Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	48×	body	1280	valid
12.0ms	45×	body	640	valid
8.0ms	159×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	82×	body	80	nan
1.0ms	6×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	102	9
5	239	9
6	553	9
7	1646	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `associate-/r*` `flip-+` `div-inv`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

5.0ms	(/ x (+ x y))
11.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x y))
79.0ms	(* x (log (/ x (+ x y))))
52.0ms	(log (/ x (+ x y)))

simplify2.5s

Counts

132 → 132

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	173	1644
1	301	1553
2	628	1464
3	1612	1425
4	4830	1422
done	5000	1422

prune290.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 148

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt x)
182.0ms	(cbrt x)
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.1s

Counts

160 → 160

Iterations

Useful iterations: 4 (586.0ms)

Iter	Nodes	Cost
0	177	2306
1	316	2146
2	573	2060
3	1243	1986
4	2666	1982
done	5001	1982

prune582.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
34.1b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
42×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
34×	`cbrt-prod`
33×	`log-prod`
30×	`add-cube-cbrt`
19×	`add-exp-log`
12×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `div-exp` `associate-r` `associate-l` `distribute-lft-out`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`prod-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `log-div` `pow-plus` `associate-/r/` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(* (cbrt x) (cbrt x))
9.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
376.0ms	(cbrt x)
202.0ms	(* (cbrt x) (cbrt x))
71.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

simplify770.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	197	1445
1	380	1330
2	1286	1127
done	5000	1127

prune404.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
1.3b	(expm1 (log1p (cbrt x)))
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))
15.1b	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

75×	`log-prod`
64×	`*-un-lft-identity`
63×	`times-frac`
60×	`cbrt-prod`
46×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`expm1-log1p` `pow1/3` `expm1-udef`

Counts

4 → 125

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(expm1 (log1p (cbrt x)))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
5.0ms	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt x)
306.0ms	(expm1 (log1p (cbrt x)))
76.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
143.0ms	(log (/ (expm1 (log1p (cbrt x))) (cbrt (+ x y))))

simplify1.1s

Counts

137 → 137

Iterations

Useful iterations: 4 (623.0ms)

Iter	Nodes	Cost
0	251	2024
1	434	1749
2	690	1683
3	1358	1621
4	2798	1612
done	5000	1612

prune535.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes71.0ms

Accuracy

10.5% (4.1b remaining)

Error of 5.2b against oracle of 1.1b and baseline of 5.7b

bsearch193.0ms

Steps

Iters	Range		Point
10	2.2283445473129873e+141	2.703506994090381e+152	1.1740213088014818e+142
9	3.9952034404095503e+118	2.258742533603766e+124	5.093209301329398e+119
7	50024088429.266525	12169712469967.395	51088118733.37021

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	113
1	64	113
done	64	113

end0.0ms

sample1.8s

Algorithm

intervals

Results

700.0ms	1582×	body	1280	valid
372.0ms	1425×	body	640	valid
226.0ms	4873×	body	80	valid
136.0ms	812×	body	320	valid
91.0ms	2981×	body	80	nan
48.0ms	453×	body	160	valid