Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	46×	body	1280	valid
4.0ms	37×	body	640	valid
4.0ms	142×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite70.0ms

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×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
62.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series738.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(cbrt (+ x 1.0))
303.0ms	(cbrt x)
272.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify843.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1404
1	459
0	194

prune529.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
0.3b	(cbrt (+ 1.0 x))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
74×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`unpow-prod-down` `cube-prod`
9×	`distribute-lft-out--`
7×	`fma-neg`
6×	`add-log-exp`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 140

Calls

4 calls:

73.0ms	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
6.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
49.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series880.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
98.0ms	(cbrt (+ 1.0 x))
245.0ms	(cbrt x)
200.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify1.7s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	4011
1	971
0	321

prune743.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`cbrt-prod`
12×	`prod-diff`
9×	`distribute-lft-out` `add-log-exp`
6×	`pow1` `associate-r` `associate-l` `add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`pow1/3` `diff-log` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`distribute-rgt-in` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

94.0ms	(* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
70.0ms	(- (+ 1.0 x) x)

series826.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))
303.0ms	(cbrt x)
255.0ms	(cbrt x)
1.0ms	(- (+ 1.0 x) x)

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2344
1	482
0	177

prune735.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3))
0.6b	(cbrt x)
0.6b	(cbrt x)
12.4b	(cbrt (/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
106×	`cbrt-prod`
83×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
76×	`unpow-prod-down` `cube-prod`
42×	`cube-mult` `unpow3` `sqr-pow`
29×	`add-exp-log`
15×	`div-exp`
14×	`pow-exp`
12×	`associate-/r*`
8×	`pow-to-exp` `associate-/l*`
6×	`add-cbrt-cube` `prod-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `1-exp`
2×	`div-inv`
1×	`cbrt-undiv` `cbrt-div` `clear-num` `frac-2neg`

Counts

4 → 281

Calls

4 calls:

21.0ms	(/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3))
1.0ms	(cbrt x)
4.0ms	(cbrt x)
7.0ms	(cbrt (/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3)))

series3.4s

Counts

4 → 12

Calls

4 calls:

2.2s	(/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3))
270.0ms	(cbrt x)
239.0ms	(cbrt x)
684.0ms	(cbrt (/ (pow (* 1 1.0) 3) (pow (fma (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)) (* (cbrt x) (+ (cbrt x) (cbrt (+ 1.0 x))))) 3)))

simplify1.4s

Counts

293 → 293

Iterations

Iter	Nodes
done	5000
1	2515
0	907

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

regimes154.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

706.0ms	4028×	body	80	valid
436.0ms	1756×	body	1280	valid
199.0ms	1266×	body	640	valid
81.0ms	644×	body	320	valid
23.0ms	306×	body	160	valid