Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	43×	body	640	valid
3.0ms	126×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	12×	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: 30.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.4b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite34.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
27.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series417.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	194	2160
1	434	1811
2	1050	1468
3	3434	1273
done	5000	1259

prune224.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
22.0b	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite34.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)
31.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
181.0ms	(cbrt x)
184.0ms	(cbrt x)
155.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify1.2s

Counts

79 → 79

Iterations

Useful iterations: 3 (530.0ms)

Iter	Nodes	Cost
0	120	1101
1	282	767
2	755	572
3	2374	509
done	5001	509

prune197.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ x 1.0))
0.4b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
31.0b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`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`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
169.0ms	(cbrt x)
243.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify1.1s

Counts

67 → 67

Iterations

Useful iterations: 3 (464.0ms)

Iter	Nodes	Cost
0	149	930
1	346	885
2	970	818
3	2941	739
done	5000	739

prune248.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
30.9b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

rewrite3.0ms

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:

0.0ms	(cbrt x)
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 (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

series799.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
184.0ms	(cbrt x)
178.0ms	(cbrt x)
253.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

simplify870.0ms

Counts

61 → 61

Iterations

Useful iterations: done (868.0ms)

Iter	Nodes	Cost
0	101	718
1	228	695
2	603	556
3	1832	495
done	5001	494

prune225.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.8b

regimes47.0ms

Accuracy

98.3% (0.4b remaining)

Error of 9.1b against oracle of 8.7b and baseline of 30.4b

bsearch82.0ms

Steps

Iters	Range		Point
9	0.00016167321766412214	1766.3470775505596	0.0021387086194756175
10	-3752817.331716861	-5.670122129476186e-07	-4234.572456934552

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample511.0ms

Algorithm

intervals

Results

174.0ms	1703×	body	1280	valid
98.0ms	1280×	body	640	valid
89.0ms	4031×	body	80	valid
36.0ms	633×	body	320	valid
13.0ms	353×	body	160	valid