Details

Time bar (total: 33.4s)

sample79.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
10.0ms256×pre80true

simplify4.9s

Counts
1 → 1
Iterations
IterNodes
411139
31615
2280
160
017

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.4b

localize36.0ms

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))))
39.9b
(/ (/ (* (* 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))
46.7b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite521.0ms

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×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u 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 → 201
Calls
4 calls:
94.0ms
(* i (+ (+ alpha beta) i))
82.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
233.0ms
(/ (/ (* (* 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))
105.0ms
(/ (* (* 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:
42.0ms
(* i (+ (+ alpha beta) i))
181.0ms
(* (* 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))
256.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.0s

Counts
213 → 213
Iterations
IterNodes
27204
11272
0359

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 37.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.2b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite770.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- flip--
Counts
4 → 264
Calls
4 calls:
199.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
309.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
68.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
189.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
325.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
406.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
153.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
180.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.3s

Counts
276 → 276
Iterations
IterNodes
24187
11119
0409

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.8b

localize87.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite752.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
173×add-sqr-sqrt
135×*-un-lft-identity
124×sqrt-prod
97×add-cube-cbrt
38×difference-of-squares
27×associate-/r*
21×associate-/r/
19×distribute-lft-out--
15×add-cbrt-cube add-exp-log
13×flip3-+ flip-+ associate-/l*
11×div-inv
8×associate-/l/
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-*r/
1×flip3-- sqrt-div div-sub prod-exp cbrt-unprod flip--
Counts
4 → 247
Calls
4 calls:
344.0ms
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
61.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
151.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
191.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
115.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
195.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
174.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.6s

Counts
259 → 259
Iterations
IterNodes
23264
11023
0402

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 37.8b

localize95.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (+ (+ alpha beta) (* 2 i))))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.4b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.4b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
39×times-frac
38×add-sqr-sqrt
36×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×associate-/r*
8×sqrt-div
7×associate-/l*
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×cbrt-undiv div-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ div-inv
1×sqrt-undiv prod-exp cbrt-unprod
Counts
4 → 132
Calls
4 calls:
35.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (+ (+ alpha beta) (* 2 i))))
84.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
6.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
6.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (+ (+ alpha beta) (* 2 i))))
144.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
92.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
107.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify4.8s

Counts
144 → 144
Iterations
IterNodes
310258
21989
1547
0220

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 37.8b

regimes268.0ms

Accuracy

0% (2.8b remaining)

Error of 36.8b against oracle of 34.1b and baseline of 36.8b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
231
131
022

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.8s8000×body80valid
394.0ms8000×pre80true