Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
7.0ms	25×	body	1280	valid
3.0ms	113×	body	80	nan
3.0ms	21×	body	640	valid
2.0ms	14×	body	1280	nan
2.0ms	19×	body	320	valid
1.0ms	9×	body	640	nan
1.0ms	8×	body	320	nan
0.0ms	6×	body	160	valid
0.0ms	1×	body	160	nan

simplify82.0ms

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	58	12
5	63	12
6	71	12
7	86	12
8	114	12
9	127	12
10	129	12
done	129	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize9.0ms

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))
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite108.0ms

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:

25.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(/ (- x y) (- 1.0 y))
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
30.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
39.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.1s

Counts

239 → 239

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	390	8619
1	974	7647
2	2762	5742
done	5001	5727

prune463.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(cbrt (- 1.0 y))
5.6b	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
12.2b	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

25556×	`times-frac`
20709×	`add-sqr-sqrt`
20585×	`*-un-lft-identity`
15974×	`cbrt-prod`
11133×	`add-cube-cbrt`
8994×	`prod-diff`
4754×	`difference-of-squares`
4726×	`distribute-lft-out--`
442×	`cbrt-div`
438×	`associate-/r/`
223×	`flip3--` `flip--`
219×	`div-inv`
19×	`log-prod`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `div-sub`
2×	`log-div` `pow1/3`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 9094

Calls

4 calls:

4.0ms	(cbrt (- 1.0 y))
2.0ms	(cbrt (- 1.0 y))
1.4s	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
1.5s	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (- 1.0 y))
90.0ms	(cbrt (- 1.0 y))
85.0ms	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
60.0ms	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

simplify6.4s

Counts

9106 → 9106

Iterations

Useful iterations: 0 (2.4s)

Iter	Nodes	Cost
0	13837	1265809
done	13837	1265809

prune33.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
0.3b	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
93×	`prod-diff`
77×	`times-frac`
76×	`add-cube-cbrt`
40×	`distribute-lft-out--`
38×	`difference-of-squares`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
10×	`pow1`
7×	`flip3--` `flip--`
6×	`add-exp-log` `log-prod` `associate-/r/` `add-log-exp`
5×	`log-pow` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `div-inv`
2×	`cube-mult` `log-div` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `associate--r-` `rem-cube-cbrt`

Counts

4 → 197

Calls

4 calls:

6.0ms	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
5.0ms	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
32.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series756.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
519.0ms	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
90.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.4s

Counts

209 → 209

Iterations

Useful iterations: 2 (767.0ms)

Iter	Nodes	Cost
0	513	8628
1	1398	7743
2	4481	5917
done	5000	5917

prune456.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

10.6b	(cbrt (- (* 1.0 1.0) (* y y)))
10.6b	(cbrt (- (* 1.0 1.0) (* y y)))
10.6b	(cbrt (- (* 1.0 1.0) (* y y)))
18.5b	(fma (- (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1) (* (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
2.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
2.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
0.0ms	(fma (- (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1) (* (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1)))

series1.4s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
194.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
203.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
813.0ms	(fma (- (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1) (* (/ (/ (cbrt (+ 1.0 y)) (sqrt (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))) (/ (/ (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (sqrt (cbrt (- 1.0 y)))) 1)))

simplify532.0ms

Counts

70 → 70

Iterations

Useful iterations: done (529.0ms)

Iter	Nodes	Cost
0	172	2221
1	475	2081
2	1544	1671
done	5000	1575

prune579.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes207.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 18.6b

bsearch128.0ms

Steps

Iters	Range		Point
9	25.411711264148785	71488358.87070206	8942476.008787071
9	-155084744.97222546	-15.991254786139553	-152049567.74437964

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	63
1	38	44
done	38	44

end0.0ms

sample988.0ms

Algorithm

intervals

Results

219.0ms	5677×	body	80	valid
161.0ms	833×	body	1280	valid
100.0ms	3682×	body	80	nan
99.0ms	731×	body	640	valid
56.0ms	370×	body	1280	nan
47.0ms	484×	body	320	valid
41.0ms	363×	body	640	nan
19.0ms	230×	body	320	nan
18.0ms	275×	body	160	valid
7.0ms	122×	body	160	nan