Details

Time bar (total: 11.5s)

sample35.0ms

Algorithm
intervals
Results
13.0ms204×body80valid
3.0ms17×body640valid
2.0ms16×body320valid
2.0ms9×body1280valid
1.0ms10×body160valid

simplify856.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11611
23511
37411
415311
541311
6166211
done500111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.4b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.7b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite104.0ms

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:
31.0ms
(* (- 1.0 x) y)
31.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
39.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series185.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (- 1.0 x) y)
87.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
56.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.0s

Counts
72 → 72
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0128885
1347828
22051752
done5002746

prune148.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b
(/ y (+ y 1.0))
2.4b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
47.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
17.0ms
(/ y (+ y 1.0))
6.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series165.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
42.0ms
(/ y (+ y 1.0))
76.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (396.0ms)

IterNodesCost
01571229
14251152
224601056
done50001056

prune240.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ y 1.0))
0.0b
(* (- 1.0 x) (* y (/ 1 (+ y 1.0))))
0.1b
(* y (/ 1 (+ y 1.0)))
4.4b
(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ y 1.0)))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
32×add-exp-log add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
20×add-cbrt-cube
19×associate-*r*
13×prod-exp
12×pow1
8×associate-*l*
7×cbrt-unprod distribute-lft-out
6×associate-*r/ div-exp add-log-exp
4×frac-times flip3-- pow-prod-down associate-/r* associate-/r/ un-div-inv flip--
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×flip3-+ associate-*l/ *-commutative flip-+ div-inv
1×sub-neg pow-flip frac-2neg diff-log clear-num distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 122
Calls
4 calls:
22.0ms
(/ 1 (+ y 1.0))
109.0ms
(* (- 1.0 x) (* y (/ 1 (+ y 1.0))))
62.0ms
(* y (/ 1 (+ y 1.0)))
8.0ms
(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ y 1.0)))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1 (+ y 1.0))
77.0ms
(* (- 1.0 x) (* y (/ 1 (+ y 1.0))))
61.0ms
(* y (/ 1 (+ y 1.0)))
120.0ms
(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ y 1.0)))))

simplify1.8s

Counts
134 → 134
Iterations

Useful iterations: 2 (529.0ms)

IterNodesCost
01911696
15221491
226861198
done50001198

prune298.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x))))
2.4b
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
2.4b
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
2.4b
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×associate--r+
10×add-log-exp
9×sub-neg
6×distribute-rgt-in distribute-lft-in
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×cbrt-prod diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
3.0ms
(cbrt (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x))))
7.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
7.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
8.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(cbrt (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x))))
123.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
124.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
92.0ms
(- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))

simplify1.9s

Counts
73 → 73
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0961329
12321280
27621171
339591128
done50011115

prune254.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.7b

bsearch91.0ms

Steps
ItersRangePoint
8
13587.758917488305
805653349.9608173
216523043.9852226
10
-1950712569354.648
-1.3483780562815135e-05
-193411162.07491866

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02143
13133
done3133

end0.0ms

sample1.5s

Algorithm
intervals
Results
501.0ms361×body1280valid
329.0ms6055×body80valid
209.0ms772×body640valid
77.0ms301×body160valid
67.0ms511×body320valid