Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	49×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	9×	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: 29.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite35.0ms

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))

series411.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
145.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

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

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite97.0ms

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))
0.0ms	(cbrt x)
55.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
30.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series560.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
151.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify69.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (45.0ms)

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

prune376.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.0b

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))
0.6b	(cbrt x)
2.4b	(- (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:

25.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
30.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series634.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
88.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify99.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	852	1820
1	3757	1458
2	5001	1454

prune386.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize16.0ms

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)))
7.7b	(- (cbrt (+ x 1.0)) (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`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 → 66

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (* (cbrt x) (cbrt x)))
3.0ms	(cbrt (* (cbrt x) (cbrt x)))
25.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))))

series915.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt (cbrt x))
263.0ms	(cbrt (* (cbrt x) (cbrt x)))
270.0ms	(cbrt (* (cbrt x) (cbrt x)))
140.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	330	774
1	938	675
2	3557	665
3	5002	664

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

regimes64.0ms

Accuracy

99.8% (0.0b remaining)

Error of 15.2b against oracle of 15.1b and baseline of 29.8b

bsearch76.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	5204.303054786619
10	-64880754058.88788	-2.651420353119469e-05	-3965.7270635849572

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	37	21

end0.0ms

sample493.0ms

Algorithm

intervals

Results

177.0ms	1735×	body	1280	valid
99.0ms	1222×	body	640	valid
81.0ms	4115×	body	80	valid
34.0ms	615×	body	320	valid
12.0ms	313×	body	160	valid