Details

sample170.0ms

Algorithm

intervals

Results

68.0ms	104×	body	1280	valid
25.0ms	55×	body	640	valid
13.0ms	158×	body	80	valid
11.0ms	19×	body	1280	nan
10.0ms	22×	body	640	nan
10.0ms	163×	body	80	nan
8.0ms	24×	body	320	valid
3.0ms	47×	body	80	overflowed
2.0ms	11×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	4×	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: 26.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite69.0ms

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))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify71.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune334.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
1.2b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

209×	`sqrt-prod`
135×	`*-un-lft-identity`
113×	`add-sqr-sqrt`
110×	`prod-diff`
105×	`unpow-prod-down`
89×	`add-cube-cbrt`
33×	`sqr-pow`
26×	`pow-unpow`
20×	`distribute-lft-out`
18×	`times-frac`
16×	`difference-of-squares`
11×	`fma-def` `fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 243

Calls

4 calls:

44.0ms	(+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
61.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))

series954.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
370.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify84.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	718	5121
1	2107	3555
2	5001	3510

prune712.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.1b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

382×	`sqrt-prod`
220×	`prod-diff`
215×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
182×	`unpow-prod-down`
151×	`add-cube-cbrt`
115×	`log-prod`
112×	`exp-sum`
61×	`sqr-pow`
32×	`difference-of-squares`
26×	`pow-unpow`
25×	`distribute-lft-out`
24×	`log-pow`
23×	`exp-prod`
18×	`times-frac`
11×	`fma-neg`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`add-exp-log` `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 → 365

Calls

4 calls:

139.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
65.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.0s

Counts

4 → 12

Calls

4 calls:

372.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
372.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify116.0ms

Algorithm

egg-herbie

Counts

377 → 377

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	913	9268
1	2325	6172
2	5001	5294

prune976.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.1b

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(log (exp (+ (- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2))) (fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2))))))
1.9b	(- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2)))
3.6b	(fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac`
7×	`unpow-prod-down` `prod-diff`
6×	`pow1` `add-log-exp`
5×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
2×	`distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `associate-+l-` `sub-neg` `log-div` `flip3--` `pow-pow` `exp-diff` `fma-neg` `diff-log` `rem-log-exp` `exp-sum` `pow-exp` `flip--` `fma-udef` `div-inv`

Counts

4 → 82

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
203.0ms	(log (exp (+ (- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2))) (fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2))))))
23.0ms	(- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2)))
0.0ms	(fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

series2.6s

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
1.3s	(log (exp (+ (- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2))) (fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2))))))
968.0ms	(- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2)))
141.0ms	(fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

simplify84.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	681	2029
1	2546	1721
2	5002	1697

prune648.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 19.0b

regimes275.0ms

Accuracy

79.6% (1.8b remaining)

Error of 21.9b against oracle of 20.1b and baseline of 28.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	60
1	49	60

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	3155×	body	1280	valid
744.0ms	1634×	body	640	valid
382.0ms	4744×	body	80	valid
361.0ms	611×	body	1280	nan
297.0ms	4971×	body	80	nan
272.0ms	637×	body	640	nan
261.0ms	852×	body	320	valid
93.0ms	1221×	body	80	overflowed
88.0ms	331×	body	320	nan
85.0ms	437×	body	160	valid
27.0ms	171×	body	160	nan