Details

sample167.0ms

Algorithm

intervals

Results

46.0ms	94×	body	1280	valid
25.0ms	64×	body	640	valid
18.0ms	56×	body	10240	exit
14.0ms	33×	body	640	nan
12.0ms	151×	body	80	valid
11.0ms	26×	body	1280	nan
9.0ms	209×	body	80	nan
7.0ms	31×	body	320	valid
2.0ms	18×	body	160	valid
2.0ms	10×	body	320	nan
1.0ms	8×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(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)))

rewrite116.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series437.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(pow x (/ 1.0 n))
135.0ms	(pow (+ x 1.0) (/ 1.0 n))
251.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify70.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

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

prune533.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 24.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite294.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
174.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ 1.0 n))
131.0ms	(pow (+ x 1.0) (/ 1.0 n))
253.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
253.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify82.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (49.0ms)

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

prune862.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 24.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* x n))
3.0b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
8.0b	(* (pow x 2) n)
8.3b	(* x (pow n 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

11.0ms	(/ 1 (* x 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)))))))
14.0ms	(* (pow x 2) n)
12.0ms	(* x (pow n 2))

series132.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1 (* x n))
80.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
16.0ms	(* (pow x 2) n)
26.0ms	(* x (pow n 2))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	383	546
1	1807	466
2	5001	459

prune490.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow x 2) n))
3.0b	(fma 1.0 (/ (/ 1 x) n) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
8.0b	(* (pow x 2) n)
8.3b	(* x (pow n 2))

rewrite44.0ms

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:

14.0ms	(/ 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)))))))
12.0ms	(* (pow x 2) n)
12.0ms	(* x (pow n 2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (* (pow x 2) n))
81.0ms	(fma 1.0 (/ (/ 1 x) n) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
16.0ms	(* (pow x 2) n)
27.0ms	(* x (pow n 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	382	604
1	1725	520
2	5001	513

prune452.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.3b

regimes385.0ms

Accuracy

82.5% (1.5b remaining)

Error of 22.6b against oracle of 21.1b and baseline of 29.6b

bsearch181.0ms

Steps

Iters	Range		Point
7	16603184964.807266	1028783679204.0626	132305818796.19409
7	-46937230644809.76	-668239200238.3602	-681378613956.7775

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	38
1	46	38

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	3177×	body	1280	valid
612.0ms	1619×	body	640	valid
541.0ms	1175×	body	10240	exit
308.0ms	625×	body	1280	nan
280.0ms	4655×	body	80	valid
224.0ms	645×	body	640	nan
216.0ms	5005×	body	80	nan
199.0ms	815×	body	320	valid
76.0ms	364×	body	320	nan
75.0ms	503×	body	160	valid
26.0ms	203×	body	160	nan