Details

Time bar (total: 11.8s)

sample29.0ms

Algorithm
intervals
Results
9.0ms202×body80valid
3.0ms21×body640valid
2.0ms16×body320valid
2.0ms8×body1280valid
1.0ms9×body160valid

simplify1.0s

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.5b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.6b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite114.0ms

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:
34.0ms
(* (- 1.0 x) y)
40.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
37.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series212.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(* (- 1.0 x) y)
92.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
68.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify623.0ms

Counts
72 → 72

prune184.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.5b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite107.0ms

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:
21.0ms
(/ y (+ y 1.0))
72.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
10.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series163.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ y (+ y 1.0))
50.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
73.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify791.0ms

Counts
97 → 97

prune278.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3)))
0.1b
(pow (/ y (+ y 1.0)) 3)
2.5b
(- 1.0 (* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3))))
20.3b
(cbrt (pow (/ y (+ y 1.0)) 3))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
90×cbrt-prod
74×add-sqr-sqrt times-frac
57×add-cube-cbrt
56×unpow-prod-down cube-prod
45×associate-*r*
18×distribute-lft-out
12×associate-/r/
9×add-exp-log
8×add-cbrt-cube
7×pow1 unswap-sqr
6×flip3-+ flip-+ div-inv add-log-exp
5×cube-div associate-*l*
4×cbrt-div sqr-pow
3×cube-mult pow-unpow flip3-- unpow3 flip--
2×frac-times associate-*l/ pow-exp rem-cube-cbrt
1×cbrt-undiv pow-to-exp sub-neg pow-pow pow1/3 diff-log associate-*r/ div-exp pow-prod-down prod-exp *-commutative rem-cbrt-cube cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 193
Calls
4 calls:
119.0ms
(* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3)))
30.0ms
(pow (/ y (+ y 1.0)) 3)
9.0ms
(- 1.0 (* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3))))
14.0ms
(cbrt (pow (/ y (+ y 1.0)) 3))

series317.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3)))
79.0ms
(pow (/ y (+ y 1.0)) 3)
106.0ms
(- 1.0 (* (- 1.0 x) (cbrt (pow (/ y (+ y 1.0)) 3))))
62.0ms
(cbrt (pow (/ y (+ y 1.0)) 3))

simplify1.5s

Counts
205 → 205

prune524.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.4b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
11.9b
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
49×frac-times
43×pow1
42×add-exp-log add-cbrt-cube
29×associate-*l/
26×flip3-- flip--
21×prod-exp cbrt-unprod
17×associate-*r/ pow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
8×add-log-exp
7×cbrt-undiv div-exp
5×difference-of-squares
4×pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×flip3-+ pow-plus associate-/r/ flip-+ associate-/l/
1×+-commutative pow2 sub-neg frac-2neg diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num sum-log *-commutative div-inv
Counts
4 → 139
Calls
4 calls:
9.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
180.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
10.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
53.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series889.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
82.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
121.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
624.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify1.8s

Counts
151 → 151

prune325.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes92.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 13.9b

bsearch68.0ms

Steps
ItersRangePoint
6
22309498.15747088
167850090.46355867
164787377.26665404
9
-1.2752251976054167e+24
-380908646326105.1
-389622710888582.7

simplify1.3s

end0.0ms

sample1.0s

Algorithm
intervals
Results
362.0ms6163×body80valid
175.0ms677×body640valid
100.0ms496×body320valid
79.0ms378×body1280valid
23.0ms286×body160valid