Details

sample2.3s

Algorithm

intervals

Results

1.9s	117×	body	10240	exit
110.0ms	58×	body	1280	nan
108.0ms	260×	body	80	valid
82.0ms	27×	body	640	nan
63.0ms	15×	body	320	nan
8.0ms	12×	body	160	nan
3.0ms	10×	body	80	nan

simplify4.3s

Counts

1 → 1

Iterations

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

prune49.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize211.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
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)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite1.4m

Algorithm

rewrite-expression-head

Rules

385×	`*-un-lft-identity`
241×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
79×	`times-frac`
46×	`flip3-+` `flip-+`
44×	`fma-def`
35×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`unpow-prod-down`
15×	`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+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `unsub-neg` `pow-prod-down` `pow-exp` `associate-+l-` `sqrt-prod`

Counts

4 → 255

Calls

4 calls:

208.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
1.4m	(+ (+ (+ (/ 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)))))) (/ 12.507343278686905 (- 5 z)))
339.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
5.0ms	(sqrt (* 2 PI))

series503.0ms

Counts

4 → 10

Calls

4 calls:

204.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
218.0ms	(+ (+ (+ (/ 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)))))) (/ 12.507343278686905 (- 5 z)))
80.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify4.0s

Counts

265 → 265

Iterations

Iter	Nodes
done	5003
1	2505
0	786

prune4.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize303.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z)))
1.0b	(sqrt (* 2 PI))

rewrite691.0ms

Algorithm

rewrite-expression-head

Rules

294×	`*-un-lft-identity`
154×	`times-frac`
98×	`add-sqr-sqrt`
84×	`distribute-lft-out`
62×	`add-cube-cbrt`
42×	`fma-def`
38×	`distribute-lft-out--`
27×	`swap-sqr`
21×	`associate-r` `associate-l`
16×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r/` `difference-of-squares`
8×	`add-log-exp`
6×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3-+` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--` `unswap-sqr`
2×	`+-commutative` `sum-log` `sqrt-pow1` `pow-prod-down` `frac-add`
1×	`pow2` `frac-times` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod`

Counts

4 → 212

Calls

4 calls:

300.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
347.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
33.0ms	(* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z)))
6.0ms	(sqrt (* 2 PI))

series215.0ms

Counts

4 → 10

Calls

4 calls:

97.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
75.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
42.0ms	(* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z)))
0.0ms	(sqrt (* 2 PI))

simplify2.4s

Counts

222 → 222

Iterations

Iter	Nodes
done	5004
2	2740
1	823
0	270

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize174.0ms

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)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
1.0b	(sqrt (* 2 PI))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

412×	`*-un-lft-identity`
239×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
99×	`times-frac`
67×	`add-sqr-sqrt` `add-cube-cbrt`
46×	`flip3-+` `flip-+`
44×	`unpow-prod-up` `fma-def`
36×	`prod-diff`
20×	`unpow-prod-down` `associate-/l*`
14×	`distribute-lft-out--`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u` `sqr-pow`
3×	`associate-/r*` `div-exp`
2×	`+-commutative` `sqrt-pow1` `associate-/r/` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `pow1/2` `pow-prod-down` `pow-exp` `sqrt-prod` `pow-sub` `associate-/l/`

Counts

4 → 281

Calls

4 calls:

1.2m	(+ (+ (+ (/ 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)))))) (/ 12.507343278686905 (- 5 z)))
279.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
58.0ms	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
4.0ms	(sqrt (* 2 PI))

series399.0ms

Counts

4 → 10

Calls

4 calls:

163.0ms	(+ (+ (+ (/ 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)))))) (/ 12.507343278686905 (- 5 z)))
52.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
183.0ms	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
0.0ms	(sqrt (* 2 PI))

simplify3.2s

Counts

291 → 291

Iterations

Iter	Nodes
done	5002
1	2635
0	841

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize137.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2))))
1.0b	(fma (/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2)))) (/ (sqrt 771.3234287776531) (cbrt (+ (- 1 z) 2))) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
1.0b	(sqrt (* 2 PI))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
66×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
44×	`unpow-prod-up`
36×	`prod-diff`
26×	`associate-/l*`
20×	`unpow-prod-down`
12×	`cbrt-div`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`associate-/r/` `distribute-lft-out`
7×	`pow1` `sqrt-prod`
6×	`flip3-+` `flip-+`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `sub-neg` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `associate-l/` `associate-r/` `div-inv`
1×	`pow-to-exp` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `fma-udef` `pow-sub` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

34.0ms	(/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2))))
0.0ms	(fma (/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2)))) (/ (sqrt 771.3234287776531) (cbrt (+ (- 1 z) 2))) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
51.0ms	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
8.0ms	(sqrt (* 2 PI))

series465.0ms

Counts

4 → 10

Calls

4 calls:

74.0ms	(/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2))))
211.0ms	(fma (/ (sqrt 771.3234287776531) (* (cbrt (+ (- 1 z) 2)) (cbrt (+ (- 1 z) 2)))) (/ (sqrt 771.3234287776531) (cbrt (+ (- 1 z) 2))) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
180.0ms	(/ (pow (+ 0.5 (- 7 z)) (- 0.5 z)) (exp 7))
0.0ms	(sqrt (* 2 PI))

simplify1.7s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	2622
1	948
0	421

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes161.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	80
1	80
0	62

end0.0ms

sample53.5s

Algorithm

intervals

Results

44.2s	3905×	body	10240	exit
3.7s	1533×	body	1280	nan
2.7s	8086×	body	80	valid
1.9s	1234×	body	640	nan
556.0ms	632×	body	320	nan
167.0ms	328×	body	160	nan
61.0ms	293×	body	80	nan