Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
6.0ms	40×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite33.0ms

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)
26.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series395.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(cbrt (+ x 1.0))
167.0ms	(cbrt x)
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

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

prune240.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
74×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`unpow-prod-down` `cube-prod`
9×	`distribute-lft-out--`
7×	`fma-neg`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

29.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
27.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series612.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
86.0ms	(cbrt (+ x 1.0))
165.0ms	(cbrt x)
143.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify100.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	852	1818
1	3757	1458
2	5001	1454

prune405.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.7b

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)))
29.9b	(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:

241.0ms	(cbrt (cbrt x))
276.0ms	(cbrt (* (cbrt x) (cbrt x)))
268.0ms	(cbrt (* (cbrt x) (cbrt x)))
264.0ms	(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

prune363.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.7b

localize25.0ms

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)))
29.9b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

rewrite8.0ms

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))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

238.0ms	(cbrt (cbrt x))
480.0ms	(cbrt (* (cbrt x) (cbrt x)))
276.0ms	(cbrt (* (cbrt x) (cbrt x)))
251.0ms	(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 (69.0ms)

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

prune369.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.7b

regimes76.0ms

Accuracy

99.7% (0.0b remaining)

Error of 15.4b against oracle of 15.3b and baseline of 30.7b

bsearch85.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	4029.1516870118044
6	-107425.82452878023	-13600.963204601821	-13791.613711332258

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	42
1	56	42
2	56	42

end0.0ms

sample544.0ms

Algorithm

intervals

Results

198.0ms	1743×	body	1280	valid
106.0ms	1305×	body	640	valid
86.0ms	4004×	body	80	valid
39.0ms	656×	body	320	valid
14.0ms	292×	body	160	valid