Details

Time bar (total: 14.1s)

sample51.0ms

Algorithm
intervals
Results
16.0ms60×body1280valid
8.0ms37×body640valid
8.0ms132×body80valid
3.0ms20×body320valid
1.0ms7×body160valid

simplify150.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
12.0ms
(/ x (+ x 1.0))
25.0ms
(/ (+ x 1.0) (- x 1.0))
161.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series255.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ x (+ x 1.0))
60.0ms
(/ (+ x 1.0) (- x 1.0))
144.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts
113 → 113

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ 1 (- x 1.0))
0.1b
(* (/ 1 (- x 1.0)) (+ x 1.0))
6.1b
(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
54×add-sqr-sqrt
44×times-frac
33×add-cube-cbrt
21×associate-*l*
19×add-exp-log
13×add-cbrt-cube
9×associate-/r*
7×pow1 distribute-lft-out-- difference-of-squares
6×associate-/r/ associate-/l* add-log-exp
5×flip3-+ div-exp frac-sub flip-+ distribute-lft-out
4×frac-times associate-*r/ associate-*r* prod-exp
3×cbrt-undiv flip3-- flip-- div-inv unswap-sqr
2×distribute-rgt-in rec-exp frac-2neg distribute-lft-in 1-exp associate-*l/ clear-num cbrt-unprod associate--r+
1×sub-neg pow-flip diff-log pow-prod-down *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
12.0ms
(/ x (+ x 1.0))
19.0ms
(/ 1 (- x 1.0))
64.0ms
(* (/ 1 (- x 1.0)) (+ x 1.0))
69.0ms
(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ x (+ x 1.0))
32.0ms
(/ 1 (- x 1.0))
42.0ms
(* (/ 1 (- x 1.0)) (+ x 1.0))
136.0ms
(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify1.1s

Counts
155 → 155

prune317.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- x 1.0))
0.0b
(* (+ x 1.0) (+ x 1.0))
0.0b
(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
19.7b
(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*r/
35×*-un-lft-identity
32×frac-sub
30×flip3-+ flip-+
25×add-sqr-sqrt
20×frac-times flip3-- flip--
19×add-cube-cbrt
18×associate-/l/
13×pow1
12×times-frac
10×add-exp-log associate-*l/ add-cbrt-cube
9×associate-*r*
7×associate-*l*
6×distribute-rgt-in distribute-lft-in swap-sqr distribute-lft-out add-log-exp
5×sub-neg difference-of-squares
4×associate--l+ associate-/r*
3×associate-/l*
2×pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod associate--r+ unswap-sqr
1×cbrt-undiv pow2 frac-2neg pow-plus diff-log div-sub div-exp clear-num pow-sqr pow-prod-up div-inv distribute-lft-out--
Counts
4 → 152
Calls
4 calls:
23.0ms
(* x (- x 1.0))
34.0ms
(* (+ x 1.0) (+ x 1.0))
72.0ms
(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
28.0ms
(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* x (- x 1.0))
16.0ms
(* (+ x 1.0) (+ x 1.0))
59.0ms
(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
43.0ms
(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify2.3s

Counts
164 → 164

prune475.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))
1.8b
(/ (- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))) (- (* x x) (* 1.0 1.0)))
20.7b
(- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))))
22.2b
(/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
14×flip3-- flip--
13×times-frac
12×frac-times associate-/l/
10×associate-*r/ associate-/r/
9×flip3-+ flip-+
6×pow1 associate-*l/ add-log-exp
5×cbrt-undiv div-exp associate-*l* prod-exp associate-/r* cbrt-unprod difference-of-squares
4×associate--l+ frac-sub associate-/l*
3×distribute-rgt-in sub-neg distribute-lft-in associate-*r*
2×frac-2neg clear-num div-inv
1×diff-log div-sub pow-prod-down *-commutative distribute-lft-out-- unswap-sqr
Counts
4 → 123
Calls
4 calls:
89.0ms
(* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))
97.0ms
(/ (- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))) (- (* x x) (* 1.0 1.0)))
32.0ms
(- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))))
78.0ms
(/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))
400.0ms
(/ (- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))) (- (* x x) (* 1.0 1.0)))
1.3s
(- (* x (- x 1.0)) (/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x))))))
145.0ms
(/ (* (- (* x x) (* 1.0 1.0)) (+ (pow x 3) (pow 1.0 3))) (* (- x 1.0) (+ (pow x 2) (* 1.0 (- 1.0 x)))))

simplify586.0ms

Counts
135 → 135

prune759.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.8b

bsearch199.0ms

Steps
ItersRangePoint
11
25.236512407247684
1.3152100289243339e+22
10072.802633631665
11
-2.8384424778333972e+23
-31.62993370098301
-12597.723661679984

simplify664.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
836.0ms1773×body1280valid
239.0ms1224×body640valid
213.0ms4106×body80valid
123.0ms600×body320valid
26.0ms297×body160valid