Details

sample64.0ms

Algorithm

intervals

Results

16.0ms	18×	body	1280	valid
10.0ms	189×	body	80	valid
6.0ms	28×	body	640	valid
5.0ms	133×	body	80	nan
3.0ms	13×	body	1280	nan
2.0ms	15×	body	320	valid
1.0ms	7×	body	640	nan
1.0ms	6×	body	160	valid
0.0ms	3×	body	320	nan
0.0ms	1×	body	160	nan

simplify106.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))))

rewrite188.0ms

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:

46.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
26.0ms	(/ (- x y) (- 1.0 y))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
53.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
41.0ms	(/ (- x y) (- 1.0 y))
63.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
97.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.7s

Counts

239 → 239

Iterations

Useful iterations: done (1.7s)

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

prune516.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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 (+ (- 1.0 (/ (- 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	(- 1.0 (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

rewrite4.8s

Algorithm

rewrite-expression-head

Rules

497×	`*-un-lft-identity`
495×	`add-sqr-sqrt`
348×	`prod-diff`
336×	`times-frac`
276×	`add-cube-cbrt`
172×	`cbrt-prod`
138×	`unpow-prod-down` `cube-prod`
107×	`difference-of-squares`
104×	`distribute-lft-out--`
18×	`sqr-pow`
17×	`cube-mult` `unpow3`
10×	`cube-div` `cbrt-div` `distribute-lft-out`
9×	`log-prod` `flip3--` `flip--`
8×	`log-div` `frac-add`
7×	`pow1` `add-exp-log`
6×	`pow-unpow` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `fma-neg` `flip-+` `div-inv`
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 → 478

Calls

4 calls:

22.0ms	(pow (cbrt (- 1.0 y)) 3)
21.0ms	(pow (cbrt (- 1.0 y)) 3)
4.6s	(log (+ (- 1.0 (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
112.0ms	(- 1.0 (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(pow (cbrt (- 1.0 y)) 3)
354.0ms	(pow (cbrt (- 1.0 y)) 3)
138.0ms	(log (+ (- 1.0 (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
97.0ms	(- 1.0 (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

simplify1.2s

Counts

490 → 490

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	735	32234
1	1775	24819
done	5000	13229

prune745.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite279.0ms

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:

63.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
34.0ms	(/ (- x y) (- 1.0 y))
78.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
76.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
51.0ms	(/ (- x y) (- 1.0 y))
174.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
90.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify3.3s

Counts

260 → 260

Iterations

Useful iterations: done (3.3s)

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

prune835.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize33.0ms

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)))))

rewrite244.0ms

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:

72.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
52.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series594.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
88.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
208.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
210.0ms	(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

prune771.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes190.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

700.0ms	796×	body	640	valid
468.0ms	5631×	body	80	valid
419.0ms	870×	body	1280	valid
192.0ms	3620×	body	80	nan
160.0ms	455×	body	320	valid
140.0ms	366×	body	640	nan
135.0ms	363×	body	1280	nan
37.0ms	224×	body	320	nan
34.0ms	248×	body	160	valid
16.0ms	139×	body	160	nan