Details

sample112.0ms

Algorithm

intervals

Results

42.0ms	61×	body	1280	valid
16.0ms	39×	body	640	valid
11.0ms	140×	body	80	valid
8.0ms	24×	body	160	valid
8.0ms	27×	body	320	valid
5.0ms	89×	body	80	nan

simplify1.4s

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	150	9
5	501	9
6	2070	9
done	5000	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
3.4b	(pow (/ x (+ x y)) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

16.0ms	(/ x (+ x y))
13.0ms	(pow (/ x (+ x y)) x)

series400.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(/ x (+ x y))
325.0ms	(pow (/ x (+ x y)) x)

simplify946.0ms

Counts

76 → 76

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	133	864
1	423	808
2	1598	782
done	5001	781

prune189.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.5b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
25.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
27.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

310.0ms	(cbrt x)
266.0ms	(cbrt x)
375.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
338.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.7s

Counts

136 → 136

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	301	2387
1	981	2215
2	3139	2077
done	5002	2023

prune604.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
4.1b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
43.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
14.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

338.0ms	(cbrt x)
249.0ms	(cbrt x)
375.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
90.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.2s

Counts

164 → 164

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	280	2535
1	808	2361
2	2494	2285
done	5000	2279

prune760.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ (exp (- y)) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

19.0ms

(/ (exp (- y)) x)

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(/ (exp (- y)) x)

simplify2.2s

Counts

34 → 34

Iterations

Useful iterations: 3 (616.0ms)

Iter	Nodes	Cost
0	66	311
1	128	300
2	473	282
3	3443	278
done	5001	278

prune69.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.3b

bsearch115.0ms

Steps

Iters	Range		Point
11	6.345396050147081e-21	1.4124627081995123	1.3959735401437345
9	-426686223388.6693	-1545395.1018140654	-1860105.1392682174

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	43
1	30	39
done	30	39

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1497×	body	1280	valid
614.0ms	1439×	body	640	valid
395.0ms	4941×	body	80	valid
242.0ms	827×	body	320	valid
238.0ms	3064×	body	80	nan
121.0ms	474×	body	160	valid