Details

sample127.0ms

Algorithm

intervals

Results

40.0ms	23×	body	1280	valid
36.0ms	201×	body	80	valid
14.0ms	256×	pre	80	true
12.0ms	17×	body	640	valid
5.0ms	8×	body	320	valid
3.0ms	7×	body	160	valid

simplify107.0ms

Calls

1 calls:

Slowest

107.0ms

(/ (+ (/ (/ (* (+ 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: 26.1b

localize26.0ms

Local error

Found 4 expressions with local error:

22.3b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.0b	(+ (/ (/ (* (+ 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))
0.0b	(* (+ alpha beta) (- beta alpha))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

4101×	`*-un-lft-identity`
2218×	`distribute-lft-out`
1938×	`times-frac`
820×	`associate-l`
787×	`add-sqr-sqrt`
495×	`add-cube-cbrt`
365×	`associate-r`
141×	`associate-/l*`
73×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
49×	`associate-/l/`
22×	`associate-/r*` `associate-/r/`
21×	`flip3-+` `flip-+`
20×	`add-cbrt-cube` `add-exp-log`
12×	`frac-times`
11×	`div-inv`
9×	`flip3--` `flip--`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `associate-l/` `associate-r/` `add-log-exp`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `pow-prod-down`

Calls

4 calls:

Slowest

963.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
300.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
132.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
30.0ms	(* (+ alpha beta) (- beta alpha))

series931.0ms

Calls

4 calls:

Slowest

416.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
333.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
125.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
57.0ms	(* (+ alpha beta) (- beta alpha))

simplify7.8m

Calls

2216 calls:

Slowest

1.1s	(/ (/ (sqrt (* (+ alpha beta) (- beta alpha))) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.1s	(/ (/ (* (sqrt (+ alpha beta)) (sqrt (- beta alpha))) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.1s	(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.1s	(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.0s	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune14.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize34.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.2b	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.1b	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b	(/ (+ alpha beta) (+ (+ alpha beta) (* 2 i)))

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

2698×	`*-un-lft-identity`
1482×	`distribute-lft-out`
1135×	`times-frac`
350×	`add-sqr-sqrt`
339×	`add-cube-cbrt`
329×	`associate-l`
278×	`associate-r`
159×	`associate-/l*`
122×	`frac-times`
77×	`associate-/l/`
67×	`associate-/r*`
62×	`flip3--` `flip--`
61×	`associate-*r/`
46×	`associate-/r/`
29×	`flip3-+` `flip-+`
23×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
11×	`clear-num`
9×	`frac-2neg`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
5×	`un-div-inv`
4×	`insert-posit16`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/` `distribute-lft-out--`
1×	`+-commutative` `sum-log` `pow-prod-down` `*-commutative` `difference-of-squares`

Calls

4 calls:

Slowest

2.6s	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
905.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
295.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
72.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2 i)))

series961.0ms

Calls

4 calls:

Slowest

334.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
267.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
240.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
120.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2 i)))