Details

sample64.0ms

Algorithm

intervals

Results

14.0ms	189×	body	80	valid
8.0ms	28×	body	640	valid
7.0ms	133×	body	80	nan
6.0ms	18×	body	1280	valid
4.0ms	13×	body	1280	nan
3.0ms	15×	body	320	valid
1.0ms	7×	body	640	nan
1.0ms	6×	body	160	valid
1.0ms	3×	body	320	nan
0.0ms	1×	body	160	nan

simplify154.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	54	12
5	62	12
6	70	12
7	85	12
8	103	12
9	116	12
done	116	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
2.2b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

41.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
32.0ms	(/ (- x y) (- 1.0 y))
72.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
78.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
56.0ms	(/ (- x y) (- 1.0 y))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
103.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.1s

Counts

239 → 239

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	390	8619
1	978	7647
2	2696	5742
done	5000	4742

prune734.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cbrt (- 1.0 y)) 3)
0.2b	(pow (cbrt (- 1.0 y)) 3)
2.8b	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
10.4b	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

rewrite8.9s

Algorithm

rewrite-expression-head

Rules

2731×	`add-sqr-sqrt`
2645×	`*-un-lft-identity`
2088×	`prod-diff`
2016×	`times-frac`
1648×	`cbrt-prod`
1464×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
622×	`difference-of-squares`
584×	`distribute-lft-out--`
222×	`sqr-pow`
209×	`cube-mult` `unpow3`
40×	`cube-div` `cbrt-div`
36×	`associate-/r/`
24×	`flip3--` `flip--`
18×	`fma-neg` `div-inv`
10×	`distribute-lft-out`
9×	`log-prod`
8×	`log-div` `frac-add`
7×	`pow1` `add-exp-log`
6×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `distribute-rgt-neg-in` `pow1/3` `pow-exp` `distribute-neg-frac` `rem-cube-cbrt`
1×	`sub-neg` `diff-log` `div-sub` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 2268

Calls

4 calls:

13.0ms	(pow (cbrt (- 1.0 y)) 3)
10.0ms	(pow (cbrt (- 1.0 y)) 3)
8.1s	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
353.0ms	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

series964.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(pow (cbrt (- 1.0 y)) 3)
376.0ms	(pow (cbrt (- 1.0 y)) 3)
138.0ms	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
78.0ms	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

simplify2.2s

Counts

2280 → 2280

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1304	187609
1	2919	133115
done	5000	68623

prune868.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.2b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

46.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
47.0ms	(/ (- x y) (- 1.0 y))
119.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
59.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
68.0ms	(/ (- x y) (- 1.0 y))
215.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
89.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.9s

Counts

260 → 260

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	432	8789
1	1066	8133
2	2916	6364
done	5001	5518

prune880.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.2b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-sqr-sqrt`
266×	`*-un-lft-identity`
186×	`prod-diff`
154×	`times-frac`
138×	`add-cube-cbrt`
68×	`difference-of-squares`
64×	`distribute-lft-out--`
18×	`log-prod`
12×	`sqrt-prod` `associate-/r/`
10×	`flip3--` `flip--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `log-pow` `div-inv`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 276

Calls

4 calls:

85.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
44.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
77.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
70.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
189.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
185.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify1.6s

Counts

288 → 288

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	323	13254
1	767	12138
2	2021	8744
done	5000	7054

prune821.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes219.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 17.4b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	63
1	33	63
done	33	63

end0.0ms

sample2.7s

Algorithm

intervals

Results

515.0ms	455×	body	320	valid
462.0ms	5631×	body	80	valid
344.0ms	870×	body	1280	valid
320.0ms	3620×	body	80	nan
260.0ms	796×	body	640	valid
210.0ms	366×	body	640	nan
109.0ms	363×	body	1280	nan
39.0ms	224×	body	320	nan
31.0ms	248×	body	160	valid
15.0ms	139×	body	160	nan