Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	36	17
2	152	17
3	499	17
4	2033	17
done	5001	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x y) (+ x y))
0.1b	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
18.4b	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-times` `flip3-+` `flip-+`
31×	`add-exp-log` `add-cbrt-cube`
30×	`associate-*l/`
27×	`*-un-lft-identity`
26×	`associate-/r/`
18×	`associate-*r/`
15×	`pow1`
13×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`associate-r` `distribute-lft-out`
8×	`add-cube-cbrt`
6×	`cbrt-undiv` `swap-sqr` `div-exp`
5×	`associate-l`
4×	`pow-prod-down`
3×	`add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `clear-num` `associate-/r` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l`

Counts

3 → 140

Calls

3 calls:

51.0ms	(* (+ x y) (+ x y))
153.0ms	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
81.0ms	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* (+ x y) (+ x y))
55.0ms	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
226.0ms	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

simplify3.2s

Counts

149 → 149

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	218	3333
1	863	3063
2	4874	2795
done	5001	2697

prune543.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) x)
0.1b	(* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0))
5.0b	(+ (* (+ x y) x) (* (+ x y) y))
18.4b	(/ (* x y) (* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

70×	`associate-*l/`
50×	`flip3-+` `flip-+`
28×	`frac-add`
24×	`frac-times`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `associate-r` `associate-l`
7×	`distribute-lft-out`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `associate-*r/` `div-exp`
3×	`unswap-sqr`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `times-frac` `clear-num` `associate-/r` `sum-log` `div-inv` `associate-/l`

Counts

4 → 122

Calls

4 calls:

21.0ms	(* (+ x y) x)
123.0ms	(* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0))
21.0ms	(+ (* (+ x y) x) (* (+ x y) y))
76.0ms	(/ (* x y) (* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ x y) x)
68.0ms	(* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0))
33.0ms	(+ (* (+ x y) x) (* (+ x y) y))
197.0ms	(/ (* x y) (* (+ (* (+ x y) x) (* (+ x y) y)) (+ (+ x y) 1.0)))

simplify2.5s

Counts

134 → 134

Iterations

Useful iterations: 2 (951.0ms)

Iter	Nodes	Cost
0	228	3868
1	844	3325
2	4631	2905
done	5000	2905

prune610.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (+ (+ x y) 1.0))
0.0b	(* (+ x y) (+ x y))
0.1b	(* (/ x (* (+ x y) (+ x y))) (/ y (+ (+ x y) 1.0)))
17.5b	(/ x (* (+ x y) (+ x y)))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
40×	`times-frac`
34×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
25×	`associate-r`
20×	`flip3-+` `associate-/r/` `flip-+`
19×	`associate-l`
13×	`pow1` `frac-times`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-r/` `associate-l/`
6×	`swap-sqr` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 170

Calls

4 calls:

57.0ms	(/ y (+ (+ x y) 1.0))
58.0ms	(* (+ x y) (+ x y))
178.0ms	(* (/ x (* (+ x y) (+ x y))) (/ y (+ (+ x y) 1.0)))
21.0ms	(/ x (* (+ x y) (+ x y)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ y (+ (+ x y) 1.0))
23.0ms	(* (+ x y) (+ x y))
248.0ms	(* (/ x (* (+ x y) (+ x y))) (/ y (+ (+ x y) 1.0)))
94.0ms	(/ x (* (+ x y) (+ x y)))

simplify2.0s

Counts

182 → 182

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	217	2873
1	621	2602
2	2627	2323
done	5001	2231

prune619.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (+ (+ x y) 1.0))
0.0b	(/ x (+ x y))
0.0b	(* (/ x (+ x y)) (/ y (+ (+ x y) 1.0)))
0.2b	(* (/ 1 (+ x y)) (* (/ x (+ x y)) (/ y (+ (+ x y) 1.0))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
97×	`add-exp-log`
70×	`times-frac`
61×	`add-cbrt-cube`
60×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
40×	`prod-exp`
36×	`associate-l`
32×	`div-exp`
31×	`distribute-lft-out`
22×	`associate-r` `cbrt-unprod`
19×	`cbrt-undiv`
11×	`pow1`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`frac-times` `associate-r/` `associate-/l`
5×	`rec-exp` `flip3-+` `1-exp` `flip-+` `div-inv`
4×	`pow-prod-down` `associate-*l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 199

Calls

4 calls:

37.0ms	(/ y (+ (+ x y) 1.0))
12.0ms	(/ x (+ x y))
122.0ms	(* (/ x (+ x y)) (/ y (+ (+ x y) 1.0)))
204.0ms	(* (/ 1 (+ x y)) (* (/ x (+ x y)) (/ y (+ (+ x y) 1.0))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ y (+ (+ x y) 1.0))
60.0ms	(/ x (+ x y))
207.0ms	(* (/ x (+ x y)) (/ y (+ (+ x y) 1.0)))
216.0ms	(* (/ 1 (+ x y)) (* (/ x (+ x y)) (/ y (+ (+ x y) 1.0))))

simplify2.1s

Counts

211 → 211

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	261	3690
1	722	3312
2	2725	2810
done	5001	2802

prune572.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	12	17
done	12	17

end0.0ms

sample861.0ms

Algorithm

intervals

Results

569.0ms

8000×

body

valid