Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	49×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	9×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite25.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series621.0ms

Counts

3 → 9

Calls

3 calls:

286.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
154.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify676.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (232.0ms)

Iter	Nodes	Cost
0	131	649
1	291	597
2	698	573
3	1808	521
done	5001	521

prune147.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite79.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
52.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
22.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series558.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
173.0ms	(cbrt x)
146.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify718.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (260.0ms)

Iter	Nodes	Cost
0	166	1057
1	340	936
2	765	887
3	1918	812
done	5000	812

prune220.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite53.0ms

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:

26.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
22.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series636.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
89.0ms	(cbrt (+ x 1.0))
182.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify616.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (227.0ms)

Iter	Nodes	Cost
0	255	1596
1	697	1441
2	2191	1368
done	5001	1368

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)
1.9b	(- (+ x 1.0) x)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`cbrt-prod`
9×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `associate-r` `associate-l`
5×	`add-cbrt-cube` `distribute-lft-out`
2×	`pow1/3` `diff-log` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

52.0ms	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
18.0ms	(- (+ x 1.0) x)

series528.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
185.0ms	(cbrt x)
178.0ms	(cbrt x)
1.0ms	(- (+ x 1.0) x)

simplify2.1s

Counts

80 → 80

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	150	801
1	379	744
2	1225	674
3	4401	626
done	5000	625

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.4b

regimes81.0ms

Accuracy

96.4% (0.2b remaining)

Error of 8.5b against oracle of 8.3b and baseline of 15.3b

bsearch49.0ms

Steps

Iters	Range		Point
9	1.9736423028239075e+152	2.7208697733301495e+159	3.4922108763538783e+154

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	27	53
1	36	49
done	36	49

end0.0ms

sample476.0ms

Algorithm

intervals

Results

169.0ms	1735×	body	1280	valid
91.0ms	1222×	body	640	valid
78.0ms	4115×	body	80	valid
37.0ms	615×	body	320	valid
11.0ms	313×	body	160	valid