Details

sample122.0ms

Algorithm

intervals

Results

48.0ms	107×	body	1280	valid
17.0ms	49×	body	640	valid
13.0ms	30×	body	10240	exit
6.0ms	130×	body	80	valid
6.0ms	17×	body	1280	nan
5.0ms	129×	body	80	nan
4.0ms	21×	body	320	valid
2.0ms	13×	body	320	nan
2.0ms	18×	body	160	valid
2.0ms	7×	body	640	nan
0.0ms	3×	body	160	nan

simplify36.0ms

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: 31.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite72.0ms

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))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
57.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series481.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(- (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

prune475.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
4.0b	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
11×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
2×	`distribute-lft-out`
1×	`fma-udef`

Counts

4 → 99

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
0.0ms	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow x (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))
473.0ms	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

simplify43.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	427	708
1	1545	663
2	5001	650

prune380.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (log x) 1.0) (* x (pow n 2)))
1.5b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.9b	(* x (pow n 2))
9.0b	(/ (/ 0.5 n) (pow x 2))

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

2617×	`times-frac`
2287×	`add-sqr-sqrt`
1245×	`*-un-lft-identity`
1154×	`add-cube-cbrt`
1099×	`prod-diff`
542×	`associate--r+`
390×	`difference-of-squares`
327×	`unpow-prod-down`
220×	`div-inv`
167×	`unpow2` `sqr-pow`
46×	`add-exp-log` `distribute-lft-out--`
43×	`fma-neg`
23×	`add-cbrt-cube`
17×	`div-exp`
14×	`associate-/l*`
13×	`prod-exp`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log` `associate-l`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 1370

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
337.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
6.0ms	(* x (pow n 2))
9.0ms	(/ (/ 0.5 n) (pow x 2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
65.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
28.0ms	(* x (pow n 2))
33.0ms	(/ (/ 0.5 n) (pow x 2))

simplify492.0ms

Algorithm

egg-herbie

Counts

1382 → 1382

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	57436

prune5.4s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 18.2b

localize31.0ms

Local error

Found 4 expressions with local error:

21.9b	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
21.9b	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
21.9b	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
36.8b	(fma (- (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
39×	`cbrt-prod`
36×	`times-frac`
27×	`difference-of-squares`
13×	`*-un-lft-identity`
9×	`cbrt-div`
7×	`add-cube-cbrt`
6×	`unpow-prod-down` `unpow2` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `frac-sub` `flip--` `distribute-lft-out--`
1×	`fma-udef`

Counts

4 → 88

Calls

4 calls:

55.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
54.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
55.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
0.0ms	(fma (- (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))))

series4.0s

Counts

4 → 12

Calls

4 calls:

710.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
718.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
705.0ms	(cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
1.8s	(fma (- (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (* (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))) (cbrt (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	442	2510
1	1472	2262
2	5001	2214

prune588.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 18.2b

regimes290.0ms

Accuracy

76.4% (2.1b remaining)

Error of 22.2b against oracle of 20.1b and baseline of 29.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	26
1	35	26

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3134×	body	1280	valid
530.0ms	1576×	body	640	valid
434.0ms	1104×	body	10240	exit
309.0ms	681×	body	1280	nan
258.0ms	4783×	body	80	valid
209.0ms	651×	body	640	nan
185.0ms	5079×	body	80	nan
182.0ms	841×	body	320	valid
70.0ms	370×	body	320	nan
55.0ms	410×	body	160	valid
20.0ms	184×	body	160	nan