Details

Time bar (total: 21.3s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify452.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01753
16052
226648
3136348
done500048

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.0b

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))))
38.2b
(/ (/ (* (* 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))
45.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite329.0ms

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:
74.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
53.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
119.0ms
(/ (/ (* (* 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))
72.0ms
(/ (* (* 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)))
114.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
777.0ms
(/ (/ (* (* 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))
182.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify410.0ms

Counts
220 → 220
Iterations

Useful iterations: done (400.0ms)

IterNodesCost
036612421
1124911265
done500111003

prune718.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 38.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))
38.2b
(/ (* (/ (* 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)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
42×add-exp-log add-cbrt-cube
24×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
17×cbrt-undiv div-exp
16×times-frac
11×pow1
10×prod-exp associate-/r* cbrt-unprod
9×flip3-+ flip-+
6×associate-/r/
5×frac-times associate-*r/ associate-/l/ associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg swap-sqr associate-*r* associate-*l* associate-*l/ clear-num div-inv
2×difference-of-squares
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 → 135
Calls
4 calls:
75.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
33.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
15.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))
108.0ms
(/ (* (/ (* 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)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
126.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))
781.0ms
(/ (* (/ (* 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)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify1.8s

Counts
147 → 147
Iterations

Useful iterations: 2 (339.0ms)

IterNodesCost
02765397
18694811
247643701
done50003701

prune471.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
31.7b
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
37.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite216.0ms

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×difference-of-squares
18×associate-/r/
17×prod-exp cbrt-unprod
16×associate-/r*
15×associate-/l*
11×sqrt-prod div-inv distribute-lft-out--
9×flip3-+ flip-+ 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 → 201
Calls
4 calls:
126.0ms
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
59.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
19.0ms
(/ (* 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:
2.3s
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
614.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
92.0ms
(/ (* 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)))

simplify364.0ms

Counts
213 → 213
Iterations

Useful iterations: done (347.0ms)

IterNodesCost
033612343
198011617
done500010580

prune651.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (sqrt (fma 2.0 i (+ alpha beta))) (sqrt (sqrt 1.0))))
31.7b
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
37.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
183×add-sqr-sqrt
174×times-frac
123×*-un-lft-identity
121×sqrt-prod
78×add-exp-log add-cbrt-cube
66×difference-of-squares
51×add-cube-cbrt
39×cbrt-undiv div-exp
28×associate-/r/
22×distribute-lft-out--
21×associate-/r*
17×prod-exp cbrt-unprod
16×div-inv
15×associate-/l*
14×flip3-+ flip-+ 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 → 256
Calls
4 calls:
75.0ms
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (sqrt (fma 2.0 i (+ alpha beta))) (sqrt (sqrt 1.0))))
59.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
18.0ms
(/ (* 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)))

series10.0s

Counts
4 → 12
Calls
4 calls:
9.1s
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (- (sqrt (fma 2.0 i (+ alpha beta))) (sqrt (sqrt 1.0))))
611.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
130.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify100.0ms

Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
034917269