Details

sample51.0ms

Algorithm

intervals

Results

29.0ms	93×	body	1280	valid
8.0ms	137×	body	80	valid
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize7.0ms

Local error

Found 1 expressions with local error:

1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

3.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	87	169
1	208	156
2	670	154
3	2027	154
4	5001	152

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`times-frac`
4×	`add-cube-cbrt` `flip3--` `associate-r/` `associate-/r` `frac-sub` `flip--` `associate-/l/`
3×	`diff-log` `distribute-lft-out--`
2×	`pow1` `cbrt-undiv` `sub-neg` `div-exp` `associate--l+` `associate-/r/` `distribute-lft-out` `difference-of-squares`
1×	`associate--l-` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

2 → 51

Calls

2 calls:

27.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
24.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series213.0ms

Counts

2 → 6

Calls

2 calls:

182.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
31.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	346	697
1	1418	605
2	5001	603

prune143.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
1.1b	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
64×	`times-frac`
57×	`add-sqr-sqrt`
48×	`frac-sub`
45×	`add-cube-cbrt`
41×	`frac-times`
39×	`flip3--` `flip--`
30×	`associate-*r/`
29×	`associate-*l/`
27×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`distribute-lft-out`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
7×	`difference-of-squares`
6×	`prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--`
4×	`associate--l+` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `frac-add` `clear-num` `flip-+`
1×	`pow2` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 208

Calls

4 calls:

25.0ms	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
51.0ms	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
13.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
12.0ms	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
94.0ms	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
23.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
56.0ms	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

simplify64.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1168	3568
1	5001	3216

prune673.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
1.0b	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

3403×	`frac-times`
1621×	`flip3--` `flip--`
1543×	`associate-r/` `associate-l/`
1200×	`frac-sub`
124×	`add-sqr-sqrt`
120×	`times-frac`
88×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
25×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
8×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
6×	`add-log-exp`
5×	`sub-neg`
3×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`diff-log` `difference-of-squares`

Counts

4 → 1422

Calls

4 calls:

13.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
16.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
13.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
113.0ms	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

series150.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
23.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
23.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
77.0ms	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

simplify802.0ms

Algorithm

egg-herbie

Counts

1434 → 1434

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5001	61012

prune8.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 11.3b

regimes63.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	64
1	61	64

end0.0ms

sample1.5s

Algorithm

intervals

Results

877.0ms	2842×	body	1280	valid
238.0ms	4044×	body	80	valid
160.0ms	659×	body	640	valid
52.0ms	297×	body	320	valid
18.0ms	158×	body	160	valid