Details

Time bar (total: 13.5s)

sample34.0ms

Algorithm
intervals
Results
10.0ms200×body80valid
3.0ms17×body640valid
3.0ms11×body1280valid
2.0ms16×body320valid
1.0ms12×body160valid

simplify828.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
3.1b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.8b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r*
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg flip3-+ diff-log pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
23.0ms
(* (- 1.0 x) y)
30.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
39.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series176.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (- 1.0 x) y)
73.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
62.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify485.0ms

Counts
72 → 72

prune201.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ y 1.0))
0.0b
(* (- 1.0 x) y)
5.0b
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
6.8b
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
32×add-exp-log
27×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube
13×prod-exp
12×pow1
8×associate-*l/
7×cbrt-unprod distribute-lft-out
6×div-exp associate-*l* add-log-exp
4×flip3-- pow-prod-down associate-/r* associate-/r/ flip--
3×cbrt-undiv rec-exp 1-exp associate-/l*
2×frac-times flip3-+ *-commutative flip-+ div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ clear-num un-div-inv distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 118
Calls
4 calls:
12.0ms
(/ 1 (+ y 1.0))
23.0ms
(* (- 1.0 x) y)
8.0ms
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
78.0ms
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ 1 (+ y 1.0))
51.0ms
(* (- 1.0 x) y)
96.0ms
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
55.0ms
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

simplify945.0ms

Counts
130 → 130

prune263.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- 1.0 x))
0.3b
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
3.1b
(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
6.8b
(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-div
37×*-un-lft-identity
35×add-sqr-sqrt flip3-- flip--
34×associate-*l/
33×cbrt-prod
32×frac-times
26×associate-/l/
24×add-exp-log
16×add-cbrt-cube
15×add-cube-cbrt
11×pow1
10×associate-*r/ swap-sqr
9×prod-exp cbrt-unprod
8×associate-*r* associate-*l* distribute-lft-out--
7×pow1/3
6×add-log-exp difference-of-squares
5×cbrt-undiv div-exp
4×times-frac associate-/r* unswap-sqr
2×pow-prod-down associate-/r/ pow-sqr pow-prod-up distribute-lft-out
1×pow2 sub-neg frac-2neg flip3-+ pow-plus diff-log clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 142
Calls
4 calls:
7.0ms
(cbrt (- 1.0 x))
70.0ms
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
19.0ms
(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
137.0ms
(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

series405.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(cbrt (- 1.0 x))
141.0ms
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
82.0ms
(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
71.0ms
(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

simplify1.2s

Counts
154 → 154

prune668.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (* (- 1.0 x) y) (+ y 1.0))
6.8b
(/ (* (- 1.0 x) y) (+ y 1.0))
6.8b
(/ (* (- 1.0 x) y) (+ y 1.0))
13.3b
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

rewrite608.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
92×*-un-lft-identity
87×times-frac
64×difference-of-squares
48×unpow-prod-down cube-prod
40×add-cube-cbrt
32×sqr-pow
28×associate-/l*
21×add-exp-log add-cbrt-cube
20×distribute-lft-out--
15×associate-/r*
8×associate-/r/ associate-/l/
7×cbrt-undiv div-exp
6×associate-*l/ distribute-lft-out
4×pow1 difference-cubes flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv add-log-exp
3×prod-exp cbrt-unprod
1×div-sub
Counts
4 → 201
Calls
4 calls:
26.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
40.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
50.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
479.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
62.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
56.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
888.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

simplify1.5s

Counts
213 → 213

prune806.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes330.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 21.9b

bsearch115.0ms

Steps
ItersRangePoint
9
24341.35050109186
2580392290222.972
341613825.0272584
10
-5.797514308125059e+19
-11579.630006502104
-129982374.7612293

simplify1.4s

end0.0ms

sample1.5s

Algorithm
intervals
Results
475.0ms6147×body80valid
464.0ms352×body1280valid
133.0ms699×body640valid
92.0ms500×body320valid
30.0ms302×body160valid