Details

Time bar (total: 3.1m)

sample50.0ms

Algorithm
intervals
Results
15.0ms39×body1280valid
12.0ms148×body80valid
9.0ms37×body640valid
4.0ms19×body320valid
2.0ms13×body160valid

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
112.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize21.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
0.0b
(+ 1 (exp (* -2 x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×add-sqr-sqrt
15×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-cbrt-cube add-exp-log distribute-lft-out
4×associate-/r* difference-of-squares
3×pow1 insert-posit16 associate-/l*
2×flip3-+ difference-of-sqr-1 associate-/r/ flip-+
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- distribute-lft-out--
Counts
3 → 67
Calls
3 calls:
Slowest
47.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
10.0ms
(/ 2 (+ 1 (exp (* -2 x))))
6.0ms
(+ 1 (exp (* -2 x)))

series100.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
68.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
20.0ms
(/ 2 (+ 1 (exp (* -2 x))))
11.0ms
(+ 1 (exp (* -2 x)))

simplify6.6s

Counts
57 → 76
Calls
57 calls:
Slowest
382.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
339.0ms
(/ (* (* 2 2) 2) (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
234.0ms
(+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x)))))
212.0ms
(- (+ x 1) (* 1/3 (pow x 3)))
186.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x))))))

prune674.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
0.0b
(/ (- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3)) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
0.0b
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
0.0b
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))

rewrite599.0ms

Algorithm
rewrite-expression-head
Rules
420×add-sqr-sqrt
286×times-frac
277×*-un-lft-identity
180×difference-of-squares
158×unpow-prod-down cube-prod
108×add-cube-cbrt
61×sqr-pow
46×associate-/l*
30×distribute-lft-out--
24×swap-sqr distribute-lft-out
21×add-cbrt-cube add-exp-log
20×associate-/r/
18×associate-*r* associate-*l*
12×pow1
10×flip3-+ flip-+
7×div-inv
6×cube-mult cbrt-undiv div-exp frac-add add-log-exp
5×difference-cubes
4×prod-exp cbrt-unprod insert-posit16 unswap-sqr
3×frac-times pow-unpow associate-/r* associate-*l/ associate-*r/
2×flip3-- pow-exp flip-- rem-cube-cbrt associate-/l/
1×cube-div pow2 pow-to-exp clear-num sub-neg pow-pow frac-2neg pow-plus diff-log unpow3 div-sub pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 413
Calls
4 calls:
Slowest
358.0ms
(/ (- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3)) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
123.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
79.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
21.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(/ (- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3)) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
124.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
37.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
30.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))

simplify2.8m

Counts
584 → 425
Calls
584 calls:
Slowest
1.2s
(* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ (* (* 1 1) (* 1 1)) (- (* (* (/ 2 (+ 1 (exp (* -2 x)))) 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)) (* (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)))))
844.0ms
(- (pow (sqrt (/ 2 (+ 1 (exp (* -2 x))))) 3) (pow (sqrt 1) 3))
801.0ms
(/ (- (pow (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) 3) (pow (sqrt 1) 3)) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
707.0ms
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
693.0ms
(+ (pow (/ 2 (+ 1 (exp (* -2 x)))) (/ 3 2)) (sqrt (pow 1 3)))

prune5.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize85.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
0.0b
(/ (/ (- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3)) (+ (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow (/ 2 (+ 1 (exp (* -2 x)))) 3)) (+ (* (pow 1 3) (pow 1 3)) (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))))) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
0.0b
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
0.0b
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
5660×add-sqr-sqrt
5579×times-frac
4209×unpow-prod-down cube-prod
3032×*-un-lft-identity
2548×difference-of-squares
1656×add-cube-cbrt
1094×sqr-pow
693×associate-/l*
351×distribute-lft-out--
80×cube-mult
48×associate-/r/
34×cube-div
30×frac-add
24×flip3-+ flip-+
15×add-cbrt-cube add-exp-log
13×difference-cubes
12×distribute-lft-out
10×frac-times associate-*l/ associate-*r/
9×div-inv
6×pow1 pow-unpow add-log-exp
5×cbrt-undiv div-exp
4×pow-exp insert-posit16 rem-cube-cbrt
3×associate-/r*
2×pow-to-exp pow-pow unpow3 div-sub
1×clear-num sub-neg frac-2neg flip3-- diff-log flip-- associate-/l/
Counts
4 → 3151
Calls
4 calls:
Slowest
830.0ms
(/ (/ (- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3)) (+ (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow (/ 2 (+ 1 (exp (* -2 x)))) 3)) (+ (* (pow 1 3) (pow 1 3)) (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))))) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
643.0ms
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
15.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
15.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

series873.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
621.0ms
(/ (/ (- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3)) (+ (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow (/ 2 (+ 1 (exp (* -2 x)))) 3)) (+ (* (pow 1 3) (pow 1 3)) (* (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))))) (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))
150.0ms
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
53.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
49.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)