Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

442×

body

valid

simplify60.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.0b	(- (+ (* x x) (* y y)) (* z z))
26.2b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

564×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
246×	`associate-l`
228×	`times-frac`
154×	`distribute-lft-out--`
131×	`distribute-lft-out`
76×	`add-cube-cbrt`
70×	`difference-of-squares`
60×	`associate-r`
58×	`swap-sqr`
34×	`*-commutative` `unswap-sqr`
19×	`associate-/l*`
12×	`associate-/r*`
10×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
3×	`pow1`
2×	`cbrt-undiv` `+-commutative` `flip3--` `diff-log` `div-exp` `associate--l+` `sum-log` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 323

Calls

3 calls:

20.0ms	(+ (* x x) (* y y))
26.0ms	(- (+ (* x x) (* y y)) (* z z))
41.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series163.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
46.0ms	(- (+ (* x x) (* y y)) (* z z))
88.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	760	3594
1	3189	3520
2	5002	3518

prune283.0ms

Filtered

332 candidates to 106 candidates (68.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	325	7	332
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	326	7	333

Merged error: 10.6b

Counts

333 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
7.8b	(/ (pow z 2) y)
10.2b	(/ (pow x 2) y)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
56×	`times-frac` `frac-sub`
52×	`add-cube-cbrt`
48×	`associate-/l*`
38×	`unpow-prod-down`
30×	`associate-*r/`
28×	`flip3-+` `flip-+`
18×	`associate-/r*`
16×	`add-exp-log`
14×	`unpow2` `sqr-pow`
10×	`associate-r` `add-cbrt-cube` `difference-of-squares`
9×	`add-log-exp`
6×	`pow1` `frac-2neg` `div-exp` `associate--l+` `clear-num`
4×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out--`
3×	`+-commutative` `sub-neg` `associate-l`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`
1×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 211

Calls

4 calls:

23.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
32.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
5.0ms	(/ (pow z 2) y)
5.0ms	(/ (pow x 2) y)

series142.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
55.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
24.0ms	(/ (pow z 2) y)
20.0ms	(/ (pow x 2) y)

simplify112.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	814	2404
1	3714	2200
2	5001	2195

prune453.0ms

Filtered

223 candidates to 144 candidates (35.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	222	8	230

Merged error: 1.5b

Counts

230 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
0.2b	(* (fabs x) (/ (fabs x) y))
0.2b	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y)))
7.8b	(/ (pow z 2) y)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
56×	`frac-sub`
45×	`add-cube-cbrt`
44×	`associate-/l*`
42×	`times-frac`
39×	`associate-*r/`
28×	`flip3-+` `flip-+`
26×	`unpow-prod-down`
24×	`associate-r`
18×	`associate-/r*`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`unpow2` `difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`pow1` `associate-l`
7×	`clear-num`
6×	`frac-2neg` `associate--l+` `distribute-lft-out--`
4×	`distribute-rgt-in` `distribute-lft-in` `div-exp` `distribute-lft-out`
3×	`+-commutative` `sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `diff-log` `pow-prod-down` `un-div-inv` `*-commutative` `flip--` `div-inv`
1×	`pow-to-exp` `pow-exp` `sum-log`

Counts

4 → 206

Calls

4 calls:

27.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
8.0ms	(* (fabs x) (/ (fabs x) y))
30.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y)))
5.0ms	(/ (pow z 2) y)

series171.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
20.0ms	(* (fabs x) (/ (fabs x) y))
76.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y)))
22.0ms	(/ (pow z 2) y)

simplify130.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	877	3012
1	4294	2719
2	5001	2713

prune483.0ms

Filtered

218 candidates to 146 candidates (33.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	218	8	226

Merged error: 0.3b

Counts

226 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
0.2b	(* z (/ z y))
0.2b	(* (fabs x) (/ (fabs x) y))
0.2b	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 189

Calls

4 calls:

25.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
8.0ms	(* z (/ z y))
8.0ms	(* (fabs x) (/ (fabs x) y))
34.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
23.0ms	(* z (/ z y))
21.0ms	(* (fabs x) (/ (fabs x) y))
76.0ms	(* 0.5 (- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y))))

simplify122.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	797	2456
1	3971	2254
2	5001	2248

prune365.0ms

Filtered

201 candidates to 128 candidates (36.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	201	8	209

Merged error: 0.3b

Counts

209 → 8

regimes152.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	16	9

end0.0ms

sample730.0ms

Algorithm

intervals

Results

450.0ms

13633×

body

valid