Details

sample256.0ms

Algorithm

intervals

Results

74.0ms	147×	body	1280	valid
55.0ms	97×	body	1280	nan
32.0ms	48×	body	10240	exit
27.0ms	62×	body	640	nan
17.0ms	50×	body	640	valid
11.0ms	24×	body	320	nan
8.0ms	186×	body	80	nan
5.0ms	23×	body	320	valid
5.0ms	83×	body	80	valid
2.0ms	13×	body	160	nan
2.0ms	13×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 120

Calls

2 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series411.0ms

Counts

2 → 6

Calls

2 calls:

138.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	542	2011
1	1694	1489
2	5001	1488

prune248.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

140×	`unpow-prod-down`
110×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
56×	`prod-diff`
50×	`add-cube-cbrt`
49×	`sqr-pow`
45×	`difference-of-squares`
36×	`cbrt-prod`
30×	`cube-prod`
16×	`pow-unpow`
15×	`distribute-lft-out--`
14×	`distribute-lft-out`
9×	`times-frac`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `pow-exp`
1×	`sub-neg` `pow1/3` `diff-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 220

Calls

4 calls:

10.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
11.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

436.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
267.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
137.0ms	(pow (+ x 1.0) (/ 1.0 n))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify98.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	870	3374
1	3459	2816
2	5001	2808

prune489.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)))
0.2b	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

140×	`unpow-prod-down`
111×	`add-sqr-sqrt`
104×	`*-un-lft-identity`
72×	`log-prod`
56×	`prod-diff`
51×	`add-cube-cbrt`
49×	`sqr-pow`
45×	`difference-of-squares`
36×	`exp-sum`
30×	`cube-prod`
15×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`pow-unpow`
9×	`times-frac`
8×	`fma-neg`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`cube-div` `expm1-log1p-u` `log-div` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `rem-log-exp` `flip--`
2×	`cube-mult` `pow-to-exp` `exp-diff` `unpow3` `pow-exp` `log-pow`
1×	`sub-neg` `pow-pow` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 223

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
13.0ms	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)))
12.0ms	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
14.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series3.1s

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
456.0ms	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)))
2.3s	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify105.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1026	3603
1	3761	2978
2	5001	2977

prune650.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(exp (cbrt (pow (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)))
0.2b	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

109×	`unpow-prod-down`
90×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
37×	`sqr-pow`
36×	`log-prod`
27×	`difference-of-squares`
19×	`cube-prod`
17×	`exp-prod`
14×	`cbrt-prod`
13×	`pow-unpow`
12×	`distribute-lft-out`
9×	`times-frac` `distribute-lft-out--`
8×	`fma-neg`
7×	`add-exp-log` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-log-exp` `log-pow`
2×	`cube-div` `cube-mult` `pow-to-exp` `log-div` `flip3--` `unpow3` `pow-exp` `flip--`
1×	`sub-neg` `pow-pow` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 198

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(exp (cbrt (pow (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)))
12.0ms	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series3.2s

Counts

4 → 12

Calls

4 calls:

144.0ms	(pow (+ x 1.0) (/ 1.0 n))
462.0ms	(exp (cbrt (pow (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)))
2.3s	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify106.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1041	3151
1	3883	2559
2	5001	2558

prune682.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.8b

regimes251.0ms

Accuracy

78.3% (2.2b remaining)

Error of 24.6b against oracle of 22.5b and baseline of 32.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	50	30

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.8s	3830×	body	1280	valid
1.3s	2147×	body	1280	nan
741.0ms	1802×	body	640	nan
658.0ms	1346×	body	10240	exit
605.0ms	1795×	body	640	valid
265.0ms	6045×	body	80	nan
212.0ms	847×	body	320	nan
206.0ms	887×	body	320	valid
149.0ms	3109×	body	80	valid
72.0ms	468×	body	160	valid
69.0ms	451×	body	160	nan