Details

Time bar (total: 4.2m)

sample117.0ms

Algorithm
intervals
Results
41.0ms202×body80valid
19.0ms22×body1280valid
14.0ms19×body640valid
14.0ms256×pre80true
4.0ms7×body320valid
2.0ms6×body160valid

simplify173.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
173.0ms
(/ (+ (/ (/ (* (+ 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: 24.4b

localize36.0ms

Local error

Found 4 expressions with local error:

23.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(+ (+ alpha beta) (* 2 i))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
4×frac-times pow1 sum-log insert-posit16
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 128
Calls
4 calls:
Slowest
523.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
155.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
47.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
22.0ms
(+ (+ alpha beta) (* 2 i))

series893.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
350.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
105.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
29.0ms
(+ (+ alpha beta) (* 2 i))

simplify25.7s

Counts
133 → 140
Calls
133 calls:
Slowest
1.1s
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
685.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
608.0ms
(/ (* (* (/ (* (+ 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)))
566.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
557.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize46.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
1.2b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
113×associate-/r*
79×distribute-lft-out-- difference-of-squares
59×associate-/r/
33×div-inv
29×flip3-+ flip-+
20×add-cbrt-cube add-exp-log
13×associate-/l*
10×cbrt-undiv div-exp
6×add-log-exp associate-/l/
4×pow1 insert-posit16
3×clear-num frac-2neg
1×+-commutative sum-log flip3-- div-sub flip--
Counts
4 → 650
Calls
4 calls:
Slowest
569.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
238.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
203.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
51.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series881.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
221.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
209.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
119.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify3.5m

Counts
1067 → 662
Calls
1067 calls:
Slowest
1.0s
(/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
1.0s
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
897.0ms
(/ 1 (/ 1 (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))))
754.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (sqrt (- beta alpha)) (sqrt (+ (+ alpha beta) (* 2 i))))))
726.0ms
(- (+ (* 8 (/ (* i beta) alpha)) (+ (* 4 (/ (* (pow i 2) beta) (pow alpha 2))) (* 4 (/ (pow i 2) alpha)))))

prune9.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize38.0ms

Local error

Found 4 expressions with local error:

3.9b
(+ (/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
1.3b
(/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.2b
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
5615×times-frac
3877×*-un-lft-identity
2481×add-sqr-sqrt
1995×add-cube-cbrt
698×distribute-lft-out
369×associate-/r*
243×distribute-lft-out-- difference-of-squares
209×associate-/r/
108×div-inv
103×flip3-+ flip-+
62×add-exp-log
43×div-exp
32×add-cbrt-cube
28×associate-/l*
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×insert-posit16
3×clear-num frac-2neg associate-/l/
2×div-sub
1×+-commutative sum-log pow-flip inv-pow
Counts
4 → 1937
Calls
4 calls:
Slowest
671.0ms
(+ (/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
229.0ms
(/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
203.0ms
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
151.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

series993.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
306.0ms
(/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
257.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
236.0ms
(+ (/ (+ beta alpha) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
195.0ms
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))