Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
4.0ms	21×	body	320	valid
3.0ms	39×	body	640	valid
3.0ms	130×	body	80	valid
0.0ms	12×	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: 30.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite60.0ms

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)
51.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series422.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
188.0ms	(cbrt x)
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

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

prune220.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.4b	(pow (cbrt (cbrt (+ x 1.0))) 3)
0.6b	(cbrt x)
22.5b	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

281×	`cbrt-prod`
156×	`prod-diff`
150×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
114×	`add-cube-cbrt`
86×	`unpow-prod-down` `cube-prod`
26×	`fma-neg`
17×	`distribute-lft-out`
16×	`difference-of-squares`
10×	`sqr-pow`
8×	`cube-mult` `unpow3`
6×	`cbrt-div` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow` `pow1/3`
2×	`cube-div` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 284

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
12.0ms	(pow (cbrt (cbrt (+ x 1.0))) 3)
1.0ms	(cbrt x)
129.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

series559.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (+ x 1.0))
145.0ms	(pow (cbrt (cbrt (+ x 1.0))) 3)
181.0ms	(cbrt x)
150.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

simplify1.0s

Counts

296 → 296

Iterations

Useful iterations: done (997.0ms)

Iter	Nodes	Cost
0	320	8178
1	740	5224
2	1690	3929
done	5000	3546

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
9.1b	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
29×	`*-un-lft-identity`
26×	`fma-neg` `prod-diff`
21×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`unpow-prod-down` `cube-prod`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
3×	`pow1/3`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `pow3` `flip--`

Counts

4 → 106

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
159.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
182.0ms	(cbrt x)
183.0ms	(cbrt x)
162.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify846.0ms

Counts

118 → 118

Iterations

Useful iterations: done (843.0ms)

Iter	Nodes	Cost
0	158	2460
1	402	1386
2	1074	898
done	5000	853

prune301.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

106×	`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`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`cube-div` `flip3--` `flip--`
1×	`cube-mult` `sub-neg` `flip3-+` `diff-log` `unpow3` `rem-cbrt-cube` `flip-+` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

42.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
52.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series569.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
90.0ms	(cbrt (+ x 1.0))
186.0ms	(cbrt x)
145.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify689.0ms

Counts

150 → 150

Iterations

Useful iterations: done (684.0ms)

Iter	Nodes	Cost
0	246	3032
1	568	2401
2	1431	2069
done	5000	1847

prune338.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.9b

regimes118.0ms

Accuracy

97.8% (0.5b remaining)

Error of 8.9b against oracle of 8.4b and baseline of 29.7b

bsearch75.0ms

Steps

Iters	Range		Point
9	5.533815706167767e-17	6.1632953816490534e-12	1.4235012643955587e-16
10	-21283307590.397102	-3.152803306627408e-07	-0.9868159492179903

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	45	63
1	53	59
done	53	59

end0.0ms

sample521.0ms

Algorithm

intervals

Results

166.0ms	1680×	body	1280	valid
92.0ms	4124×	body	80	valid
91.0ms	1236×	body	640	valid
35.0ms	644×	body	320	valid
12.0ms	316×	body	160	valid