Details

Time bar (total: 17.0s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123
done500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.9b

localize20.0ms

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)))
41.0b
(/ (* 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)))))
41.6b
(/ (* (* (- (* (+ (+ 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))))

rewrite835.0ms

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:
265.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
184.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
165.0ms
(/ (* 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)))))
216.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.7s

Counts
4 → 12
Calls
4 calls:
516.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
274.0ms
(* (- (* (+ (+ 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))))

simplify52.0ms

Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435
done50022435

prune458.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 46.5b

localize17.0ms

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)))
7.9b
(/ (* (- (* (+ (+ 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))))
34.4b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
41.0b
(/ (* 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)))))

rewrite358.0ms

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:
183.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
84.0ms
(/ (* (- (* (+ (+ 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)))
78.0ms
(/ (* 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)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
280.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
2.2s
(/ (* (- (* (+ (+ 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))))
125.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
858.0ms
(/ (* 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 (27.0ms)

IterNodesCost
09814480
150013634
done50013634

prune592.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 36.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
34.3b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.3b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
40.6b
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
315×times-frac
136×add-sqr-sqrt
132×add-cube-cbrt *-un-lft-identity
75×associate-/r*
63×add-exp-log add-cbrt-cube
60×sqrt-prod
32×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
10×div-inv
6×pow1
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num associate-/l* difference-of-squares
1×flip3-- flip3-+ associate-*l/ flip-- flip-+
Counts
4 → 240
Calls
4 calls:
157.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
120.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
845.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
64.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
59.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
152.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify93.0ms

Counts
252 → 252
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014958015
150017100
done50017100

prune793.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
3.1b
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
34.3b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.3b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
329×times-frac
147×add-sqr-sqrt
145×add-cube-cbrt *-un-lft-identity
99×add-exp-log add-cbrt-cube
74×associate-/r*
72×sqrt-prod
49×cbrt-undiv div-exp
27×prod-exp cbrt-unprod
10×div-inv
7×associate-/l*
6×pow1
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×associate-/r/ associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×frac-times associate-*r/
Counts
4 → 266
Calls
4 calls:
6.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
599.0ms
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series2.5s

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
2.3s
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
66.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify100.0ms

Counts
278 → 278
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015089526
150018233
done50018233

prune945.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.3b

regimes154.0ms

Accuracy

35.8% (2.2b remaining)

Error of 36.5b against oracle of 34.3b and baseline of 37.8b

bsearch51.0ms

Steps
ItersRangePoint
7
4.3937702386440575e+210
1.1253432725521615e+212
4.4417126888079337e+210

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03533
13533
done3533

end0.0ms

sample680.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid
105.0ms8000×pre80true