Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	80×	body	1280	valid
4.0ms	137×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	8×	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: 16.5b

localize8.0ms

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 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

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:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
30.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
82.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite18.0ms

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:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify139.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (29.0ms)

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

prune251.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
28×	`associate-l`
26×	`*-un-lft-identity`
16×	`add-cube-cbrt` `difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `sqr-pow`
6×	`associate-r/` `associate-r` `associate-l/` `add-log-exp`
5×	`distribute-lft-out--`
4×	`flip3--` `frac-sub` `flip--`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`difference-cubes` `cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 109

Calls

4 calls:

20.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
9.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
3.0ms	(/ 1.0 (hypot 1.0 x))
18.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
20.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
5.0ms	(/ 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))))

simplify84.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	563	1053
1	2945	974
2	5003	974

prune468.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite21.0ms

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`
4×	`pow1` `add-exp-log` `associate-*r/` `associate--l+` `add-cbrt-cube`
3×	`sub-neg` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `frac-sub` `flip--`
1×	`diff-log`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
241.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
234.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	236	839
1	693	777
2	3836	744
3	5002	738

prune215.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.6b

regimes134.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms

sample804.0ms

Algorithm

intervals

Results

462.0ms	2847×	body	1280	valid
118.0ms	4058×	body	80	valid
79.0ms	608×	body	640	valid
28.0ms	320×	body	320	valid
10.0ms	167×	body	160	valid