Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

415×

body

valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune9.0ms

Filtered

1 candidates to 1 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: 29.2b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (fma x x (- (* y y) (* z z))) 2.0)
4.0b	(- (* y y) (* z z))
27.1b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

322×	`add-sqr-sqrt`
225×	`prod-diff`
222×	`*-un-lft-identity`
210×	`add-cube-cbrt`
105×	`swap-sqr`
97×	`associate-l`
93×	`associate-r`
84×	`times-frac`
41×	`*-commutative` `unswap-sqr`
25×	`difference-of-squares`
19×	`associate-/l*`
15×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `associate-/l/`
6×	`div-inv`
5×	`distribute-lft-out--` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 393

Calls

3 calls:

3.0ms	(/ (fma x x (- (* y y) (* z z))) 2.0)
27.0ms	(- (* y y) (* z z))
8.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series220.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (fma x x (- (* y y) (* z z))) 2.0)
36.0ms	(- (* y y) (* z z))
109.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify195.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	978	4625
1	3257	3483
2	5001	2820

prune376.0ms

Filtered

402 candidates to 124 candidates (30.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	395	7	402
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	397	7	404

Merged error: 14.3b

Counts

404 → 7

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
9.1b	(/ (pow z 2) y)
11.4b	(/ (pow x 2) y)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
148×	`times-frac`
144×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
112×	`prod-diff`
67×	`unpow-prod-down`
32×	`associate-/l*`
30×	`distribute-lft-out`
28×	`frac-sub`
23×	`unpow2` `sqr-pow`
14×	`flip3-+` `flip-+`
13×	`add-exp-log`
12×	`associate-/r*`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`div-exp` `div-inv`
5×	`difference-of-squares`
4×	`frac-2neg` `fma-neg` `clear-num`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-to-exp` `diff-log` `pow-exp` `associate--l+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

3 → 270

Calls

3 calls:

28.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
6.0ms	(/ (pow z 2) y)
6.0ms	(/ (pow x 2) y)

series99.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
22.0ms	(/ (pow z 2) y)
30.0ms	(/ (pow x 2) y)

simplify220.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	1220	5108
1	4575	3715
2	5001	3705

prune442.0ms

Filtered

279 candidates to 126 candidates (45.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	272	7	279
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	278	8	286

Merged error: 1.5b

Counts

286 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
0.2b	(/ x (/ y x))
9.1b	(/ (pow z 2) y)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

222×	`*-un-lft-identity`
199×	`times-frac`
171×	`add-sqr-sqrt`
159×	`add-cube-cbrt`
112×	`prod-diff`
55×	`unpow-prod-down`
30×	`distribute-lft-out` `associate-/l*`
28×	`frac-sub`
25×	`associate-/r*`
19×	`unpow2` `sqr-pow`
14×	`flip3-+` `flip-+`
13×	`add-exp-log`
10×	`add-cbrt-cube` `div-inv`
9×	`associate-/r/`
8×	`add-log-exp`
6×	`div-exp`
5×	`frac-2neg` `clear-num` `difference-of-squares`
4×	`cbrt-undiv` `fma-neg`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`diff-log` `associate--l+` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `sum-log` `flip--`

Counts

3 → 299

Calls

3 calls:

35.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
8.0ms	(/ x (/ y x))
6.0ms	(/ (pow z 2) y)

series99.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
22.0ms	(/ x (/ y x))
23.0ms	(/ (pow z 2) y)

simplify109.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	1413	5336
1	5001	4027

prune496.0ms

Filtered

308 candidates to 152 candidates (49.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	303	5	308
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	309	7	316

Merged error: 0b

Counts

316 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
155×	`add-sqr-sqrt`
126×	`times-frac`
121×	`add-cube-cbrt`
92×	`prod-diff`
65×	`associate-r`
27×	`associate-*r/`
26×	`distribute-lft-out`
25×	`associate-/r*`
22×	`frac-sub`
18×	`associate-/l*`
17×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube`
12×	`unswap-sqr`
11×	`flip3-+` `flip-+`
10×	`div-inv`
9×	`associate-/r/`
8×	`clear-num` `add-log-exp`
6×	`un-div-inv`
5×	`pow1` `frac-2neg` `*-commutative`
4×	`cbrt-undiv` `fma-neg` `div-exp` `distribute-lft-out--`
3×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`diff-log` `prod-exp` `associate--l+` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `pow-prod-down` `sum-log` `flip--`

Counts

3 → 266

Calls

3 calls:

39.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
7.0ms	(/ x (/ y x))
9.0ms	(* (fabs z) (/ (fabs z) y))

series103.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
22.0ms	(/ x (/ y x))
24.0ms	(* (fabs z) (/ (fabs z) y))

simplify102.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	1216	5121
1	5002	3701

prune451.0ms

Filtered

275 candidates to 143 candidates (52.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	271	4	275
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	275	7	282

Merged error: 0b

Counts

282 → 7

regimes103.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample780.0ms

Algorithm

intervals

Results

487.0ms

13869×

body

valid