Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	57×	body	1280	valid
3.0ms	138×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	14×	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: 28.1b

localize6.0ms

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))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series401.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(cbrt (+ x 1.0))
168.0ms	(cbrt x)
147.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify161.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	287	358
1	934	344
2	4833	322
3	5001	322

prune157.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.6b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.9b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`cbrt-prod`
11×	`log-pow`
10×	`exp-prod`
8×	`add-cube-cbrt` `difference-of-squares`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
9.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series558.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x 1.0))
175.0ms	(cbrt x)
151.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
145.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	336	568
1	1025	536
2	5001	505

prune261.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
2.9b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
31×	`log-pow`
30×	`exp-prod`
24×	`times-frac`
22×	`cbrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`distribute-lft-out`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod`
2×	`pow1/3` `associate-/r/`
1×	`sub-neg` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
20.0ms	(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
175.0ms	(cbrt x)
394.0ms	(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
175.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	750	1315
1	3389	1203
2	5001	1200

prune330.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize19.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
2.6b	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
2.9b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
2.9b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
66×	`log-pow`
62×	`sqrt-pow1`
60×	`exp-prod`
48×	`times-frac`
32×	`cbrt-prod` `distribute-lft-out`
30×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`log-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `sqrt-prod`
4×	`associate-/r/` `add-cbrt-cube`
2×	`sub-neg` `log-div` `flip3--` `flip3-+` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 122

Calls

4 calls:

22.0ms	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
22.0ms	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
15.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

744.0ms	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
738.0ms	(log (sqrt (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x))))))
179.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
173.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	752	2808
1	3300	2604
2	5001	2596

prune618.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.4b

regimes70.0ms

Accuracy

99.1% (0.2b remaining)

Error of 11.8b against oracle of 11.6b and baseline of 30.1b

bsearch105.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	0.0005833549905030771
10	-1.0571996836653623e+65	-1.2789128298244494e+54	-4.4684458085938983e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	40
1	76	40
2	76	40

end0.0ms

sample496.0ms

Algorithm

intervals

Results

178.0ms	1734×	body	1280	valid
93.0ms	1268×	body	640	valid
83.0ms	4049×	body	80	valid
33.0ms	613×	body	320	valid
12.0ms	336×	body	160	valid