Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	58×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	135×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	7×	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: 28.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite17.0ms

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)
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series427.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
181.0ms	(cbrt x)
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

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

prune266.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.4b

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)
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite29.0ms

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:

10.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series655.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
89.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
158.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify98.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (82.0ms)

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

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
9.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `prod-diff` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `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 → 69

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
14.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series526.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
98.0ms	(cbrt (cbrt (+ x 1.0)))
182.0ms	(cbrt x)
156.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	485	808
1	1750	729
2	5001	703

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
9.1b	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

rewrite13.0ms

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:

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

series705.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt x)
180.0ms	(cbrt x)
180.0ms	(cbrt x)
158.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

simplify97.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	278	677
1	832	602
2	3218	584
3	5001	583

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.8b

regimes64.0ms

Accuracy

99.5% (0.1b remaining)

Error of 14.8b against oracle of 14.7b and baseline of 28.7b

bsearch89.0ms

Steps

Iters	Range		Point
9	1078.5849367128544	2491217878.346211	82414.02441059977
9	-4696503048995838.0	-66949431.36780037	-715053332982360.9

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

sample717.0ms

Algorithm

intervals

Results

280.0ms	4138×	body	80	valid
186.0ms	1701×	body	1280	valid
104.0ms	1226×	body	640	valid
36.0ms	610×	body	320	valid
13.0ms	325×	body	160	valid