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 (2.0ms)

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: 21.3b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

290×	`*-un-lft-identity`
120×	`times-frac`
116×	`associate-l`
94×	`distribute-lft-out`
88×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
39×	`associate-r`
37×	`swap-sqr`
15×	`fma-def` `associate-/l*`
10×	`*-commutative` `unswap-sqr`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv`

Counts

2 → 202

Calls

2 calls:

15.0ms	(+ (* x x) (* y y))
27.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x x) (* y y))
64.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	572	1845
1	2941	1681
2	5001	1655

prune257.0ms

Filtered

208 candidates to 95 candidates (45.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	206	4	210

Merged error: 0.0b

Counts

210 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

179×	`*-un-lft-identity`
156×	`frac-times`
146×	`add-sqr-sqrt`
132×	`associate-/l*`
94×	`add-cube-cbrt`
87×	`associate-/r*`
58×	`times-frac` `associate-/l/`
30×	`clear-num`
29×	`frac-2neg`
22×	`distribute-lft-out`
20×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
19×	`associate-l`
16×	`associate-r`
15×	`flip3-+` `flip-+`
14×	`flip3--` `flip--`
13×	`associate-*l/`
12×	`associate-*r/`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`un-div-inv`
1×	`hypot-udef` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 327

Calls

4 calls:

1.0ms	(hypot x y)
6.0ms	(/ (- x y) (hypot x y))
22.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
6.0ms	(/ (+ x y) (hypot x y))

series314.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot x y)
89.0ms	(/ (- x y) (hypot x y))
91.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
88.0ms	(/ (+ x y) (hypot x y))

simplify65.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1324	3115
1	5002	3011

prune601.0ms

Filtered

339 candidates to 214 candidates (63.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	338	5	343

Merged error: 0b

Counts

343 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x y)
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
0.2b	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

759×	`*-un-lft-identity`
720×	`associate-/r*`
664×	`add-sqr-sqrt`
603×	`times-frac`
504×	`frac-times`
452×	`add-cube-cbrt`
200×	`associate-r`
198×	`associate-/l*`
136×	`associate-l`
96×	`distribute-lft-out`
82×	`associate-/r/`
57×	`distribute-lft-out--`
56×	`difference-of-squares`
53×	`clear-num`
52×	`frac-2neg`
47×	`add-exp-log` `add-cbrt-cube`
44×	`unswap-sqr`
40×	`associate-/l/`
34×	`div-inv`
33×	`*-commutative`
31×	`flip3-+` `flip-+`
28×	`associate-*r/`
20×	`flip3--` `flip--`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
12×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
1×	`hypot-udef` `div-sub` `pow-prod-down`

Counts

4 → 922

Calls

4 calls:

1.0ms	(hypot x y)
5.0ms	(/ (hypot x y) (+ x y))
13.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
91.0ms	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot x y)
88.0ms	(/ (hypot x y) (+ x y))
87.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
90.0ms	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))

simplify192.0ms

Algorithm

egg-herbie

Counts

934 → 934

Iterations

Useful iterations: 1 (73.0ms)

Iter	Nodes	Cost
0	4134	12025
1	5001	11903

prune1.8s

Filtered

934 candidates to 578 candidates (61.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	933	1	934
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	935	4	939

Merged error: 0b

Counts

939 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
0.0b	(log1p (expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))))
0.2b	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))
0.4b	(expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y)))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
716×	`associate-/r*`
655×	`add-sqr-sqrt`
591×	`times-frac`
504×	`frac-times`
443×	`add-cube-cbrt`
200×	`associate-r`
195×	`associate-/l*`
136×	`associate-l`
92×	`distribute-lft-out`
80×	`associate-/r/`
57×	`distribute-lft-out--`
56×	`difference-of-squares`
52×	`clear-num`
51×	`frac-2neg`
45×	`add-exp-log` `add-cbrt-cube`
44×	`unswap-sqr`
40×	`associate-/l/`
33×	`*-commutative` `div-inv`
30×	`flip3-+` `flip-+`
28×	`associate-*r/`
20×	`flip3--` `flip--`
18×	`cbrt-undiv` `div-exp` `associate-*l/`
12×	`prod-exp` `cbrt-unprod`
6×	`pow1`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`add-log-exp`
3×	`un-div-inv`
2×	`log1p-expm1`
1×	`log1p-udef` `expm1-log1p` `div-sub` `pow-prod-down` `expm1-udef`

Counts

4 → 900

Calls

4 calls:

13.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
1.0ms	(log1p (expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))))
93.0ms	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))
1.0ms	(expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
139.0ms	(log1p (expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))))
91.0ms	(* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y))))
129.0ms	(expm1 (* (/ 2 (* (hypot x y) 2)) (/ (- x y) (/ (hypot x y) (+ x y)))))

simplify197.0ms

Algorithm

egg-herbie

Counts

912 → 912

Iterations

Useful iterations: 1 (73.0ms)

Iter	Nodes	Cost
0	4169	12082
1	5002	11917

prune2.2s

Filtered

912 candidates to 560 candidates (61.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	912	0	912
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	912	4	916

Merged error: 0b

Counts

916 → 4

regimes38.0ms

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	10	7
1	10	7

end0.0ms

sample487.0ms

Algorithm

intervals

Results

225.0ms	8000×	body	80	valid
117.0ms	8000×	pre	80	true