Details

sample14.0ms

Algorithm

intervals

Results

6.0ms

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

localize7.0ms

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)))

rewrite41.0ms

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:

23.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
13.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
60.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (50.0ms)

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

prune166.0ms

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)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
359×	`*-un-lft-identity`
271×	`add-sqr-sqrt`
257×	`add-cube-cbrt`
192×	`prod-diff`
48×	`associate-/r/` `distribute-lft-out`
31×	`associate-/r*`
25×	`associate-/l*`
19×	`div-inv`
16×	`add-exp-log`
10×	`add-cbrt-cube` `associate-/l/`
8×	`div-exp`
7×	`clear-num`
6×	`frac-2neg`
5×	`flip3-+` `flip-+` `add-log-exp` `difference-of-squares`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u` `remove-double-div`
2×	`rec-exp` `1-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `inv-pow`

Counts

3 → 355

Calls

3 calls:

35.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
17.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
17.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

series146.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(- x (/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y)))
57.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
54.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

simplify103.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1548	10166
1	5001	6933

prune339.0ms

Filtered

364 candidates to 119 candidates (32.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	363	1	364
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	365	4	369

Merged error: 0b

Counts

369 → 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)))

rewrite144.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `pow1/3` `prod-exp` `flip-+`

Counts

4 → 934

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
19.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
39.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt y)
169.0ms	(cbrt y)
138.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y))
89.0ms	(/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 (/ (* x y) 2.0)) (cbrt y)))

simplify200.0ms

Algorithm

egg-herbie

Counts

946 → 946

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2607	17185
1	5001	16829

prune2.0s

Filtered

946 candidates to 534 candidates (56.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	946	0	946
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	946	4	950

Merged error: 0b

Counts

950 → 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)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

7630×	`add-sqr-sqrt`
4285×	`times-frac`
3070×	`*-un-lft-identity`
2742×	`add-cube-cbrt`
2340×	`prod-diff`
2203×	`associate-l`
1814×	`associate-r`
1732×	`unswap-sqr`
1511×	`swap-sqr`
828×	`difference-of-squares`
626×	`*-commutative`
502×	`frac-times`
470×	`associate-/l*`
446×	`associate-/r*`
122×	`distribute-rgt-in` `distribute-lft-in`
107×	`associate-*l/`
93×	`flip3--` `flip--`
72×	`div-inv`
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`
15×	`fma-neg`
14×	`cbrt-undiv` `div-exp`
13×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `un-div-inv`
2×	`pow-prod-down`
1×	`pow2` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 3883

Calls

4 calls:

162.0ms	(- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))
53.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
125.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
202.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))
37.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
57.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
123.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

3895 → 3895

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	133095

prune11.2s

Filtered

3895 candidates to 2597 candidates (66.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	3894	1	3895
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	3895	4	3899

Merged error: 0b

Counts

3899 → 4

regimes36.0ms

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

sample332.0ms

Algorithm

intervals

Results

205.0ms	7998×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid