Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify69.0ms

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

prune7.0ms

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: 18.0b

Counts

2 → 2

localize12.0ms

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)))
17.4b	(/ (fma x x (* y y)) (+ x y))

rewrite26.0ms

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))

series172.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma x x (* y y))
66.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
70.0ms	(/ (fma x x (* y y)) (+ x y))

simplify87.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (67.0ms)

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

prune315.0ms

Filtered

187 candidates to 127 candidates (67.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	185	4	189

Merged error: 0.0b

Counts

189 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

1.0ms	(hypot x y)
9.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))
11.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot x y)
86.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
87.0ms	(/ (hypot x y) (+ x y))
91.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))

simplify49.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	378	858
1	1715	740
2	5002	733

prune204.0ms

Filtered

129 candidates to 96 candidates (74.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	128	5	133

Merged error: 0b

Counts

133 → 5

localize10.0ms

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 211

Calls

4 calls:

1.0ms	(hypot x y)
6.0ms	(/ (+ x y) (hypot x y))
8.0ms	(/ (/ (+ x y) (hypot x y)) (hypot x y))
21.0ms	(* (- x y) (/ (/ (+ x y) (hypot x y)) (hypot x y)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot x y)
88.0ms	(/ (+ x y) (hypot x y))
71.0ms	(/ (/ (+ x y) (hypot x y)) (hypot x y))
93.0ms	(* (- x y) (/ (/ (+ x y) (hypot x y)) (hypot x y)))

simplify79.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	627	1971
1	2902	1796
2	5001	1780

prune338.0ms

Filtered

223 candidates to 155 candidates (69.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	223	5	228

Merged error: 0b

Counts

228 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y)))))
0.0b	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
0.3b	(expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y))))
17.4b	(/ (fma x x (* y y)) (+ x y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y)))))
15.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
1.0ms	(expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y))))
5.0ms	(/ (fma x x (* y y)) (+ x y))

series349.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(log1p (expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y)))))
67.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
97.0ms	(expm1 (/ (- x y) (/ (fma x x (* y y)) (+ x y))))
68.0ms	(/ (fma x x (* y y)) (+ x y))

simplify84.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	671	2196
1	2797	2000
2	5002	1993

prune401.0ms

Filtered

202 candidates to 139 candidates (68.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	202	5	207

Merged error: 0b

Counts

207 → 5

regimes42.0ms

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

sample494.0ms

Algorithm

intervals

Results

241.0ms	8000×	body	80	valid
110.0ms	8000×	pre	80	true