Details

Time bar (total: 13.8s)

sample28.0ms

Algorithm
intervals
Results
8.0ms198×body80valid
3.0ms22×body640valid
2.0ms20×body320valid
2.0ms8×body1280valid
1.0ms8×body160valid

simplify907.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite102.0ms

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:
21.0ms
(* (- 1.0 x) y)
24.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
54.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series195.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* (- 1.0 x) y)
90.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
59.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify621.0ms

Counts
72 → 72

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.3b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt associate-*r*
13×times-frac
11×add-cube-cbrt
7×add-exp-log add-cbrt-cube
5×associate-*l*
4×pow1 add-log-exp
3×flip3-- flip-- distribute-lft-out
2×frac-times associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv sub-neg flip3-+ diff-log associate-*r/ div-exp pow-prod-down *-commutative flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 55
Calls
2 calls:
46.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
6.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series130.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
69.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify604.0ms

Counts
61 → 61

prune131.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
5.2b
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
5.9b
(/ y (+ (pow y 3) (pow 1.0 3)))
14.3b
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
55×times-frac
40×add-sqr-sqrt
36×associate-*r*
35×distribute-lft-out
33×add-cube-cbrt
28×unpow-prod-down cube-prod
20×add-exp-log add-cbrt-cube
18×frac-times
13×associate-*l/
11×pow1
9×flip3-- associate-/r* flip--
8×flip3-+ flip-+
7×prod-exp sum-cubes cbrt-unprod
6×associate-*r/ associate-*l* add-log-exp
4×pow-prod-down associate-/r/
3×cbrt-undiv div-exp associate-/l*
2×distribute-rgt-in distribute-lft-in *-commutative div-inv associate--r+ unswap-sqr
1×sub-neg frac-2neg diff-log clear-num distribute-lft-out-- difference-of-squares
Counts
4 → 164
Calls
4 calls:
121.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
5.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
67.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
251.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
363.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
143.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
173.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify2.3s

Counts
176 → 176

prune552.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ y (+ (pow y 3) (pow 1.0 3)))
5.9b
(/ y (+ (pow y 3) (pow 1.0 3)))
9.7b
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
15.0b
(* (* y y) (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
54×times-frac
40×distribute-lft-out
38×add-exp-log add-cbrt-cube
33×add-sqr-sqrt add-cube-cbrt
32×unpow-prod-down cube-prod
21×pow1
18×frac-times prod-exp associate-/r* cbrt-unprod
14×flip3-- flip--
13×associate-*l/
11×associate-*r/ pow-prod-down
8×sum-cubes
6×associate-/l*
5×cbrt-undiv div-exp associate-*r*
4×associate-/r/ add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ associate-*l* clear-num *-commutative flip-+ div-inv
1×distribute-rgt-out--
Counts
4 → 179
Calls
4 calls:
40.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
40.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
169.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
179.0ms
(* (* y y) (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
141.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
124.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
100.0ms
(* (* y y) (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))))

simplify1.8s

Counts
191 → 191

prune708.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes126.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.4b

bsearch128.0ms

Steps
ItersRangePoint
10
1810750790637.4219
3.7273233967199085e+29
528433753610563.25
8
-1.6853749013735252e+30
-4.159371291780153e+27
-4.2011980442598443e+27

simplify1.8s

end0.0ms

sample1.2s

Algorithm
intervals
Results
604.0ms6091×body80valid
136.0ms754×body640valid
96.0ms505×body320valid
67.0ms354×body1280valid
22.0ms296×body160valid