Details

Time bar (total: 3.9m)

sample128.0ms

Algorithm
intervals
Results
38.0ms207×body80valid
29.0ms256×pre80true
17.0ms18×body1280valid
14.0ms19×body640valid
4.0ms7×body320valid
2.0ms5×body160valid

simplify165.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
164.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize50.0ms

Local error

Found 3 expressions with local error:

22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite784.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-cbrt-cube add-exp-log
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
5×add-log-exp
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 162
Calls
3 calls:
Slowest
539.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
170.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
70.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series885.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
413.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
332.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
140.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.1s

Counts
169 → 171
Calls
169 calls:
Slowest
802.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
760.0ms
(/ (* (+ alpha beta) (- beta alpha)) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
750.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
732.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
706.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize38.0ms

Local error

Found 4 expressions with local error:

5.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.2b
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1015×times-frac
755×*-un-lft-identity
655×add-sqr-sqrt
413×add-cube-cbrt
333×sqrt-prod
153×associate-*r*
121×distribute-lft-out
118×associate-*l*
64×add-exp-log
50×add-cbrt-cube
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
37×associate-/l*
35×div-exp unswap-sqr
34×div-inv
24×cbrt-undiv
20×flip3-+ flip-+
14×associate-/r*
12×prod-exp
9×cbrt-unprod
8×sqrt-div
6×pow1 add-log-exp
4×expm1-log1p-u 1-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg div-sub associate-/l/
1×frac-times +-commutative sum-log fma-def pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 709
Calls
4 calls:
Slowest
574.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
205.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
179.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
150.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
384.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
336.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
288.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
174.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify2.4m

Counts
963 → 721
Calls
963 calls:
Slowest
801.0ms
(* (/ (/ (sqrt (+ alpha beta)) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (sqrt (- beta alpha)) (sqrt (+ (+ alpha beta) (* 2 i)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
734.0ms
(* (/ (* (* (/ (+ alpha beta) 1) (/ (+ alpha beta) 1)) (/ (+ alpha beta) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
729.0ms
(/ (/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))) (sqrt 1))
714.0ms
(* (/ (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* 1 1) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
664.0ms
(/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (sqrt (+ (+ alpha beta) (* 2 i)))) (* (cbrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (cbrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))

prune11.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize86.0ms

Local error

Found 4 expressions with local error:

5.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
5.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
5.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite635.0ms

Algorithm
rewrite-expression-head
Rules
208×times-frac
184×*-un-lft-identity
102×add-sqr-sqrt add-cube-cbrt
68×sqrt-prod
41×distribute-lft-out
16×associate-/l*
11×add-exp-log
10×add-log-exp
9×add-cbrt-cube div-inv
7×associate-/r*
5×div-exp
4×expm1-log1p-u pow1 flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×cbrt-undiv +-commutative sum-log fma-def
2×sqrt-div associate-/r/
1×clear-num frac-2neg 1-exp associate-/l/
Counts
4 → 201
Calls
4 calls:
Slowest
206.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
174.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
133.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
114.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
427.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
376.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
333.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
145.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify29.9s

Counts
272 → 213
Calls
272 calls:
Slowest
535.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
483.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
478.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
441.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
329.0ms
(- (+ (* (sqrt 0.5) beta) (* (sqrt 0.5) alpha)) (* 1/2 (* (sqrt 0.125) (pow alpha 2))))

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize88.0ms

Local error

Found 4 expressions with local error:

6.8b
(+ (* (/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite970.0ms

Algorithm
rewrite-expression-head
Rules
5299×times-frac
4048×sqrt-prod
3717×*-un-lft-identity
2227×add-sqr-sqrt
2179×add-cube-cbrt
745×distribute-lft-out
203×associate-/l*
143×div-inv
54×sqrt-div
44×associate-/r/
28×add-exp-log
27×associate-/r*
24×distribute-lft-out-- difference-of-squares
23×flip3-+ add-cbrt-cube flip-+
17×div-exp
12×cbrt-undiv
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg associate-/l/
2×1-exp div-sub
1×+-commutative sum-log fma-def
Counts
4 → 2277
Calls
4 calls:
Slowest
296.0ms
(/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
226.0ms
(+ (* (/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
145.0ms
(/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
142.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
438.0ms
(+ (* (/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
333.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
199.0ms
(/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
162.0ms
(/ (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))