Details

Time bar (total: 36.7s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123
done500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
42.2b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite818.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp prod-exp cbrt-unprod
16×add-sqr-sqrt times-frac
13×add-cube-cbrt *-un-lft-identity
11×pow1
10×associate-*l/ associate-/r*
6×associate-*r*
5×associate-*l*
4×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u div-inv associate-/l/ add-log-exp
3×flip3-- flip--
2×distribute-rgt-in frac-2neg distribute-lft-in associate-*r/ clear-num *-commutative associate-/l*
1×flip3-+ associate-/r/ flip-+ difference-of-squares unswap-sqr
Counts
4 → 122
Calls
4 calls:
253.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
181.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
164.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
215.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.6s

Counts
4 → 12
Calls
4 calls:
510.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
268.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
846.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
2.0s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify51.0ms

Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435
done50022435

prune453.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 46.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
8.5b
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
35.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
61×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
34×associate-/r*
29×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×div-inv
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*l* associate-*l/ associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num
2×flip3-- associate-*r/ flip-- fma-udef
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down *-commutative flip-+ difference-of-squares unswap-sqr
Counts
4 → 176
Calls
4 calls:
184.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
83.0ms
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
6.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
79.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
278.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
2.1s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
127.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
852.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

simplify60.0ms

Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09814480
150013634
done50013634

prune598.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.1b
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
35.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
38.2b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
15510×times-frac
8295×*-un-lft-identity
6251×add-sqr-sqrt
5570×add-cube-cbrt
1635×distribute-lft-out
681×difference-of-squares
524×div-inv
403×associate-/r/
136×flip3-+ flip-+
93×associate-/l*
65×associate-/r*
49×add-exp-log add-cbrt-cube
32×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 3960
Calls
4 calls:
9.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
251.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
150.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

series1.3s

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
844.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
121.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
150.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

simplify1.6s

Counts
3972 → 3972
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
05297194379
done5297194379

prune16.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
0.0b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.1b
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
35.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
1388×times-frac
531×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
162×add-exp-log
151×associate-/r/
122×add-cbrt-cube
108×div-exp
97×div-inv
76×cbrt-undiv
61×associate-/r*
46×frac-times associate-*r/ associate-*l/
24×prod-exp
19×associate-/l*
16×cbrt-unprod
8×1-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 685
Calls
4 calls:
145.0ms
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
8.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
169.0ms
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

series2.8s

Counts
4 → 12
Calls
4 calls:
253.0ms
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
149.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
2.3s
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
135.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

simplify274.0ms

Counts
697 → 697
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0369926860
1500226009
done500226009

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

regimes136.0ms

Accuracy

44.5% (9.0b remaining)

Error of 11.0b against oracle of 2.0b and baseline of 18.2b

bsearch47.0ms

Steps
ItersRangePoint
5
8.474492538649088e+117
1.9837139634492472e+118
1.9634404194750732e+118

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04350
14350
done4350

end0.0ms

sample696.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid
114.0ms8000×pre80true