Details

sample52.0ms

Algorithm

intervals

Results

27.0ms	396×	body	80	valid
8.0ms	135×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

5.0ms	(* a (pow k m))
2.0ms	(+ 1.0 (* 10.0 k))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
13.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* a (pow k m))
2.0ms	(+ 1.0 (* 10.0 k))
3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
36.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune701.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(fma 10.0 k 1.0)
0.9b	(/ 1 (fma k k (fma 10.0 k 1.0)))
1.6b	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
10×	`div-exp`
7×	`pow1` `cbrt-unprod`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
2×	`*-commutative` `div-inv` `sqr-pow`
1×	`pow-flip` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `fma-udef` `inv-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(* a (pow k m))
0.0ms	(fma 10.0 k 1.0)
2.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
13.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* a (pow k m))
3.0ms	(fma 10.0 k 1.0)
5.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
39.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	512	805
1	2653	698
2	5001	671

prune700.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
0.9b	(/ 1 (fma k k (fma 10.0 k 1.0)))
1.6b	(* (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

240×	`add-exp-log`
184×	`prod-exp`
44×	`pow-exp`
34×	`div-exp`
32×	`pow-to-exp`
27×	`add-cbrt-cube`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`rec-exp` `1-exp`
13×	`associate-r`
12×	`cbrt-unprod`
7×	`pow1`
6×	`cbrt-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `associate-l` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 156

Calls

4 calls:

0.0ms	(cbrt k)
0.0ms	(cbrt k)
2.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
37.0ms	(* (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt k)
9.0ms	(cbrt k)
5.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
122.0ms	(* (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	723	1806
1	3098	1527
2	5002	1427

prune847.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
16.6b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.6b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `fma-def` `sum-log` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 72

Calls

4 calls:

10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
11.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
11.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify82.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	198	532
1	774	478
2	3383	450
3	5001	444

prune772.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

98.3% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch16.0ms

Steps

Iters	Range		Point
4	7.8930669794294e+68	1.3771687752437002e+69	1.1085263457066272e+69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	39
1	56	39
2	56	39

end0.0ms

sample1.4s

Algorithm

intervals

Results

820.0ms	11884×	body	80	valid
254.0ms	4145×	body	80	nan