sum-log`
45×	`flip3-+` `flip-+`
35×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`fma-def`
25×	`unpow-prod-down`
19×	`distribute-lft-out--`
11×	`exp-sum`
10×	`associate-/l*`
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` `sqrt-pow1` `div-inv` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `unsub-neg` `pow-prod-down` `pow-exp` `associate-+l-` `sqrt-prod`

Counts

4 → 237

Calls

4 calls:

12.5s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
211.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
307.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
9.0ms	(sqrt (* 2 PI))

series458.0ms

Counts

4 → 10

Calls

4 calls:

186.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
214.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
58.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify4.2s

Counts

247 → 247

Iterations

Iter	Nodes
done	5000
1	1993
0	602

prune4.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize302.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.5s

Algorithm

rewrite-expression-head

Rules

344×	`*-un-lft-identity`
110×	`distribute-lft-out`
96×	`times-frac`
48×	`distribute-lft-out--`
27×	`frac-add`
22×	`swap-sqr`
20×	`unpow-prod-down` `cube-prod`
19×	`flip3-+` `flip-+`
16×	`add-sqr-sqrt` `pow1`
15×	`cube-div`
14×	`add-cube-cbrt`
9×	`frac-times`
8×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
6×	`pow-unpow`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `unpow3` `pow-prod-down` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow1/2` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

4 → 183

Calls

4 calls:

285.0ms	(* (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
8.2s	(pow (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))) 3)
67.0ms	(pow (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) 3)
8.0ms	(sqrt (* 2 PI))

series379.0ms

Counts

4 → 10

Calls

4 calls:

95.0ms	(* (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))))
165.0ms	(pow (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))) 3)
118.0ms	(pow (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) 3)
0.0ms	(sqrt (* 2 PI))

simplify3.1s

Counts

193 → 193

Iterations

Iter	Nodes
done	5003
1	1529
0	360

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize200.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.4s

Algorithm

rewrite-expression-head

Rules

287×	`*-un-lft-identity`
147×	`distribute-lft-out`
110×	`add-log-exp`
103×	`frac-add`
85×	`sum-log`
51×	`flip3-+` `flip-+`
47×	`times-frac`
36×	`cbrt-prod`
30×	`add-sqr-sqrt`
29×	`fma-def`
22×	`add-cube-cbrt` `distribute-lft-out--`
14×	`pow1` `swap-sqr`
12×	`cbrt-div`
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` `sqrt-pow1` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `associate-+l+` `associate-+r+` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `div-inv`

Counts

4 → 225

Calls

4 calls:

13.0s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
302.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
144.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
4.0ms	(sqrt (* 2 PI))

series437.0ms

Counts

4 → 10

Calls

4 calls:

200.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
69.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
168.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify4.0s

Counts

235 → 235

Iterations

Iter	Nodes
done	5002
1	1867
0	535

prune4.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize211.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.1s

Algorithm

rewrite-expression-head

Rules

288×	`*-un-lft-identity`
147×	`distribute-lft-out`
110×	`add-log-exp`
103×	`frac-add`
85×	`sum-log`
51×	`flip3-+` `flip-+`
47×	`times-frac`
36×	`cbrt-prod`
32×	`add-sqr-sqrt`
29×	`fma-def`
23×	`add-cube-cbrt`
22×	`distribute-lft-out--`
14×	`swap-sqr`
12×	`pow1` `cbrt-div`
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×	`sqrt-prod`
2×	`+-commutative` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `associate-+l+` `associate-+r+` `sqrt-pow1` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 227

Calls

4 calls:

12.6s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
278.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
150.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
3.0ms	(sqrt PI)

series393.0ms

Counts

4 → 10

Calls

4 calls:

189.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
64.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
139.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
0.0ms	(sqrt PI)

simplify3.6s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
1	1847
0	528

prune4.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes250.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify53.0ms

Iterations

Iter	Nodes
done	87
1	87
0	66

end0.0ms

sample1.4m

Algorithm

intervals

Results

1.1m	3678×	body	10240	exit
6.4s	1401×	body	1280	nan
6.2s	8091×	body	80	valid
3.2s	1181×	body	640	nan
1.7s	601×	body	320	nan
393.0ms	319×	body	160	nan
162.0ms	287×	body	80	nan