Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	54×	body	1280	valid
9.0ms	46×	body	640	valid
7.0ms	129×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
92.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series643.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(cbrt (+ x 1.0))
312.0ms	(cbrt x)
201.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.4s

Counts

53 → 53

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	131	649
1	312	597
2	928	573
3	3661	539
done	5003	513

prune232.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.0b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`cbrt-prod`
11×	`log-pow`
10×	`exp-prod`
8×	`add-cube-cbrt` `difference-of-squares`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

5.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
139.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
80.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series836.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ x 1.0))
283.0ms	(cbrt x)
223.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
206.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	166	1057
1	371	936
2	1057	887
3	3817	839
done	5000	801

prune358.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.2b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
31×	`cbrt-prod`
12×	`difference-of-squares`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`distribute-lft-out`
3×	`pow-unpow`
2×	`cube-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

73.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
88.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series980.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
138.0ms	(cbrt (+ x 1.0))
316.0ms	(cbrt x)
191.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.7s

Counts

95 → 95

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	255	1596
1	808	1441
2	3261	1368
done	5000	1312

prune435.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3)
0.5b	(cbrt x)
0.5b	(cbrt x)
14.3b	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

97×	`cbrt-div`
84×	`flip3-+` `flip-+`
80×	`cbrt-prod` `associate-*r/`
72×	`associate-/r/`
68×	`unpow-prod-down` `cube-prod`
64×	`*-un-lft-identity` `frac-add`
48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`frac-times`
16×	`associate-*l/`
12×	`distribute-lft-out`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp` `rem-cbrt-cube`

Counts

4 → 194

Calls

4 calls:

77.0ms	(pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
62.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3))

series2.3s

Counts

4 → 12

Calls

4 calls:

843.0ms	(pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3)
308.0ms	(cbrt x)
342.0ms	(cbrt x)
812.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3))

simplify933.0ms

Counts

206 → 206

Iterations

Useful iterations: done (916.0ms)

Iter	Nodes	Cost
0	550	13589
1	1994	11616
done	5001	11327

prune792.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes109.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	26
1	17	26
done	17	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

398.0ms	1742×	body	1280	valid
303.0ms	1242×	body	640	valid
293.0ms	4095×	body	80	valid
73.0ms	613×	body	320	valid
24.0ms	308×	body	160	valid