Details

sample118.0ms

Algorithm

intervals

Results

42.0ms	47×	body	1280	valid
21.0ms	43×	body	640	valid
14.0ms	160×	body	80	valid
8.0ms	25×	body	320	valid
7.0ms	109×	body	80	nan
3.0ms	16×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1961
5	488
4	149
3	52
2	24
1	15
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ y x))
0.0b	(/ (pow (/ x (+ y x)) x) x)
6.6b	(pow (/ x (+ y x)) x)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`associate-/r*` `add-cbrt-cube` `div-exp` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

9.0ms	(/ x (+ y x))
39.0ms	(/ (pow (/ x (+ y x)) x) x)
24.0ms	(pow (/ x (+ y x)) x)

series669.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ x (+ y x))
229.0ms	(/ (pow (/ x (+ y x)) x) x)
395.0ms	(pow (/ x (+ y x)) x)

simplify1.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	2829
1	650
0	276

prune895.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(* (cbrt (+ y x)) (cbrt (+ y x)))
0.7b	(pow (/ (cbrt x) (cbrt (+ y x))) x)
1.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

85×	`cbrt-prod`
76×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
61×	`unpow-prod-down`
50×	`add-cube-cbrt`
43×	`times-frac`
26×	`cbrt-div`
24×	`add-exp-log`
20×	`pow1`
15×	`swap-sqr`
13×	`flip3-+` `associate-r` `associate-l` `flip-+`
12×	`pow1/3` `distribute-lft-out`
10×	`associate-/r/`
8×	`frac-times` `unswap-sqr`
7×	`pow-exp`
6×	`pow-unpow` `prod-exp`
5×	`div-exp`
4×	`add-cbrt-cube` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `add-log-exp`
2×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `*-commutative` `cbrt-unprod` `div-inv` `sqr-pow`

Counts

4 → 187

Calls

4 calls:

11.0ms	(* (cbrt x) (cbrt x))
52.0ms	(* (cbrt (+ y x)) (cbrt (+ y x)))
18.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
29.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

301.0ms	(* (cbrt x) (cbrt x))
265.0ms	(* (cbrt (+ y x)) (cbrt (+ y x)))
415.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
393.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

simplify626.0ms

Counts

199 → 199

Iterations

Iter	Nodes
done	5001
1	1157
0	354

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.7b	(pow (/ (cbrt x) (cbrt (+ y x))) x)
2.1b	(log (/ (cbrt x) (cbrt (+ y x))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod` `unpow-prod-down`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `add-cbrt-cube` `associate-/r/` `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 → 144

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
17.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
15.0ms	(log (/ (cbrt x) (cbrt (+ y x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt x)
312.0ms	(cbrt x)
458.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
122.0ms	(log (/ (cbrt x) (cbrt (+ y x))))

simplify1.2s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	2458
1	794
0	274

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.7b	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
0.7b	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
2.1b	(log (/ (cbrt x) (cbrt (+ y x))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

138×	`cbrt-prod`
126×	`*-un-lft-identity` `times-frac`
102×	`unpow-prod-down`
96×	`sqrt-prod`
90×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
18×	`distribute-lft-out`
9×	`pow1` `add-exp-log`
6×	`pow-unpow` `cbrt-div` `pow-pow` `associate-/r/`
4×	`add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `sqrt-pow2` `sqr-pow`
1×	`log-div` `pow1/3` `div-exp` `log-pow`

Counts

4 → 206

Calls

4 calls:

2.0ms	(cbrt x)
38.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
36.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
14.0ms	(log (/ (cbrt x) (cbrt (+ y x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt x)
445.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
424.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ y x)))) x)
128.0ms	(log (/ (cbrt x) (cbrt (+ y x))))

simplify1.3s

Counts

218 → 218

Iterations

Iter	Nodes
done	5000
2	2548
1	875
0	339

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes107.0ms

Accuracy

97.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.1b

bsearch145.0ms

Steps

Iters	Range		Point
9	1.6675236871481135e-12	5.1798647897020696e-05	5.105764663642185e-05
6	-3.812236742374531e+23	-6.2573470230411204e+22	-3.381665497082661e+23

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1478×	body	1280	valid
820.0ms	1550×	body	640	valid
398.0ms	4791×	body	80	valid
280.0ms	826×	body	320	valid
204.0ms	2943×	body	80	nan
85.0ms	480×	body	160	valid