Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	48×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite37.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
30.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series431.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
182.0ms	(cbrt x)
158.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	430	1315
1	1394	1045
2	5001	981

prune247.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.2b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite100.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
57.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
31.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
182.0ms	(cbrt x)
152.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	567	2459
1	1651	1917
2	5001	1581

prune389.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
29.6b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
6×	`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 → 48

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (* (cbrt x) (cbrt x)))
3.0ms	(cbrt (* (cbrt x) (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 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt (cbrt x))
271.0ms	(cbrt (* (cbrt x) (cbrt x)))
264.0ms	(cbrt (* (cbrt x) (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 x))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	276	535
1	746	472
2	2677	454
3	5001	451

prune380.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
29.6b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
6×	`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 → 48

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (* (cbrt x) (cbrt x)))
3.0ms	(cbrt (* (cbrt x) (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 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt (cbrt x))
272.0ms	(cbrt (* (cbrt x) (cbrt x)))
268.0ms	(cbrt (* (cbrt x) (cbrt x)))
255.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	276	535
1	746	472
2	2677	454
3	5001	451

prune377.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.3b

regimes131.0ms

Accuracy

98.1% (0.2b remaining)

Error of 19.1b against oracle of 18.9b and baseline of 29.8b

bsearch103.0ms

Steps

Iters	Range		Point
9	1.2499789889099044	556939279.5099251	4040.649618864342
9	-2.290788576086156e+63	-2.7943718184696317e+58	-4.4954988095195466e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	26
1	53	26

end0.0ms

sample552.0ms

Algorithm

intervals

Results

191.0ms	1729×	body	1280	valid
112.0ms	1236×	body	640	valid
97.0ms	4111×	body	80	valid
39.0ms	607×	body	320	valid
14.0ms	317×	body	160	valid