Details

sample31.0ms

Algorithm

intervals

Results

15.0ms	98×	body	1280	valid
4.0ms	122×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

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: 18.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

10.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
80.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2323	463
3	5001	463

prune164.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
14.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series132.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
81.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
36.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify138.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4851	560
3	5001	560

prune458.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `flip3-+` `associate-r/` `associate-l/` `frac-sub` `flip-+`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`+-commutative` `sum-log` `distribute-lft-out` `associate--r+`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 69

Calls

4 calls:

12.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
57.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(/ 1.0 (hypot 1.0 x))
80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
33.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	487	796
1	2180	736
2	5002	736

prune325.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
0.5b	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
0.5b	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
1.3b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `associate-r/` `associate-l/` `frac-sub` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out`
2×	`associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log`

Counts

4 → 60

Calls

4 calls:

8.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
8.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
8.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
57.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
140.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
144.0ms	(cbrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
35.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	360	829
1	1622	760
2	5003	754

prune333.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.6b

regimes83.0ms

Accuracy

0% (0.1b remaining)

Error of 15.4b against oracle of 15.4b and baseline of 15.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms

sample803.0ms

Algorithm

intervals

Results

432.0ms	2825×	body	1280	valid
116.0ms	4043×	body	80	valid
78.0ms	653×	body	640	valid
27.0ms	327×	body	320	valid
8.0ms	152×	body	160	valid