Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	25	5
3	26	5
4	26	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

localize8.0ms

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)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`times-frac`
11×	`add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 48

Calls

2 calls:

22.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
14.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
70.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify186.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	268	432
1	956	411
2	4742	403
3	5001	403

prune125.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0b

Counts

55 → 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)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
105×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
22×	`associate-/r*`
18×	`distribute-lft-out`
16×	`add-exp-log`
13×	`associate-/l*`
12×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`div-inv`
5×	`add-log-exp` `difference-of-squares`
4×	`pow1` `cbrt-undiv` `clear-num` `associate-/l/`
3×	`frac-2neg` `remove-double-div`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `inv-pow`

Counts

3 → 154

Calls

3 calls:

30.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
19.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
19.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

series162.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
67.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
59.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	546	1469
1	2403	1257
2	5002	1242

prune246.0ms

Filtered

163 candidates to 81 candidates (49.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	164	4	168

Merged error: 0b

Counts

168 → 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)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

1452×	`times-frac`
1059×	`*-un-lft-identity`
939×	`add-sqr-sqrt`
824×	`cbrt-prod`
707×	`add-cube-cbrt`
176×	`distribute-lft-out`
174×	`swap-sqr` `associate-r` `associate-l`
116×	`unswap-sqr`
42×	`add-cbrt-cube`
40×	`associate-/r*`
35×	`associate-/l*`
30×	`div-inv`
29×	`*-commutative`
27×	`cbrt-undiv`
18×	`add-exp-log`
15×	`associate-/r/`
12×	`cbrt-unprod`
7×	`div-exp`
4×	`pow1` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `pow1/3` `prod-exp` `flip-+`

Counts

4 → 926

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
16.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
46.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt y)
185.0ms	(cbrt y)
146.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
95.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

simplify208.0ms

Algorithm

egg-herbie

Counts

938 → 938

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	2594	17147
1	5001	16795

prune2.1s

Filtered

938 candidates to 526 candidates (56.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	938	0	938
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	938	4	942

Merged error: 0b

Counts

942 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))
0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
4.9b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
13.8b	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

rewrite675.0ms

Algorithm

rewrite-expression-head

Rules

4100×	`add-sqr-sqrt`
1549×	`times-frac`
1168×	`unswap-sqr`
828×	`difference-of-squares`
578×	`*-un-lft-identity`
502×	`frac-times`
496×	`associate-l`
470×	`associate-/l*`
446×	`associate-/r*`
430×	`add-cube-cbrt`
398×	`swap-sqr`
272×	`*-commutative`
197×	`associate-r`
107×	`associate-*l/`
93×	`flip3--` `flip--`
56×	`distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
43×	`clear-num`
42×	`frac-2neg`
20×	`associate-*r/`
17×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`pow1`
6×	`div-inv` `add-log-exp`
4×	`associate-/r/`
3×	`sub-neg` `un-div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
1×	`pow2` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 1520

Calls

4 calls:

113.0ms	(- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))
54.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
127.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
195.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))
39.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
63.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
131.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

simplify311.0ms

Algorithm

egg-herbie

Counts

1532 → 1532

Iterations

Useful iterations: 1 (80.0ms)

Iter	Nodes	Cost
0	4404	22607
1	5003	21238

prune2.3s

Filtered

1532 candidates to 563 candidates (36.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1531	1	1532
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	1532	4	1536

Merged error: 0b

Counts

1536 → 4

regimes37.0ms

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

sample347.0ms

Algorithm

intervals

Results

210.0ms	7998×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid