Details

Time bar (total: 2.3m)

sample35.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
5.0ms256×pre80true

simplify721.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01753
16052
226548
3134948
done500048

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
40.5b
(/ (/ (* (* 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))
46.5b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 208
Calls
4 calls:
71.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
51.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
116.0ms
(/ (/ (* (* 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))
68.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
104.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
754.0ms
(/ (/ (* (* 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))
179.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify500.0ms

Counts
220 → 220
Iterations

Useful iterations: done (490.0ms)

IterNodesCost
036612421
1123111265
done500210981

prune945.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.9b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
36.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.8b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
104×times-frac
85×add-sqr-sqrt
81×*-un-lft-identity
78×add-exp-log add-cbrt-cube
41×add-cube-cbrt
39×cbrt-undiv div-exp
22×associate-/r/ difference-of-squares
17×prod-exp cbrt-unprod
16×associate-/r*
15×associate-/l*
11×flip3-+ sqrt-prod flip-+ div-inv distribute-lft-out--
9×distribute-lft-out
6×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-*r/
1×frac-times flip3-- associate-*l/ flip--
Counts
4 → 205
Calls
4 calls:
223.0ms
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
127.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
14.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

series3.6s

Counts
4 → 12
Calls
4 calls:
2.8s
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
636.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

simplify1.7s

Counts
217 → 217
Iterations

Useful iterations: 2 (707.0ms)

IterNodesCost
035113147
1102711651
2499010045
done500010045

prune744.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 37.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
0.1b
(/ (/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.9b
(/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
37.8b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
116×times-frac
109×*-un-lft-identity
93×add-sqr-sqrt
75×add-exp-log add-cbrt-cube
49×add-cube-cbrt
42×cbrt-undiv div-exp
22×associate-/r/ difference-of-squares
21×distribute-lft-out
18×associate-/r*
17×associate-/l*
12×prod-exp cbrt-unprod
11×sqrt-prod div-inv distribute-lft-out--
10×flip3-+ flip-+
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
1×frac-times flip3-- associate-*r/ associate-*l/ flip--
Counts
4 → 217
Calls
4 calls:
18.0ms
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
187.0ms
(/ (/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
91.0ms
(/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
15.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

series3.7s

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
2.8s
(/ (/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
675.0ms
(/ (* (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
135.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

simplify1.7s

Counts
229 → 229
Iterations

Useful iterations: 2 (754.0ms)

IterNodesCost
036213150
1101611908
2473810294
done500010294

prune938.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
0.1b
(/ (/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
37.8b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite7.9s

Algorithm
rewrite-expression-head
Rules
151634×times-frac
91713×*-un-lft-identity
64722×add-sqr-sqrt
49194×add-cube-cbrt
19436×distribute-lft-out
7764×difference-of-squares
4564×div-inv
3955×associate-/l*
3882×sqrt-prod distribute-lft-out--
3756×associate-/r/
1372×flip3-+ flip-+
91×add-exp-log add-cbrt-cube
71×associate-/r*
66×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×flip3-- flip--
Counts
4 → 31309
Calls
4 calls:
27.0ms
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
1.3s
(/ (/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
140.0ms
(/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
2.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series3.1s

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))
2.3s
(/ (/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
602.0ms
(/ (/ i (/ (fma 2.0 i (+ alpha beta)) (+ (+ alpha beta) i))) (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
124.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify13.6s

Counts
31321 → 31321
Iterations

Useful iterations: 0 (5.6s)

IterNodesCost
0225603167871
done225603167871

prune1.6m

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.6b

regimes153.0ms

Accuracy

41.5% (9.3b remaining)

Error of 11.3b against oracle of 2.0b and baseline of 17.9b

bsearch119.0ms

Steps
ItersRangePoint
5
7.401617870339687e+153
2.6261402334042752e+154
1.577106933202304e+154
7
1.37378254103246e+141
3.6561773763313927e+142
1.0260692187665977e+142

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
040145
151145
done51145

end0.0ms

sample713.0ms

Algorithm
intervals
Results
369.0ms8000×body80valid
143.0ms8000×pre80true