Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

428×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	55	7
2	101	7
3	182	7
4	335	7
5	731	7
6	1828	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
6.2b	(- (+ (* x x) (* y y)) (* z z))
28.4b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(- (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series153.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
45.0ms	(- (+ (* x x) (* y y)) (* z z))
80.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	520
1	1492	454
2	5001	446

prune159.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
10.1b	(/ (pow x 2) y)
10.5b	(/ (pow z 2) y)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
52×	`times-frac`
44×	`*-un-lft-identity`
39×	`add-cube-cbrt`
25×	`unpow-prod-down`
16×	`associate-/l*`
15×	`add-exp-log`
10×	`associate-r`
9×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1` `difference-of-squares`
4×	`associate-*r/`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow-exp` `associate--l+` `clear-num` `frac-sub` `div-inv` `distribute-lft-out--`
1×	`flip3--` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

3 → 133

Calls

3 calls:

23.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
7.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series92.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
18.0ms	(/ (pow x 2) y)
18.0ms	(/ (pow z 2) y)

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	481	830
1	1901	743
2	5003	737

prune333.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* z (/ z y))
0.4b	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
10.1b	(/ (pow x 2) y)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
15×	`add-exp-log`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`associate-/l*`
7×	`pow1` `associate-*r/`
6×	`associate-l`
4×	`div-exp` `unpow2` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative` `frac-sub` `div-inv`
1×	`pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip--` `flip-+`

Counts

3 → 109

Calls

3 calls:

7.0ms	(* z (/ z y))
15.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
5.0ms	(/ (pow x 2) y)

series97.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* z (/ z y))
59.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
19.0ms	(/ (pow x 2) y)

simplify66.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	470	677
1	2128	601
2	5001	598

prune268.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* z (/ z y))
0.2b	(* (fabs x) (/ (fabs x) y))
0.4b	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-l`
8×	`associate-*r/`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `add-log-exp`
2×	`cbrt-undiv` `sub-neg` `div-exp` `associate--l+` `frac-sub` `div-inv`
1×	`flip3--` `flip3-+` `flip--` `flip-+`

Counts

3 → 92

Calls

3 calls:

6.0ms	(* z (/ z y))
7.0ms	(* (fabs x) (/ (fabs x) y))
7.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

series107.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(* z (/ z y))
19.0ms	(* (fabs x) (/ (fabs x) y))
67.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	491	718
1	2434	627
2	5001	618

prune236.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes113.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	16	9

end0.0ms

sample754.0ms

Algorithm

intervals

Results

469.0ms

13842×

body

valid