Details

Time bar (total: 9.4s)

sample32.0ms

Algorithm
intervals
Results
8.0ms59×body640valid
5.0ms139×body80valid
3.0ms28×body320valid
2.0ms14×body1280valid
1.0ms17×body160valid

simplify10.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.1b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite537.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
35×times-frac
33×add-sqr-sqrt
14×distribute-lft-out--
13×add-cube-cbrt
10×add-log-exp
9×distribute-lft-out
8×difference-of-squares
5×add-exp-log associate-/r* add-cbrt-cube
3×pow1 flip3-- frac-add flip-- associate-/l*
2×sub-neg associate-+l+ diff-log sum-log associate-/r/ frac-sub
1×cbrt-undiv +-commutative associate-+l- frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
3 → 81
Calls
3 calls:
22.0ms
(/ 1.0 (- x 1.0))
80.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
428.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series461.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(/ 1.0 (- x 1.0))
64.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
354.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify112.0ms

Counts
90 → 90

prune354.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.3b
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.1b
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
14.4b
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
340×*-un-lft-identity
225×times-frac
176×add-sqr-sqrt
150×frac-sub
101×distribute-lft-out--
94×frac-times
65×add-cube-cbrt
64×flip3-- flip--
52×associate-*r/ associate-*l/
51×difference-of-squares
47×associate-/l/
41×swap-sqr
31×associate-*r* associate-*l*
20×add-exp-log add-cbrt-cube
18×pow1
16×distribute-lft-out
13×associate-/r/
11×associate-/r*
6×add-log-exp
5×cbrt-undiv sub-neg div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×distribute-rgt-in distribute-lft-in associate--l+ associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×frac-2neg diff-log div-sub clear-num
Counts
4 → 352
Calls
4 calls:
95.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
547.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
190.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
936.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
76.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
342.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.0s
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify141.0ms

Counts
364 → 364

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
0.2b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.3b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
22×flip3-- flip--
16×frac-times frac-add
13×add-sqr-sqrt
12×flip3-+ flip-+
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
10×associate-*r*
8×associate-*r/ add-log-exp
7×add-cube-cbrt sub-neg
6×distribute-rgt-in distribute-lft-in
4×associate-+l+ associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative distribute-lft-out-- difference-of-squares
1×+-commutative diff-log sum-log unswap-sqr
Counts
4 → 107
Calls
4 calls:
42.0ms
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
56.0ms
(* (* (+ x 1.0) x) (- x 1.0))
13.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
48.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series227.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
119.0ms
(* (* (+ x 1.0) x) (- x 1.0))
41.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
2.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify114.0ms

Counts
119 → 119

prune368.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log associate-*l/ add-cbrt-cube
8×frac-times associate-/r/
7×pow1 add-sqr-sqrt *-un-lft-identity
6×flip3-- flip3-+ prod-exp flip-- cbrt-unprod flip-+
5×add-cube-cbrt associate-*r*
4×associate-*r/
3×cbrt-undiv times-frac div-exp pow-prod-down associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in add-log-exp
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 63
Calls
2 calls:
36.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
53.0ms
(* (* (+ x 1.0) x) (- x 1.0))

series205.0ms

Counts
2 → 6
Calls
2 calls:
103.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
102.0ms
(* (* (+ x 1.0) x) (- x 1.0))

simplify43.0ms

Counts
69 → 69

prune144.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify108.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
850.0ms4123×body80valid
349.0ms1878×body640valid
134.0ms944×body320valid
129.0ms565×body1280valid
45.0ms491×body160valid