Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	126×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	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: 30.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.7b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite112.0ms

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:

8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
96.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series621.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(cbrt (+ x 1.0))
266.0ms	(cbrt x)
207.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	194	2160
1	459	1790
2	1408	1468
done	5001	1288

prune397.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
22.2b	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
15×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-neg` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
80.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(cbrt x)
352.0ms	(cbrt x)
278.0ms	(cbrt x)
211.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify904.0ms

Counts

79 → 79

Iterations

Useful iterations: done (902.0ms)

Iter	Nodes	Cost
0	120	1101
1	288	767
2	986	572
done	5000	509

prune319.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
12.0b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`prod-diff` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
55.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt x)
280.0ms	(cbrt x)
268.0ms	(cbrt x)
227.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify799.0ms

Counts

72 → 72

Iterations

Useful iterations: done (795.0ms)

Iter	Nodes	Cost
0	132	982
1	332	882
2	1087	798
done	5001	749

prune443.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.4b	(pow (cbrt (cbrt (+ x 1.0))) 3)
0.7b	(cbrt x)
20.0b	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

288×	`cbrt-prod`
156×	`prod-diff`
151×	`*-un-lft-identity`
145×	`add-sqr-sqrt`
115×	`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` `cbrt-div` `unpow3`
6×	`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 → 287

Calls

4 calls:

5.0ms	(cbrt (cbrt (+ x 1.0)))
17.0ms	(pow (cbrt (cbrt (+ x 1.0))) 3)
2.0ms	(cbrt x)
204.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

series948.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (cbrt (+ x 1.0)))
256.0ms	(pow (cbrt (cbrt (+ x 1.0))) 3)
301.0ms	(cbrt x)
236.0ms	(- (pow (cbrt (cbrt (+ x 1.0))) 3) (cbrt x))

simplify2.5s

Counts

299 → 299

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	349	8239
1	925	5491
2	3541	3985
done	5000	3979

prune637.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.7b

regimes69.0ms

Accuracy

97.2% (0.6b remaining)

Error of 9.2b against oracle of 8.6b and baseline of 29.3b

bsearch127.0ms

Steps

Iters	Range		Point
8	3.8036156446576786e-07	0.00010543070903258476	8.802284754780285e-06
10	-2676750800.736259	-2.9526231381329305e-09	-0.994187787075435

simplify27.0ms

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	54	86
1	66	84
2	67	84
done	67	84

end0.0ms

sample1.7s

Algorithm

intervals

Results

885.0ms	1751×	body	1280	valid
249.0ms	4076×	body	80	valid
242.0ms	1244×	body	640	valid
71.0ms	634×	body	320	valid
23.0ms	295×	body	160	valid