Details

sample205.0ms

Algorithm

intervals

Results

55.0ms	122×	body	1280	valid
38.0ms	68×	body	1280	nan
23.0ms	60×	body	640	nan
21.0ms	45×	body	10240	exit
16.0ms	50×	body	640	valid
9.0ms	224×	body	80	nan
7.0ms	26×	body	320	nan
7.0ms	32×	body	320	valid
4.0ms	95×	body	80	valid
3.0ms	21×	body	160	nan
2.0ms	16×	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: 32.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite24.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series418.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify59.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

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

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

287×	`unpow-prod-down`
231×	`prod-diff`
210×	`*-un-lft-identity`
192×	`add-sqr-sqrt`
156×	`add-cube-cbrt`
102×	`sqrt-prod`
79×	`distribute-rgt-in` `distribute-lft-in`
71×	`sqr-pow`
26×	`pow-unpow`
25×	`distribute-lft-out`
24×	`difference-of-squares`
18×	`times-frac`
16×	`associate-r`
11×	`fma-neg`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-l` `flip--` `log1p-expm1-u`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv` `distribute-lft-out--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 387

Calls

4 calls:

31.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
10.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

series2.0s

Counts

4 → 12

Calls

4 calls:

888.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2))))
346.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
345.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
456.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

simplify134.0ms

Algorithm

egg-herbie

Counts

399 → 399

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1474	12696
1	5001	10152

prune753.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
4.6b	(fma (pow (sqrt x) (/ (/ 1.0 n) 2)) (- (pow (sqrt x) (/ (/ 1.0 n) 2))) (pow (sqrt x) (* 2 (/ (/ 1.0 n) 2))))
4.8b	(fma (pow (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0)))) (/ 1.0 n)) (pow (cbrt (sqrt (+ x 1.0))) (/ 1.0 n)) (- (* (pow (sqrt x) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
40×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`sqrt-prod`
18×	`add-cube-cbrt`
14×	`cbrt-div` `sqrt-div` `swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`unswap-sqr`
7×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

4.0ms	(cbrt (sqrt (+ x 1.0)))
13.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
1.0ms	(fma (pow (sqrt x) (/ (/ 1.0 n) 2)) (- (pow (sqrt x) (/ (/ 1.0 n) 2))) (pow (sqrt x) (* 2 (/ (/ 1.0 n) 2))))
1.0ms	(fma (pow (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0)))) (/ 1.0 n)) (pow (cbrt (sqrt (+ x 1.0))) (/ 1.0 n)) (- (* (pow (sqrt x) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (sqrt (+ x 1.0)))
91.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
1.2s	(fma (pow (sqrt x) (/ (/ 1.0 n) 2)) (- (pow (sqrt x) (/ (/ 1.0 n) 2))) (pow (sqrt x) (* 2 (/ (/ 1.0 n) 2))))
1.2s	(fma (pow (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0)))) (/ 1.0 n)) (pow (cbrt (sqrt (+ x 1.0))) (/ 1.0 n)) (- (* (pow (sqrt x) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	688	1661
1	2439	1509
2	5002	1428

prune872.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
0.1b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

90×	`unpow-prod-down`
86×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
56×	`prod-diff`
47×	`add-cube-cbrt`
35×	`sqr-pow`
30×	`log-prod`
27×	`difference-of-squares`
15×	`exp-sum`
13×	`pow-unpow`
12×	`distribute-lft-out`
9×	`times-frac` `distribute-lft-out--`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log-div` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`exp-diff` `log-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `div-inv` `rem-exp-log`

Counts

4 → 179

Calls

4 calls:

8.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
12.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
450.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify76.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	674	2835
1	2017	2271
2	5003	2254

prune478.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

regimes401.0ms

Accuracy

75.7% (2.7b remaining)

Error of 24.8b against oracle of 22.1b and baseline of 33.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	107
1	86	107

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3910×	body	1280	valid
1.2s	2178×	body	1280	nan
731.0ms	1824×	body	640	nan
621.0ms	1421×	body	10240	exit
602.0ms	1838×	body	640	valid
259.0ms	6366×	body	80	nan
223.0ms	902×	body	320	nan
197.0ms	881×	body	320	valid
145.0ms	3099×	body	80	valid
69.0ms	456×	body	160	nan
60.0ms	444×	body	160	valid