Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	56×	body	1280	valid
6.0ms	39×	body	640	valid
5.0ms	123×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite110.0ms

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)
100.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series624.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(cbrt (+ x 1.0))
277.0ms	(cbrt x)
201.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.5s

Counts

108 → 108

Iterations

Useful iterations: done (2.5s)

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

prune320.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.6b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
16×	`distribute-lft-out`
11×	`log-pow`
10×	`exp-prod`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 168

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
155.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
62.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series875.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (+ x 1.0))
307.0ms	(cbrt x)
210.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
239.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.3s

Counts

180 → 180

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	315	4214
1	567	3263
2	1179	2644
3	3321	2271
done	5000	2267

prune557.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.3b

localize12.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
3.6b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

220×	`cbrt-prod`
198×	`*-un-lft-identity`
168×	`prod-diff`
150×	`add-sqr-sqrt`
118×	`add-cube-cbrt`
100×	`log-prod`
94×	`sqrt-prod`
88×	`exp-sum`
30×	`distribute-lft-out`
26×	`log-pow`
22×	`sqrt-pow1`
20×	`exp-prod`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 288

Calls

4 calls:

184.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
168.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
80.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
99.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series1.2s

Counts

4 → 12

Calls

4 calls:

359.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
351.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
207.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
242.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.7s

Counts

300 → 300

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	368	8224
1	633	6780
2	1299	5534
3	3629	4690
done	5000	4686

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
3.6b	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`fma-neg`
9×	`add-log-exp`
8×	`difference-of-squares`
6×	`distribute-lft-out--`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`exp-prod` `exp-to-pow` `pow1/3` `rem-log-exp`

Counts

4 → 169

Calls

4 calls:

1.0ms	(cbrt x)
4.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
81.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
75.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series840.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt x)
190.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
178.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
211.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify3.3s

Counts

181 → 181

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	193	4306
1	400	3362
2	886	2727
3	2729	2351
done	5001	1972

prune662.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.3b

regimes165.0ms

Accuracy

98.2% (0.4b remaining)

Error of 9.3b against oracle of 9.0b and baseline of 29.7b

bsearch117.0ms

Steps

Iters	Range		Point
7	4.772092826529504e-10	9.85435867085541e-08	4.799156511993158e-08
8	-66911392.43097515	-3231.0590912120524	-3865.3828611493445

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	45	71
1	50	69
done	50	69

end0.0ms

sample781.0ms

Algorithm

intervals

Results

259.0ms	1742×	body	1280	valid
139.0ms	1256×	body	640	valid
120.0ms	4104×	body	80	valid
52.0ms	592×	body	320	valid
23.0ms	306×	body	160	valid