Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune6.0ms

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: 22.2b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
21.4b	(/ (fma x x (* y y)) (+ x y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
161×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 178

Calls

3 calls:

1.0ms	(fma x x (* y y))
12.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
5.0ms	(/ (fma x x (* y y)) (+ x y))

series167.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma x x (* y y))
68.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
63.0ms	(/ (fma x x (* y y)) (+ x y))

simplify89.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	652	2043
1	2939	1866
2	5001	1860

prune297.0ms

Filtered

187 candidates to 127 candidates (67.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	186	3	189

Merged error: 0.0b

Counts

189 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))
0.0b	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(/ (hypot x y) (+ x y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
30×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r`
8×	`associate-/l*`
7×	`distribute-lft-out`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `associate-/r*` `associate-/r/`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`flip3--` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

3 → 107

Calls

3 calls:

10.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
12.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
5.0ms	(/ (hypot x y) (+ x y))

series261.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
88.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
87.0ms	(/ (hypot x y) (+ x y))

simplify50.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	372	831
1	1709	716
2	5001	709

prune177.0ms

Filtered

116 candidates to 82 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	115	4	119

Merged error: 0b

Counts

119 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(- (/ x (* (hypot x y) (/ (hypot x y) (+ x y)))) (/ y (* (hypot x y) (/ (hypot x y) (+ x y)))))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (hypot x y) (+ x y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
78×	`*-un-lft-identity`
64×	`prod-diff`
60×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
24×	`associate-/r/`
22×	`div-inv`
20×	`associate-*r/`
17×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
8×	`fma-neg` `distribute-lft-out`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-rgt-out--` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div` `difference-of-squares`

Counts

4 → 189

Calls

4 calls:

8.0ms	(/ x (* (hypot x y) (/ (hypot x y) (+ x y))))
18.0ms	(- (/ x (* (hypot x y) (/ (hypot x y) (+ x y)))) (/ y (* (hypot x y) (/ (hypot x y) (+ x y)))))
5.0ms	(/ (hypot x y) (+ x y))
5.0ms	(/ (hypot x y) (+ x y))

series360.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ x (* (hypot x y) (/ (hypot x y) (+ x y))))
104.0ms	(- (/ x (* (hypot x y) (/ (hypot x y) (+ x y)))) (/ y (* (hypot x y) (/ (hypot x y) (+ x y)))))
85.0ms	(/ (hypot x y) (+ x y))
87.0ms	(/ (hypot x y) (+ x y))

simplify86.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	566	3724
1	2166	2768
2	5001	2680

prune249.0ms

Filtered

201 candidates to 112 candidates (55.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	201	4	205

Merged error: 0b

Counts

205 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
155×	`*-un-lft-identity`
114×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
52×	`associate-r`
25×	`distribute-lft-out`
20×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1` `associate-l`
3×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-times` `flip3--` `frac-2neg` `associate-*l/` `clear-num` `flip--`
1×	`flip3-+` `associate-r/` `pow-prod-down` `-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 201

Calls

3 calls:

8.0ms	(/ (/ (+ x y) (hypot x y)) (hypot x y))
5.0ms	(/ (+ x y) (hypot x y))
22.0ms	(* (- x y) (/ (/ (+ x y) (hypot x y)) (hypot x y)))

series245.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (/ (+ x y) (hypot x y)) (hypot x y))
86.0ms	(/ (+ x y) (hypot x y))
88.0ms	(* (- x y) (/ (/ (+ x y) (hypot x y)) (hypot x y)))

simplify79.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	620	1944
1	2893	1772
2	5001	1748

prune306.0ms

Filtered

210 candidates to 142 candidates (67.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	210	4	214

Merged error: 0b

Counts

214 → 4

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms

sample465.0ms

Algorithm

intervals

Results

228.0ms	8000×	body	80	valid
104.0ms	8000×	pre	80	true