Details

Time bar (total: 19.1s)

sample43.0ms

Algorithm
intervals
Results
18.0ms208×body80valid
3.0ms18×body640valid
2.0ms10×body1280valid
2.0ms12×body320valid
1.0ms8×body160valid

simplify1.2s

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: 18.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.8b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-exp-log add-cbrt-cube
6×add-sqr-sqrt
4×add-cube-cbrt times-frac associate-/r* add-log-exp
2×pow1 cbrt-undiv flip3-- div-exp associate-*l/ associate-/r/ flip-- associate-/l/ distribute-lft-out
1×sub-neg frac-2neg flip3-+ diff-log prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
34.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
28.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series133.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
57.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify875.0ms

Counts
47 → 47
Iterations

Useful iterations: 2 (223.0ms)

IterNodesCost
0104694
1296648
21680584
done5000584

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
5.0b
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
10.6b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
14.6b
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
18×add-exp-log times-frac add-cbrt-cube
15×associate-*l* distribute-lft-out
12×unpow-prod-down cube-prod
11×add-sqr-sqrt add-log-exp
9×add-cube-cbrt associate-/r*
6×pow1
5×flip3-+ prod-exp cbrt-unprod flip-+
4×cbrt-undiv div-exp associate-/r/
3×associate-*r* associate-*l/ sum-cubes
2×distribute-rgt-in frac-times sub-neg associate-+r+ flip3-- distribute-lft-in diff-log associate-*r/ sum-log flip-- div-inv associate-/l/ associate--r+
1×+-commutative associate-+r- frac-2neg pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 107
Calls
4 calls:
27.0ms
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
10.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
76.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
214.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series672.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
356.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
116.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
174.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify4.0s

Counts
119 → 119
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
01912958
16842585
248972281
done50002281

prune693.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y))
5.4b
(- 1.0 (* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
14.0b
(/ (+ (* y y) (* 1.0 (- 1.0 y))) y)
14.6b
(* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite510.0ms

Algorithm
rewrite-expression-head
Rules
854×times-frac
608×*-un-lft-identity
482×add-sqr-sqrt
336×add-cube-cbrt
286×associate-*l*
70×distribute-lft-out
66×distribute-lft-out-- difference-of-squares
33×div-inv
25×add-exp-log add-cbrt-cube
16×associate-/r*
10×cbrt-undiv div-exp
8×associate-/l*
7×associate-/r/
6×pow1 add-log-exp
4×flip3-+ prod-exp cbrt-unprod flip-+ associate-/l/ unswap-sqr
3×associate-*r*
2×distribute-rgt-in frac-times flip3-- frac-2neg distribute-lft-in associate-*r/ clear-num flip-- associate--r+
1×sub-neg diff-log div-sub pow-prod-down associate-*l/ *-commutative
Counts
4 → 461
Calls
4 calls:
47.0ms
(/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y))
5.0ms
(- 1.0 (* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
41.0ms
(/ (+ (* y y) (* 1.0 (- 1.0 y))) y)
335.0ms
(* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y))
105.0ms
(- 1.0 (* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
76.0ms
(/ (+ (* y y) (* 1.0 (- 1.0 y))) y)
70.0ms
(* (/ (/ (- 1.0 x) (/ (+ (* y y) (* 1.0 (- 1.0 y))) y)) (+ y 1.0)) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify1.3s

Counts
473 → 473
Iterations

Useful iterations: done (1.3s)

IterNodesCost
064115215
1289414292
done500213796

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

10.6b
(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
10.6b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
10.6b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
15.1b
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* y y))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
44×add-exp-log add-cbrt-cube
36×times-frac
30×distribute-lft-out
24×unpow-prod-down cube-prod
19×associate-*l*
18×associate-/r*
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r*
13×add-cube-cbrt
11×pow1
10×cbrt-undiv div-exp
8×associate-/r/
7×associate-*l/
6×sum-cubes
4×flip3-- flip3-+ pow-prod-down flip-- flip-+ div-inv associate-/l/ add-log-exp
2×frac-times frac-2neg clear-num *-commutative associate-/l* unswap-sqr
1×distribute-rgt-out-- associate-*r/
Counts
4 → 154
Calls
4 calls:
160.0ms
(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
59.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
64.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
122.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* y y))

series441.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
108.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
107.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
132.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* y y))

simplify3.2s

Counts
166 → 166
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
01953422
16803089
249702561
done50012561

prune861.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes442.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 22.9b

bsearch168.0ms

Steps
ItersRangePoint
10
441222170824.8676
2.0110076054247779e+21
892748271927.3169
10
-4211402014892830.5
-43.17511262056913
-100475634.7367845

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02971
13961
done3961

end0.0ms

sample1.1s

Algorithm
intervals
Results
417.0ms6084×body80valid
124.0ms712×body640valid
103.0ms364×body1280valid
70.0ms531×body320valid
62.0ms309×body160valid