Details

sample14.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	26	5
3	29	5
4	30	5
5	30	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
7.6b	(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
54×	`add-cube-cbrt` `prod-diff`
49×	`times-frac`
13×	`distribute-lft-out`
8×	`associate-/r/`
4×	`add-exp-log` `flip3-+` `associate-/r*` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
3×	`fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

2 → 109

Calls

2 calls:

12.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
68.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	574	2548
1	2067	1795
2	5001	1637

prune175.0ms

Filtered

115 candidates to 57 candidates (49.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	5	116

Merged error: 0b

Counts

116 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
0.1b	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
7.5b	(/ (+ 1.0 (/ (* x y) 2.0)) y)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
329×	`*-un-lft-identity`
252×	`add-sqr-sqrt`
238×	`add-cube-cbrt`
159×	`prod-diff`
43×	`distribute-lft-out`
19×	`associate-/r*` `div-inv`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
5×	`add-log-exp` `difference-of-squares`
4×	`pow1` `cbrt-undiv` `associate-/r/`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `flip--` `flip-+` `inv-pow`

Counts

3 → 308

Calls

3 calls:

23.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
9.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
7.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

series145.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
62.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
50.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

simplify90.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1350	9058
1	5002	6271

prune314.0ms

Filtered

317 candidates to 107 candidates (33.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	316	1	317
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	318	4	322

Merged error: 0b

Counts

322 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.3b	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
5.6b	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
91×	`*-un-lft-identity`
53×	`add-sqr-sqrt` `add-cube-cbrt`
45×	`cbrt-prod`
34×	`associate-/r*`
19×	`distribute-lft-out`
18×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`cbrt-undiv` `div-exp`
5×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `pow1/3` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 154

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
8.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
23.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(cbrt y)
220.0ms	(cbrt y)
159.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
83.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

simplify75.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	1629
1	2692	1456
2	5001	1410

prune416.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Merged error: 0b

Counts

170 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
4.9b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
7.9b	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
13.8b	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
55×	`times-frac`
42×	`prod-diff`
23×	`associate-+l+` `associate-+r+` `distribute-neg-in`
21×	`add-log-exp`
18×	`associate-r` `difference-of-squares`
14×	`distribute-lft-neg-in` `fma-def` `distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-rgt-neg-in`
9×	`distribute-rgt-out` `flip3--` `flip--` `div-inv` `distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `sum-log` `associate-/r/` `associate-/l*`
5×	`diff-log` `associate-l`
4×	`expm1-log1p-u` `neg-mul-1` `neg-log` `frac-add` `log1p-expm1-u` `distribute-neg-frac`
3×	`cbrt-undiv` `distribute-lft1-in` `div-exp`
2×	`frac-times` `sub-neg` `frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `associate-+r-` `flip3-+` `associate-r/` `pow-prod-down` `-commutative` `flip-+`

Counts

4 → 220

Calls

4 calls:

5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
20.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
15.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
61.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
1.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
108.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

simplify185.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	840	2715
1	4423	2133
2	5001	2104

prune733.0ms

Filtered

232 candidates to 181 candidates (78.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	232	4	236

Merged error: 0b

Counts

236 → 4

regimes41.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	6
1	15	6

end0.0ms

sample349.0ms

Algorithm

intervals

Results

217.0ms	7998×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid