Details

sample134.0ms

Algorithm

intervals

Results

45.0ms	93×	body	1280	valid
18.0ms	54×	body	640	valid
10.0ms	42×	body	320	valid
9.0ms	24×	body	1280	nan
8.0ms	25×	body	640	nan
7.0ms	147×	body	80	valid
7.0ms	27×	body	10240	exit
6.0ms	187×	body	80	nan
3.0ms	22×	body	160	valid
2.0ms	12×	body	320	nan
0.0ms	1×	body	160	nan

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: 32.8b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series489.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune333.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 25.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

158×	`*-un-lft-identity`
147×	`add-sqr-sqrt`
141×	`times-frac`
130×	`add-cube-cbrt`
99×	`pow-unpow`
86×	`unpow-prod-down`
80×	`prod-diff`
65×	`sqrt-prod`
29×	`sqr-pow`
13×	`distribute-lft-out`
12×	`difference-of-squares`
9×	`div-inv`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 264

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
55.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
152.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
341.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify105.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	989	4310
1	3508	3229
2	5001	3224

prune852.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 25.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
105.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow x (/ 1.0 n))
155.0ms	(pow (+ x 1.0) (/ 1.0 n))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune530.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 25.7b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.2b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
46.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
47.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
299.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
466.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
467.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	665	7966
1	1642	6298
2	5001	5480

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.6b

regimes242.0ms

Accuracy

83% (1.5b remaining)

Error of 22.3b against oracle of 20.8b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	49
1	49	49

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3167×	body	1280	valid
553.0ms	1604×	body	640	valid
400.0ms	1047×	body	10240	exit
318.0ms	669×	body	1280	nan
245.0ms	4666×	body	80	valid
210.0ms	643×	body	640	nan
199.0ms	872×	body	320	valid
185.0ms	5016×	body	80	nan
69.0ms	472×	body	160	valid
66.0ms	357×	body	320	nan
18.0ms	169×	body	160	nan