Details

Time bar (total: 33.5s)

sample86.0ms

Algorithm
intervals
Results
42.0ms256×body80valid
24.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5000
31754
2282
158
017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.0b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
45.1b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite551.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down insert-posit16 add-log-exp
3×distribute-lft-out
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 193
Calls
4 calls:
48.0ms
(* i (+ (+ alpha beta) i))
86.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
246.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
167.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
34.0ms
(* i (+ (+ alpha beta) i))
176.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
242.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.7s

Counts
205 → 205
Iterations
IterNodes
done5001
11276
0351

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-cbrt-cube add-exp-log
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 308
Calls
4 calls:
206.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
713.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
73.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
143.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.3s

Counts
4 → 12
Calls
4 calls:
288.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.7s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
106.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
151.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.8s

Counts
320 → 320
Iterations
IterNodes
done5000
11694
0465

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite997.0ms

Algorithm
rewrite-expression-head
Rules
193×add-exp-log
145×add-cbrt-cube
98×div-exp
68×cbrt-undiv
65×prod-exp
58×times-frac
48×*-un-lft-identity
47×cbrt-unprod
42×associate-*l*
39×add-sqr-sqrt
28×add-cube-cbrt
14×associate-/r/
12×associate-*r*
9×flip3-+ flip-+ distribute-lft-out
8×pow1 1-exp
7×sqrt-prod div-inv
4×sqrt-div insert-posit16 add-log-exp
3×associate-/r* associate-*r/
2×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares unswap-sqr associate-/l/
1×frac-times clear-num frac-2neg flip3-- pow-prod-down associate-*l/ *-commutative flip-- associate-/l* distribute-lft-out--
Counts
4 → 183
Calls
4 calls:
880.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
11.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
20.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.1s

Counts
4 → 12
Calls
4 calls:
2.8s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
100.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
77.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
84.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify2.0s

Counts
195 → 195
Iterations
IterNodes
done5000
11337
0362

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize103.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
29.5b
(/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0)))
33.8b
(/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta)))
34.7b
(/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))

rewrite802.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
79×*-un-lft-identity
78×add-cbrt-cube add-exp-log
67×add-sqr-sqrt
39×cbrt-undiv div-exp add-cube-cbrt
18×associate-/r/
17×prod-exp cbrt-unprod associate-/l*
16×associate-/r*
14×difference-of-squares
13×distribute-lft-out
9×div-inv
8×associate-/l/
7×sqrt-prod distribute-lft-out--
6×flip3-- flip--
5×flip3-+ flip-+
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
3×associate-*r/
1×frac-times associate-*l/
Counts
4 → 195
Calls
4 calls:
450.0ms
(/ (/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
205.0ms
(/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0)))
43.0ms
(/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta)))
95.0ms
(/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))

series4.2s

Counts
4 → 12
Calls
4 calls:
3.1s
(/ (/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
862.0ms
(/ (* (/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta))) (/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))) (- (+ (* i 2) (+ alpha beta)) (sqrt 1.0)))
121.0ms
(/ (* i (+ alpha (+ beta i))) (+ (* i 2) (+ alpha beta)))
139.0ms
(/ (+ (* i (+ alpha (+ beta i))) (* beta alpha)) (+ (* i 2) (+ alpha beta)))

simplify1.9s

Counts
207 → 207
Iterations
IterNodes
done5001
11045
0338

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.7b

regimes260.0ms

Accuracy

46.5% (1.5b remaining)

Error of 35.8b against oracle of 34.4b and baseline of 37.1b

bsearch111.0ms

Steps
ItersRangePoint
7
1.5185210340582453e+216
6.531618038873483e+217
1.605441052792236e+216

simplify10.0ms

Iterations
IterNodes
done37
137
027

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.0s8000×body80valid
363.0ms8000×pre80true