Details

sample31.0ms

Algorithm

intervals

Results

7.0ms	50×	body	1280	valid
7.0ms	51×	body	640	valid
4.0ms	119×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	13×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite102.0ms

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)
92.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series692.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(cbrt (+ x 1.0))
323.0ms	(cbrt x)
225.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.6s

Counts

108 → 108

Iterations

Useful iterations: done (2.6s)

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

prune319.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

174×	`cbrt-prod`
152×	`*-un-lft-identity`
126×	`prod-diff`
113×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
24×	`distribute-lft-out`
21×	`fma-neg`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow1/3`

Counts

4 → 223

Calls

4 calls:

1.0ms	(cbrt x)
86.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
62.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
82.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series967.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt x)
258.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
225.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
215.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.9s

Counts

235 → 235

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	172	5645
1	377	4593
2	846	3676
3	2616	3151
done	5000	2587

prune738.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
33.0b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 94

Calls

4 calls:

7.0ms	(cbrt (+ x 1.0))
78.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (+ x 1.0))
186.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
324.0ms	(cbrt x)
368.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify2.7s

Counts

106 → 106

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	213	1541
1	484	1406
2	1302	1313
3	3748	1175
done	5000	1174

prune579.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
32.7b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

278.0ms	(cbrt x)
347.0ms	(cbrt x)
295.0ms	(cbrt x)
411.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

simplify1.9s

Counts

61 → 61

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	101	718
1	228	695
2	585	556
3	1799	495
done	5001	482

prune328.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.5b

regimes104.0ms

Accuracy

98.3% (0.4b remaining)

Error of 8.8b against oracle of 8.5b and baseline of 29.7b

bsearch114.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.00031979440843076613
9	-7465.585501010854	-0.008005822963963436	-5010.644987029124

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	47	73
1	53	71
done	53	71

end0.0ms

sample1.6s

Algorithm

intervals

Results

860.0ms	1697×	body	1280	valid
310.0ms	1274×	body	640	valid
195.0ms	4118×	body	80	valid
75.0ms	600×	body	320	valid
31.0ms	311×	body	160	valid