Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

422×

body

valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune8.0ms

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: 27.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma x x (- (* y y) (* z z)))
4.4b	(- (* y y) (* z z))
25.7b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite17.0ms

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

series195.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma x x (- (* y y) (* z z)))
40.0ms	(- (* y y) (* z z))
104.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify68.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

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

prune337.0ms

Filtered

108 candidates to 87 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Merged error: 14.4b

Counts

109 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ (pow x 2) y))
0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
10.1b	(/ (pow z 2) y)
11.6b	(/ (pow x 2) y)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

193×	`*-un-lft-identity`
148×	`times-frac`
140×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
112×	`prod-diff`
61×	`unpow-prod-down`
31×	`distribute-lft-out`
21×	`unpow2` `sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*` `div-inv`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 260

Calls

4 calls:

11.0ms	(+ y (/ (pow x 2) y))
31.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.0ms	(/ (pow z 2) y)
6.0ms	(/ (pow x 2) y)

series127.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ y (/ (pow x 2) y))
45.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
28.0ms	(/ (pow z 2) y)
22.0ms	(/ (pow x 2) y)

simplify141.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	966	4460
1	3272	3145
2	5001	2950

prune470.0ms

Filtered

272 candidates to 118 candidates (43.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	266	6	272
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	271	8	279

Merged error: 3.0b

Counts

279 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* x (/ x y)))
0.0b	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
0.2b	(* x (/ x y))
10.1b	(/ (pow z 2) y)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt`
110×	`times-frac`
106×	`*-un-lft-identity`
104×	`add-cube-cbrt`
84×	`prod-diff`
40×	`unpow-prod-down`
14×	`add-exp-log` `unpow2` `sqr-pow`
13×	`associate-r`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
5×	`div-inv` `difference-of-squares`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 212

Calls

4 calls:

8.0ms	(+ y (* x (/ x y)))
16.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
8.0ms	(* x (/ x y))
6.0ms	(/ (pow z 2) y)

series119.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ y (* x (/ x y)))
48.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
21.0ms	(* x (/ x y))
21.0ms	(/ (pow z 2) y)

simplify140.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	994	3551
1	3667	2455
2	5001	2446

prune449.0ms

Filtered

224 candidates to 116 candidates (51.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	225	7	232

Merged error: 0.0b

Counts

232 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`associate-r`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
11×	`add-log-exp`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `fma-neg` `prod-diff`
2×	`cbrt-undiv` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `sum-log` `*-commutative` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 108

Calls

4 calls:

3.0ms	(+ y (* x (/ x y)))
6.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
7.0ms	(* z (/ z y))
8.0ms	(* x (/ x y))

series122.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ y (* x (/ x y)))
43.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
19.0ms	(* z (/ z y))
26.0ms	(* x (/ x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	471	621
1	2270	544
2	5002	536

prune255.0ms

Filtered

120 candidates to 86 candidates (71.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

regimes109.0ms

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	15	7
1	15	7

end0.0ms

sample796.0ms

Algorithm

intervals

Results

489.0ms

13793×

body

valid