Details

sample59.0ms

Algorithm

intervals

Results

20.0ms	48×	body	1280	valid
11.0ms	45×	body	640	valid
7.0ms	159×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	82×	body	80	nan
1.0ms	6×	body	160	valid

simplify1.3s

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	241	9
6	579	9
7	2884	9
done	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
5.3b	(pow (/ x (+ x y)) x)

rewrite16.0ms

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:

5.0ms	(/ x (+ x y))
8.0ms	(pow (/ x (+ x y)) x)

series285.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ x (+ x y))
244.0ms	(pow (/ x (+ x y)) x)

simplify814.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	133	864
1	319	808
2	1041	780
done	5000	780

prune172.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(* (cbrt (+ x y)) (cbrt (+ x y)))
0.6b	(* (cbrt x) (cbrt x))
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
39×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
24×	`cbrt-div`
23×	`add-cube-cbrt`
21×	`add-exp-log`
19×	`pow1`
15×	`swap-sqr`
13×	`unpow-prod-down` `pow1/3` `associate-r` `associate-l`
12×	`flip3-+` `flip-+`
8×	`frac-times` `associate-/r/` `unswap-sqr`
6×	`prod-exp` `distribute-lft-out`
5×	`pow-exp`
4×	`expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow2` `pow-plus` `*-commutative` `cbrt-unprod`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 143

Calls

4 calls:

1.0ms	(cbrt x)
20.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
6.0ms	(* (cbrt x) (cbrt x))
16.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series876.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt x)
179.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
208.0ms	(* (cbrt x) (cbrt x))
297.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify850.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	228	2149
1	526	1814
2	1920	1729
done	5000	1729

prune478.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

2.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series881.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (+ x y))
180.0ms	(cbrt x)
378.0ms	(cbrt x)
185.0ms	(cbrt x)

simplify720.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	73	384
1	151	361
2	365	335
3	978	322
done	5001	322

prune234.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite7.0ms

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:

6.0ms

(/ (exp (- y)) x)

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(/ (exp (- y)) x)

simplify1.0s

Counts

34 → 34

Iterations

Useful iterations: 3 (228.0ms)

Iter	Nodes	Cost
0	66	311
1	120	300
2	335	280
3	1595	278
done	5000	278

prune72.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

96.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 5.7b

bsearch74.0ms

Steps

Iters	Range		Point
5	2.0587583544234707e-06	6.651833699959797e-06	6.552630352198267e-06
7	-3.430057490437851e+43	-2.7564750964835823e+41	-3.371891914955366e+41

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	49
1	24	45
done	24	45

end0.0ms

sample1.7s

Algorithm

intervals

Results

663.0ms	1582×	body	1280	valid
346.0ms	1425×	body	640	valid
205.0ms	4873×	body	80	valid
125.0ms	812×	body	320	valid
86.0ms	2981×	body	80	nan
43.0ms	453×	body	160	valid