Details

sample20.0ms

Algorithm

intervals

Results

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

simplify67.0ms

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

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: 20.2b

Counts

2 → 2

localize9.0ms

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)))
19.5b	(/ (fma x x (* y y)) (+ x y))

rewrite27.0ms

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))

series169.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma x x (* y y))
68.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
68.0ms	(/ (fma x x (* y y)) (+ x y))

simplify90.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (69.0ms)

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

prune360.0ms

Filtered

187 candidates to 127 candidates (67.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	1	0	1
Picked	1	0	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	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))

rewrite30.0ms

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:

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

series262.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
86.0ms	(/ (hypot x y) (+ x y))
87.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))

simplify54.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (41.0ms)

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

prune229.0ms

Filtered

116 candidates to 82 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Merged error: 0b

Counts

119 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

894×	`times-frac`
603×	`*-un-lft-identity`
475×	`add-sqr-sqrt`
353×	`add-cube-cbrt`
64×	`distribute-lft-out`
61×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r/`
42×	`div-inv`
27×	`associate-/l*`
25×	`associate-/r*`
21×	`flip3-+` `flip-+`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `div-sub` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

3 → 477

Calls

3 calls:

19.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))
6.0ms	(/ (- x y) (hypot x y))

series273.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
90.0ms	(/ (hypot x y) (+ x y))
93.0ms	(/ (- x y) (hypot x y))

simplify110.0ms

Algorithm

egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1827	7457
1	5001	7288

prune981.0ms

Filtered

486 candidates to 312 candidates (64.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	484	2	486
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	486	3	489

Merged error: 0b

Counts

489 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

1170×	`times-frac`
696×	`*-un-lft-identity`
512×	`add-sqr-sqrt` `add-cube-cbrt`
92×	`distribute-lft-out`
70×	`div-inv`
62×	`associate-/r/`
44×	`associate-/r*`
32×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
30×	`flip3-+` `flip-+`
18×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 644

Calls

4 calls:

14.0ms	(/ (/ x (hypot x y)) (/ (hypot x y) (+ x y)))
17.0ms	(/ (/ y (hypot x y)) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))
5.0ms	(/ (hypot x y) (+ x y))

series346.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (/ x (hypot x y)) (/ (hypot x y) (+ x y)))
85.0ms	(/ (/ y (hypot x y)) (/ (hypot x y) (+ x y)))
87.0ms	(/ (hypot x y) (+ x y))
89.0ms	(/ (hypot x y) (+ x y))

simplify136.0ms

Algorithm

egg-herbie

Counts

656 → 656

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2421	9128
1	5001	8882

prune1.7s

Filtered

656 candidates to 464 candidates (70.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	655	1	656
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	656	3	659

Merged error: 0b

Counts

659 → 3

regimes33.0ms

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	9	7
1	9	7

end0.0ms

sample486.0ms

Algorithm

intervals

Results

234.0ms	8000×	body	80	valid
111.0ms	8000×	pre	80	true