Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	53×	body	1280	valid
7.0ms	137×	body	80	valid
5.0ms	25×	body	640	valid
5.0ms	33×	body	320	valid
1.0ms	8×	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: 28.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.9b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite70.0ms

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:

8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
58.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series621.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(cbrt (+ x 1.0))
303.0ms	(cbrt x)
211.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify3.8s

Counts

53 → 53

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	131	649
1	290	597
2	672	573
3	1717	521
4	4878	501
done	5000	501

prune213.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.7b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.9b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite219.0ms

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:

8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
129.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
77.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series896.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (+ x 1.0))
281.0ms	(cbrt x)
226.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
254.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.1s

Counts

81 → 81

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	166	1057
1	338	936
2	737	887
3	1819	812
done	5000	783

prune401.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
10.0b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 51

Calls

4 calls:

8.0ms	(cbrt (+ x 1.0))
8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
68.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series844.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (+ x 1.0))
134.0ms	(cbrt (+ x 1.0))
308.0ms	(cbrt x)
268.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.6s

Counts

63 → 63

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	126	993
1	291	945
2	708	866
3	1877	740
done	5001	571

prune342.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
16.3b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`pow3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
107.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

403.0ms	(cbrt (cbrt x))
378.0ms	(cbrt (cbrt x))
375.0ms	(cbrt (cbrt x))
231.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify1.8s

Counts

67 → 67

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	121	1028
1	292	986
2	742	735
3	2117	643
done	5001	631

prune289.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes46.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 30.3b

bsearch129.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	49305.120151597
10	-6045414056204.408	-123.41774798665298	-107349.34060706355

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	30	66
1	38	47
done	38	47

end0.0ms

sample1.2s

Algorithm

intervals

Results

429.0ms	1757×	body	1280	valid
255.0ms	1250×	body	640	valid
193.0ms	4045×	body	80	valid
103.0ms	626×	body	320	valid
24.0ms	322×	body	160	valid