Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	60×	body	1280	valid
3.0ms	124×	body	80	valid
3.0ms	32×	body	640	valid
2.0ms	33×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

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: 31.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite37.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
30.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series425.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
184.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	194	2160
1	427	1776
2	1032	1468
3	3261	1349
done	5000	1335

prune244.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

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)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite64.0ms

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:

25.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
31.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series581.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
89.0ms	(cbrt (+ x 1.0))
182.0ms	(cbrt x)
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify673.0ms

Counts

150 → 150

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	246	3032
1	555	2401
2	1461	2069
done	5000	1851

prune363.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
12.7b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

41×	`cbrt-prod`
33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`cbrt-div`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `prod-diff` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

20.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
3.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
25.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series549.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
93.0ms	(cbrt (cbrt (+ x 1.0)))
187.0ms	(cbrt x)
161.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify648.0ms

Counts

120 → 120

Iterations

Useful iterations: done (644.0ms)

Iter	Nodes	Cost
0	268	1974
1	604	1775
2	1646	1638
done	5000	1591

prune351.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
0.6b	(cbrt x)
31.8b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`flip3-+` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
0.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (cbrt (+ x 1.0)))
189.0ms	(cbrt x)
189.0ms	(cbrt x)
264.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify1.2s

Counts

67 → 67

Iterations

Useful iterations: 3 (528.0ms)

Iter	Nodes	Cost
0	172	831
1	381	800
2	1033	733
3	3070	680
done	5001	680

prune257.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.8b

regimes129.0ms

Accuracy

98.2% (0.4b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 29.9b

bsearch63.0ms

Steps

Iters	Range		Point
6	0.0591185632533196	0.44834868164545755	0.10532502913683747
8	-133622.27441454158	-436.72743869654124	-3435.2945499089387

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	47	69
1	55	67
done	55	67

end0.0ms

sample543.0ms

Algorithm

intervals

Results

187.0ms	1680×	body	1280	valid
111.0ms	1245×	body	640	valid
90.0ms	4078×	body	80	valid
41.0ms	660×	body	320	valid
14.0ms	337×	body	160	valid