Details

Time bar (total: 8.4m)

sample83.0ms

Algorithm
intervals
Results
29.0ms201×body80valid
13.0ms18×body1280valid
11.0ms256×pre80true
11.0ms19×body640valid
5.0ms12×body320valid
1.0ms6×body160valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
159.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize55.0ms

Local error

Found 3 expressions with local error:

21.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.2b
(+ (/ (/ (* (+ 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))

rewrite779.0ms

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
571.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
160.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
46.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series886.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
432.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
331.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
123.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify34.0s

Counts
169 → 171
Calls
169 calls:
Slowest
765.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
752.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
741.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
713.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
693.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize73.0ms

Local error

Found 4 expressions with local error:

7.6b
(+ (* (/ (/ (+ 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)))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite1.1s

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
573.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
186.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
178.0ms
(+ (* (/ (/ (+ 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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(+ (* (/ (/ (+ 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)
345.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
322.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
173.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify2.5m

Counts
963 → 721
Calls
963 calls:
Slowest
743.0ms
(* (/ (* (* (/ (+ 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)))))
730.0ms
(* (/ (/ (* (* (+ 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)))))
689.0ms
(* (/ (/ (sqrt (+ alpha beta)) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (sqrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
649.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ 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))))
621.0ms
(* (/ (+ alpha beta) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

prune11.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize90.0ms

Local error

Found 4 expressions with local error:

7.6b
(+ (* (/ (/ (+ 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)
7.6b
(+ (* (/ (/ (+ 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)
7.6b
(+ (* (/ (/ (+ 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)))

rewrite637.0ms

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
184.0ms
(+ (* (/ (/ (+ 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)
152.0ms
(+ (* (/ (/ (+ 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)
148.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
144.0ms
(+ (* (/ (/ (+ 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)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
464.0ms
(+ (* (/ (/ (+ 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)
455.0ms
(+ (* (/ (/ (+ 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)
413.0ms
(+ (* (/ (/ (+ 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)
176.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify31.0s

Counts
272 → 213
Calls
272 calls:
Slowest
525.0ms
(/ (/ (+ alpha beta) (sqrt 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
466.0ms
(* (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))
459.0ms
(* (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))
455.0ms
(* (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))
311.0ms
(- (+ (* (sqrt 0.5) beta) (* (sqrt 0.5) alpha)) (* 1/2 (* (sqrt 0.125) (pow alpha 2))))

prune4.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.8b

localize98.0ms

Local error

Found 4 expressions with local error:

9.0b
(+ (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
0.6b
(* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.4b
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
964×times-frac
688×add-sqr-sqrt
669×*-un-lft-identity
457×sqrt-prod
378×add-cube-cbrt
166×associate-*l*
153×associate-*r*
93×distribute-lft-out
61×add-exp-log
50×unswap-sqr
47×add-cbrt-cube
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
32×div-exp
29×div-inv
24×associate-/l*
22×cbrt-undiv
20×flip3-+ flip-+
17×associate-/r*
12×sqrt-div prod-exp
9×pow1 cbrt-unprod
6×add-log-exp
5×pow-flip
4×expm1-log1p-u sqrt-pow1 1-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg pow1/2 div-sub
1×frac-times +-commutative rec-exp sum-log fma-def pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow associate-/l/
Counts
4 → 684
Calls
4 calls:
Slowest
638.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
576.0ms
(+ (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
204.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
119.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

series4.4m

Counts
4 → 12
Calls
4 calls:
Slowest
4.4m
(* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
403.0ms
(+ (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (/ (/ (+ alpha beta) 1) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
336.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
241.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))