Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

422×

body

valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.2b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (- (* y y) (* z z)))
5.3b	(- (* y y) (* z z))
26.2b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `fma-udef` `associate-/l/` `difference-of-squares`

Counts

3 → 99

Calls

3 calls:

1.0ms	(fma x x (- (* y y) (* z z)))
4.0ms	(- (* y y) (* z z))
7.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series191.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma x x (- (* y y) (* z z)))
35.0ms	(- (* y y) (* z z))
98.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	466	1096
1	1881	1029
2	5001	1026

prune353.0ms

Filtered

108 candidates to 87 candidates (80.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 13.3b

Counts

109 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
10.4b	(/ (pow x 2) y)
11.1b	(/ (pow z 2) y)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

332×	`*-un-lft-identity`
244×	`times-frac`
229×	`add-sqr-sqrt`
224×	`prod-diff`
215×	`add-cube-cbrt`
115×	`distribute-rgt-in` `distribute-lft-in`
97×	`unpow-prod-down`
57×	`distribute-lft-out`
33×	`unpow2` `sqr-pow`
16×	`associate-/l*`
15×	`add-exp-log`
10×	`associate-r` `div-inv`
9×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*`
5×	`pow1` `difference-of-squares`
4×	`associate-*r/`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow-exp` `associate--l+` `clear-num` `frac-sub` `distribute-lft-out--`
1×	`flip3--` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 363

Calls

3 calls:

36.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
6.0ms	(/ (pow x 2) y)
6.0ms	(/ (pow z 2) y)

series109.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
20.0ms	(/ (pow x 2) y)
22.0ms	(/ (pow z 2) y)

simplify175.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1256	8458
1	4758	6147
2	5001	6143

prune465.0ms

Filtered

372 candidates to 114 candidates (30.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	367	5	372
Fresh	6	0	6
Picked	1	0	1
Done	0	1	1
Total	374	6	380

Merged error: 2.3b

Counts

380 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ z (/ y z))
0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
10.4b	(/ (pow x 2) y)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

630×	`times-frac`
613×	`*-un-lft-identity`
443×	`add-sqr-sqrt`
432×	`add-cube-cbrt`
352×	`prod-diff`
179×	`distribute-rgt-in` `distribute-lft-in`
89×	`distribute-lft-out`
38×	`div-inv`
16×	`associate-/r*`
15×	`add-exp-log`
12×	`unpow-prod-down` `add-cbrt-cube`
11×	`associate-/l*`
9×	`associate-/r/`
8×	`associate-r`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-*r/` `unpow2` `sqr-pow`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`sub-neg` `frac-2neg` `associate--l+` `clear-num` `frac-sub` `distribute-lft-out--`
1×	`pow-to-exp` `flip3--` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 510

Calls

3 calls:

6.0ms	(/ z (/ y z))
49.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
6.0ms	(/ (pow x 2) y)

series109.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ z (/ y z))
61.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
22.0ms	(/ (pow x 2) y)

simplify172.0ms

Algorithm

egg-herbie

Counts

519 → 519

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	1864	15006
1	5001	11885

prune738.0ms

Filtered

519 candidates to 185 candidates (35.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	518	1	519
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	520	5	525

Merged error: 0.0b

Counts

525 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (/ x y))
0.1b	(/ z (/ y z))
0.2b	(* 0.5 (- (+ y (* x (/ x y))) (/ z (/ y z))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

484×	`times-frac`
369×	`add-sqr-sqrt`
355×	`*-un-lft-identity`
353×	`add-cube-cbrt`
264×	`prod-diff`
135×	`distribute-rgt-in` `distribute-lft-in`
30×	`div-inv`
20×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
7×	`pow1` `associate-/r/`
6×	`associate-l`
5×	`associate-*r/`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares` `unswap-sqr`
2×	`sub-neg` `pow-prod-down` `associate--l+` `*-commutative` `frac-sub`
1×	`flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `distribute-lft-out--`

Counts

3 → 404

Calls

3 calls:

7.0ms	(* x (/ x y))
7.0ms	(/ z (/ y z))
32.0ms	(* 0.5 (- (+ y (* x (/ x y))) (/ z (/ y z))))

series111.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* x (/ x y))
21.0ms	(/ z (/ y z))
69.0ms	(* 0.5 (- (+ y (* x (/ x y))) (/ z (/ y z))))

simplify147.0ms

Algorithm

egg-herbie

Counts

413 → 413

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	1880	11740
1	5001	9150

prune642.0ms

Filtered

413 candidates to 178 candidates (43.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	412	1	413
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	412	6	418

Merged error: 0.0b

Counts

418 → 6

regimes113.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample765.0ms

Algorithm

intervals

Results

487.0ms

13623×

body

valid