Details

Time bar (total: 9.7s)

sample28.0ms

Algorithm
intervals
Results
8.0ms274×body80valid
7.0ms258×body80nan

simplify91.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12414
24714
37514
49214
510914
612414
715514
816614
done16614

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
0.2b
(* 3.0 (sqrt x))
0.3b
(/ y (* 3.0 (sqrt x)))
0.4b
(/ 1.0 (* x 9.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
63×*-un-lft-identity
56×prod-diff
42×add-cube-cbrt
30×times-frac
23×associate--l+
16×add-exp-log add-cbrt-cube
11×distribute-lft-out--
10×div-inv
9×add-log-exp difference-of-squares
6×pow1 associate-*r* associate-/l*
5×fma-neg
4×cbrt-undiv expm1-log1p-u div-exp sqrt-prod log1p-expm1-u
3×diff-log associate-*l* prod-exp cbrt-unprod
2×sub-neg flip3-- frac-2neg clear-num associate-/r* frac-sub flip-- unswap-sqr
1×associate--l- pow-prod-down *-commutative
Counts
4 → 154
Calls
4 calls:
58.0ms
(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
5.0ms
(* 3.0 (sqrt x))
4.0ms
(/ y (* 3.0 (sqrt x)))
3.0ms
(/ 1.0 (* x 9.0))

series161.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
37.0ms
(* 3.0 (sqrt x))
59.0ms
(/ y (* 3.0 (sqrt x)))
16.0ms
(/ 1.0 (* x 9.0))

simplify879.0ms

Counts
166 → 166
Iterations

Useful iterations: done (873.0ms)

IterNodesCost
03093815
17623277
224172669
done50002648

prune390.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))
0.2b
(/ (/ 1.0 x) 9.0)
0.2b
(* 3.0 (sqrt x))
0.3b
(/ y (* 3.0 (sqrt x)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
299×add-sqr-sqrt
242×*-un-lft-identity
221×add-cube-cbrt
178×prod-diff
131×associate--l+
25×div-inv difference-of-squares
16×add-exp-log add-cbrt-cube associate-/l*
11×distribute-lft-out--
9×add-log-exp
7×fma-neg
6×pow1 associate-*r*
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-/r* sqrt-prod log1p-expm1-u
3×diff-log associate-*l*
2×sub-neg flip3-- frac-2neg prod-exp clear-num frac-sub flip-- cbrt-unprod unswap-sqr
1×associate--l- pow-prod-down *-commutative associate-/l/
Counts
4 → 327
Calls
4 calls:
222.0ms
(- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))
6.0ms
(/ (/ 1.0 x) 9.0)
5.0ms
(* 3.0 (sqrt x))
4.0ms
(/ y (* 3.0 (sqrt x)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))
16.0ms
(/ (/ 1.0 x) 9.0)
38.0ms
(* 3.0 (sqrt x))
67.0ms
(/ y (* 3.0 (sqrt x)))

simplify1.8s

Counts
339 → 339
Iterations

Useful iterations: 2 (967.0ms)

IterNodesCost
056610014
114839008
247837186
done50007186

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ 1 x) (cbrt 9.0)) (/ 1.0 (* (cbrt 9.0) (cbrt 9.0))))
1.0b
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
1.0b
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
17.9b
(+ (/ -1 (* (cbrt 9.0) x)) (/ (/ 1 x) (cbrt 9.0)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
125×add-sqr-sqrt
87×*-un-lft-identity
82×associate-*l*
81×add-cube-cbrt
74×add-exp-log
45×cbrt-prod
34×add-cbrt-cube
32×div-exp
22×prod-exp
19×cbrt-undiv
14×cbrt-unprod unswap-sqr
11×div-inv
7×fma-def associate-*r*
6×pow1 associate-/l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp
2×frac-2neg clear-num associate-/r*
1×+-commutative frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ frac-add sum-log *-commutative flip-+ distribute-lft-out
Counts
4 → 209
Calls
4 calls:
50.0ms
(* (/ (/ 1 x) (cbrt 9.0)) (/ 1.0 (* (cbrt 9.0) (cbrt 9.0))))
4.0ms
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
4.0ms
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
51.0ms
(+ (/ -1 (* (cbrt 9.0) x)) (/ (/ 1 x) (cbrt 9.0)))

series109.0ms

Counts
4 → 8
Calls
4 calls:
106.0ms
(* (/ (/ 1 x) (cbrt 9.0)) (/ 1.0 (* (cbrt 9.0) (cbrt 9.0))))
0.0ms
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
0.0ms
(/ 1.0 (* (cbrt 9.0) (cbrt 9.0)))
3.0ms
(+ (/ -1 (* (cbrt 9.0) x)) (/ (/ 1 x) (cbrt 9.0)))

simplify885.0ms

Counts
217 → 217
Iterations

Useful iterations: done (878.0ms)

IterNodesCost
02763504
18613306
224122510
done50002401

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ y (* 3.0 (sqrt x)))
0.3b
(/ (/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x)) (cbrt 9.0))
0.3b
(* (* (cbrt 9.0) (cbrt 9.0)) x)
0.4b
(/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
37×add-exp-log
27×add-cbrt-cube
24×cbrt-prod
13×associate-/l*
12×cbrt-undiv div-exp
10×prod-exp cbrt-unprod div-inv
9×pow1
8×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* pow-prod-down clear-num
1×associate-*l* *-commutative associate-/l/ unswap-sqr
Counts
4 → 145
Calls
4 calls:
4.0ms
(/ y (* 3.0 (sqrt x)))
18.0ms
(/ (/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x)) (cbrt 9.0))
12.0ms
(* (* (cbrt 9.0) (cbrt 9.0)) x)
13.0ms
(/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x))

series325.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ y (* 3.0 (sqrt x)))
99.0ms
(/ (/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x)) (cbrt 9.0))
70.0ms
(* (* (cbrt 9.0) (cbrt 9.0)) x)
96.0ms
(/ 1.0 (* (* (cbrt 9.0) (cbrt 9.0)) x))

simplify758.0ms

Counts
157 → 157
Iterations

Useful iterations: done (753.0ms)

IterNodesCost
02622374
16162125
221741883
done50011880

prune464.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02652
13752
24352
34552
done4552

end0.0ms

sample780.0ms

Algorithm
intervals
Results
274.0ms8525×body80valid
243.0ms8510×body80nan