Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	52×	body	1280	valid
3.0ms	42×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 99

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
48.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series422.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
186.0ms	(cbrt x)
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	194	2160
1	433	1776
2	994	1468
3	2999	1265
done	5000	1254

prune233.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt (- x))
2.8b	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
17×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-neg` `prod-diff`
5×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-div` `pow1/3`
1×	`neg-mul-1` `sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 64

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (- x))
51.0ms	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

series431.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
194.0ms	(cbrt (- x))
148.0ms	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

simplify1.5s

Counts

73 → 73

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	155	1017
1	351	954
2	929	871
3	3107	810
done	5000	808

prune239.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt (- x))
9.9b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

35×	`cbrt-prod`
32×	`cbrt-div`
29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`swap-sqr`
8×	`frac-times` `pow1/3`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-mul-1` `sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `prod-diff` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

36.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
13.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
2.0ms	(cbrt (- x))
48.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
105.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
201.0ms	(cbrt (- x))
143.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

simplify964.0ms

Counts

122 → 122

Iterations

Useful iterations: done (959.0ms)

Iter	Nodes	Cost
0	267	2110
1	596	1951
2	1606	1801
done	5001	1743

prune440.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt (- x))
9.9b	(- (* (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

rewrite836.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-div`
12×	`cbrt-prod` `flip3-+` `flip-+`
8×	`frac-times`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `associate-r/` `associate-l/` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow1/3`
1×	`neg-mul-1` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 74

Calls

4 calls:

13.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
13.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
2.0ms	(cbrt (- x))
806.0ms	(- (* (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
102.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
191.0ms	(cbrt (- x))
151.0ms	(- (* (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt -1) (cbrt (- x))))

simplify1.8s

Counts

86 → 86

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	212	2214
1	467	2140
2	1231	1588
3	3950	1403
done	5000	1402

prune414.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.9b

regimes85.0ms

Accuracy

97.9% (0.4b remaining)

Error of 8.7b against oracle of 8.3b and baseline of 29.4b

bsearch85.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.00102788486376527
9	-76786.820650899	-0.0002772006047103471	-0.9952950592534084

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	52	81
1	64	79
2	66	79
done	66	79

end0.0ms

sample543.0ms

Algorithm

intervals

Results

174.0ms	1671×	body	1280	valid
101.0ms	1233×	body	640	valid
87.0ms	4157×	body	80	valid
34.0ms	602×	body	320	valid
13.0ms	337×	body	160	valid