Details

Time bar (total: 25.3s)

sample41.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
6.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
01753
16052
229548
3165148
done500248

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize40.0ms

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))))
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))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.1s

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:
148.0ms
(* i (+ (+ alpha beta) i))
213.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
466.0ms
(/ (/ (* (* 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))
292.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series2.1s

Counts
4 → 12
Calls
4 calls:
27.0ms
(* i (+ (+ alpha beta) i))
141.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.6s
(/ (/ (* (* 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))
305.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify794.0ms

Counts
209 → 209
Iterations

Useful iterations: done (780.0ms)

IterNodesCost
035311780
1119010755
done50009194

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 37.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
4.0b
(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
37.5b
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
41.7b
(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite375.0ms

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×difference-of-squares
12×prod-exp cbrt-unprod
11×pow1
8×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg swap-sqr associate-*r* associate-*l* clear-num associate-/l/
2×associate-*r/ fma-udef
1×pow2 distribute-rgt-in flip3-- distribute-lft-in flip3-+ pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip-- flip-+ unswap-sqr
Counts
4 → 187
Calls
4 calls:
16.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
70.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
249.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
24.0ms
(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
254.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.2s
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
198.0ms
(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.6s

Counts
199 → 199
Iterations

Useful iterations: done (2.6s)

IterNodesCost
033010445
19099614
239758391
done50017837

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.9b
(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
37.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
2093×times-frac
1742×*-un-lft-identity
1206×add-sqr-sqrt
740×add-cube-cbrt
462×distribute-lft-out
437×sqrt-prod
232×difference-of-squares
118×associate-/l*
116×distribute-lft-out--
44×div-inv
22×add-exp-log add-cbrt-cube
14×associate-/r/
10×cbrt-undiv div-exp
7×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*l/ prod-exp clear-num cbrt-unprod flip-+
1×flip3-- associate-*r/ flip-- associate-/l/
Counts
4 → 892
Calls
4 calls:
187.0ms
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
33.0ms
(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
3.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
496.0ms
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
771.0ms
(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
97.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
124.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.7s

Counts
904 → 904
Iterations

Useful iterations: done (1.5s)

IterNodesCost
082056632
1213253860
done500053067

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.8b
(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
37.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
2093×times-frac
1742×*-un-lft-identity
1206×add-sqr-sqrt
740×add-cube-cbrt
462×distribute-lft-out
437×sqrt-prod
232×difference-of-squares
116×associate-/l* distribute-lft-out--
44×div-inv
22×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
9×associate-/r* associate-/r/
6×pow1 associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*l/ prod-exp clear-num cbrt-unprod flip-+
1×flip3-- associate-*r/ flip--
Counts
4 → 892
Calls
4 calls:
188.0ms
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
26.0ms
(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
15.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
470.0ms
(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
678.0ms
(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
96.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
91.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.6s

Counts
904 → 904
Iterations

Useful iterations: done (1.5s)

IterNodesCost
083256641
1218053854
done500053061

prune2.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.4b

regimes174.0ms

bsearch3.0ms