Details

Time bar (total: 12.6s)

sample43.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify446.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
01753
16052
226648
3136348
done500048

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.0b

localize15.0ms

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))))
37.5b
(/ (/ (* (* 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))
47.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite312.0ms

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:
70.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
50.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
114.0ms
(/ (/ (* (* 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))
69.0ms
(/ (* (* 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)))
102.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
758.0ms
(/ (/ (* (* 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))
180.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify384.0ms

Counts
220 → 220
Iterations

Useful iterations: done (375.0ms)

IterNodesCost
036612421
1124911265
done500011003

prune686.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 37.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
6.8b
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
37.5b
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
42.3b
(/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
61×add-exp-log add-cbrt-cube
57×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
29×cbrt-undiv div-exp
15×div-inv
14×associate-/r* associate-/l*
13×flip3-+ flip-+ difference-of-squares
12×prod-exp cbrt-unprod
11×pow1 associate-/l/
8×frac-times associate-/r/
6×associate-*r/
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×frac-2neg swap-sqr associate-*r* associate-*l* clear-num
1×pow2 distribute-rgt-in flip3-- distribute-lft-in pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip-- unswap-sqr
Counts
4 → 203
Calls
4 calls:
71.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
34.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
77.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
36.0ms
(/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
178.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
759.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
149.0ms
(/ (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify369.0ms

Counts
215 → 215
Iterations

Useful iterations: done (359.0ms)

IterNodesCost
035511530
1110810867
done500210613

prune637.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.3b
(/ (/ (+ (+ alpha beta) i) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
36.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
2108×times-frac
1755×*-un-lft-identity
1219×add-sqr-sqrt
753×add-cube-cbrt
462×distribute-lft-out
449×sqrt-prod
232×difference-of-squares
118×associate-/l*
116×distribute-lft-out--
44×div-inv
15×add-exp-log add-cbrt-cube
12×associate-/r*
9×associate-/r/
7×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip3-+ flip-- flip-+
Counts
4 → 905
Calls
4 calls:
32.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
153.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series834.0ms

Counts
4 → 12
Calls
4 calls:
429.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
288.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
56.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify685.0ms

Counts
917 → 917
Iterations

Useful iterations: done (615.0ms)

IterNodesCost
077159704
1205757033
done500056881

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
36.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
56×*-un-lft-identity
54×times-frac
46×sqrt-prod
42×add-cube-cbrt
14×difference-of-squares
12×associate-/r*
9×associate-/l*
8×add-exp-log add-cbrt-cube
7×distribute-lft-out--
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
1×flip3-- flip3-+ div-sub flip-- flip-+
Counts
4 → 138
Calls
4 calls:
151.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
32.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
635.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
421.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
54.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
58.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify451.0ms

Counts
150 → 150
Iterations

Useful iterations: done (446.0ms)

IterNodesCost
01894490
14444215
213873854
done50003837

prune540.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 34.5b

regimes128.0ms

Accuracy

38.1% (2.4b remaining)

Error of 36.3b against oracle of 33.9b and baseline of 37.8b

bsearch62.0ms

Steps
ItersRangePoint
8
2.791389625835243e+210
9.613021115241036e+213
2.851610750442873e+210

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
030108
137108
done37108

end0.0ms

sample688.0ms

Algorithm
intervals
Results
373.0ms8000×body80valid
131.0ms8000×pre80true