Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	53×	body	1280	valid
8.0ms	137×	body	80	valid
3.0ms	25×	body	640	valid
2.0ms	33×	body	320	valid
0.0ms	8×	body	160	valid

simplify8.0ms

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: 28.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.9b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite118.0ms

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)
99.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series634.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(cbrt (+ x 1.0))
259.0ms	(cbrt x)
232.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.4s

Counts

108 → 108

Iterations

Useful iterations: done (2.4s)

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

prune443.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.7b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.9b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite318.0ms

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:

9.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
207.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
79.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series943.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (+ x 1.0))
344.0ms	(cbrt x)
245.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
211.0ms	(- (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

prune465.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
10.0b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-diff` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 66

Calls

4 calls:

7.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
54.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series651.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ x 1.0))
125.0ms	(cbrt (+ x 1.0))
216.0ms	(cbrt x)
208.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify2.3s

Counts

78 → 78

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	159	1302
1	371	1190
2	968	1088
3	3018	922
done	5001	906

prune374.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
20.9b	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-diff` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 66

Calls

4 calls:

8.0ms	(cbrt (+ x 1.0))
9.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
134.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series806.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (+ x 1.0))
161.0ms	(cbrt (+ x 1.0))
296.0ms	(cbrt x)
225.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify2.3s

Counts

78 → 78

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	159	1328
1	371	1216
2	961	814
3	3055	696
done	5000	692

prune270.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.9b

regimes76.0ms

Accuracy

98.3% (0.4b remaining)

Error of 9.0b against oracle of 8.6b and baseline of 30.3b

bsearch125.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.00014218096555382583
10	-6045414056204.408	-123.41774798665298	-4661.327623294633

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	46	70
1	52	68
done	52	68

end0.0ms

sample1.2s

Algorithm

intervals

Results

394.0ms	1757×	body	1280	valid
278.0ms	1250×	body	640	valid
200.0ms	4045×	body	80	valid
119.0ms	626×	body	320	valid
23.0ms	322×	body	160	valid