Details

Time bar (total: 31.4s)

sample74.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
9.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
01753
16052
229548
3165148
done500248

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.7b

localize38.0ms

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))))
35.2b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
44.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite894.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
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 log1p-expm1-u add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 197
Calls
4 calls:
147.0ms
(* i (+ (+ alpha beta) i))
153.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
338.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
243.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.9s

Counts
4 → 12
Calls
4 calls:
43.0ms
(* i (+ (+ alpha beta) i))
183.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.4s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
265.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify784.0ms

Counts
209 → 209
Iterations

Useful iterations: done (770.0ms)

IterNodesCost
035311780
1119010755
done50009194

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
4.1b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
32.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
43×times-frac
40×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
22×cbrt-undiv div-exp
16×associate-*l*
14×associate-/l*
12×prod-exp cbrt-unprod
7×associate-/r* associate-/r/ difference-of-squares
6×pow1 div-inv
5×associate-/l/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num
2×associate-*r/ associate-*l/ fma-udef unswap-sqr
1×distribute-rgt-in flip3-- distribute-lft-in div-sub pow-prod-down *-commutative flip--
Counts
4 → 153
Calls
4 calls:
39.0ms
(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
148.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
113.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

series2.1s

Counts
4 → 12
Calls
4 calls:
410.0ms
(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
1.2s
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
127.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
301.0ms
(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.8s

Counts
165 → 165
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02897425
18377228
240345617
done50005613

prune869.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
4.1b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
32.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite451.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
167×*-un-lft-identity
160×add-sqr-sqrt
101×associate-*l*
87×add-cube-cbrt
74×add-exp-log add-cbrt-cube
35×cbrt-undiv div-exp
32×difference-of-squares
24×distribute-lft-out
18×associate-/r/
17×prod-exp cbrt-unprod
16×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r* div-inv
6×pow1
5×flip3-- flip--
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l/ unswap-sqr
2×associate-*r/ associate-*l/ fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 254
Calls
4 calls:
140.0ms
(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
173.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
24.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series4.7s

Counts
4 → 12
Calls
4 calls:
606.0ms
(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
3.5s
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
127.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
510.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify704.0ms

Counts
266 → 266
Iterations

Useful iterations: done (690.0ms)

IterNodesCost
041812069
1114211504
done50019518

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.2b

localize47.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
32.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
32.9b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
121×add-exp-log add-cbrt-cube
64×add-sqr-sqrt
54×cbrt-undiv times-frac div-exp
48×*-un-lft-identity
38×prod-exp cbrt-unprod
32×add-cube-cbrt
16×associate-/r* associate-/l* difference-of-squares
13×associate-/r/
8×sqrt-prod distribute-lft-out--
6×div-inv
4×pow1 expm1-log1p-u frac-2neg flip3-+ clear-num flip-+ log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/ associate-/l/
2×flip3-- flip--
1×frac-times
Counts
4 → 190
Calls
4 calls:
302.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
30.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
14.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series5.4s

Counts
4 → 12
Calls
4 calls:
4.2s
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
119.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
547.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
554.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify2.6s

Counts
202 → 202
Iterations

Useful iterations: done (2.6s)

IterNodesCost
030914413
187713197
241477697
done50007684

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.2b

regimes243.0ms

Accuracy

35.4% (2.4b remaining)

Error of 36.7b against oracle of 34.3b and baseline of 38.1b

bsearch130.0ms

Steps
ItersRangePoint
8
1.4228466486321157e+203
4.845497225576045e+206
1.4407489768135957e+203

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02794
13494
done3494

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.5s8000×body80valid
273.0ms8000×pre80true