Details

sample190.0ms

Algorithm

intervals

Results

67.0ms	117×	body	1280	valid
25.0ms	39×	body	10240	exit
20.0ms	48×	body	640	valid
15.0ms	155×	body	80	valid
14.0ms	197×	body	80	nan
10.0ms	23×	body	640	nan
9.0ms	18×	body	1280	nan
5.0ms	16×	body	320	valid
4.0ms	15×	body	320	nan
3.0ms	13×	body	160	valid
0.0ms	2×	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: 29.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite70.0ms

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))
54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series462.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
264.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.7b	(pow x (/ 1.0 n))
0.8b	(pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
1.8b	(- (pow (pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

156×	`unpow-prod-down`
84×	`prod-diff`
83×	`*-un-lft-identity`
82×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
41×	`sqr-pow`
18×	`pow-unpow`
15×	`difference-of-squares`
12×	`fma-neg`
10×	`times-frac`
9×	`distribute-lft-out`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

0.0ms	(cbrt n)
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
108.0ms	(- (pow (pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt n)
55.0ms	(pow x (/ 1.0 n))
424.0ms	(pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
711.0ms	(- (pow (pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

simplify119.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1025	5369
1	4233	4230
2	5001	4226

prune585.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 18.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow x 2) n))
2.8b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
7.7b	(* x (pow n 2))
9.7b	(* (pow x 2) n)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
24×	`add-sqr-sqrt`
15×	`prod-exp`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
8×	`unpow-prod-down` `div-exp` `unswap-sqr`
5×	`pow1` `pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`times-frac` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `*-commutative`
1×	`pow-flip` `frac-2neg` `clear-num` `associate-/r*` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 103

Calls

4 calls:

6.0ms	(/ 1 (* (pow x 2) n))
0.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series158.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (* (pow x 2) n))
89.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
33.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify53.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	377	604
1	1714	520
2	5001	513

prune342.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow x 2) n))
2.8b	(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
7.7b	(* x (pow n 2))
9.7b	(* (pow x 2) n)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
43×	`fma-def`
36×	`add-exp-log`
15×	`prod-exp`
13×	`add-cbrt-cube`
11×	`associate-r` `associate-l`
8×	`unpow-prod-down` `div-exp` `add-log-exp` `unswap-sqr`
5×	`pow1` `pow-to-exp` `pow-exp` `div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `unpow2` `sqr-pow`
3×	`cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `sum-log` `*-commutative` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+r-` `associate-+r+` `distribute-neg-in` `pow-flip` `distribute-rgt-neg-in` `frac-2neg` `flip3-+` `unsub-neg` `neg-log` `clear-num` `associate-/r*` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 156

Calls

4 calls:

6.0ms	(/ 1 (* (pow x 2) n))
45.0ms	(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series139.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1 (* (pow x 2) n))
66.0ms	(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
33.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify63.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	468	757
1	2235	667
2	5001	660

prune540.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.4b

regimes141.0ms

Accuracy

84.2% (1.4b remaining)

Error of 22.7b against oracle of 21.3b and baseline of 30.3b

bsearch262.0ms

Steps

Iters	Range		Point
9	0.24914757354793585	16478977.782200867	7221255.7902708035
11	-897362988193.2484	-1.3005244035742512e-14	-27760508.405810945

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	47
1	55	47
2	55	47

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.8s	3253×	body	1280	valid
717.0ms	1632×	body	640	valid
571.0ms	1111×	body	10240	exit
455.0ms	4572×	body	80	valid
370.0ms	5135×	body	80	nan
365.0ms	637×	body	1280	nan
259.0ms	876×	body	320	valid
251.0ms	606×	body	640	nan
102.0ms	380×	body	320	nan
92.0ms	451×	body	160	valid
32.0ms	183×	body	160	nan