Details

Time bar (total: 7.1m)

sample83.0ms

Algorithm
intervals
Results
27.0ms39×body1280valid
18.0ms37×body640valid
15.0ms148×body80valid
7.0ms19×body320valid
3.0ms13×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
139.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize27.0ms

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)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
63×times-frac add-cube-cbrt
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-exp-log
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube div-inv
4×associate-/r* difference-of-squares
3×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l*
2×expm1-def difference-of-sqr-1 div-exp
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 150
Calls
3 calls:
Slowest
76.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
11.0ms
(/ 2 (+ 1 (exp (* -2 x))))
5.0ms
(+ 1 (exp (* -2 x)))

series124.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
85.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
22.0ms
(/ 2 (+ 1 (exp (* -2 x))))
18.0ms
(+ 1 (exp (* -2 x)))

simplify22.3s

Counts
185 → 159
Calls
185 calls:
Slowest
588.0ms
(- (log 2) (log (+ 1 (exp (* -2 x)))))
531.0ms
(/ 2 (- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x)))))
433.0ms
(/ (* (* 2 2) 2) (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
418.0ms
(fma (/ 2 (+ (pow 1 3) (pow (exp (* -2 x)) 3))) (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
367.0ms
(+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x)))))

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

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)))))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
780×*-un-lft-identity
767×add-sqr-sqrt
598×times-frac
518×unpow-prod-down cube-prod
504×prod-diff
455×add-cube-cbrt
180×difference-of-squares
116×sqr-pow
102×distribute-lft-out
72×associate-/r/
61×cube-mult
56×unpow3
46×associate-/l*
42×fma-neg
36×flip3-+ flip-+
33×div-inv
30×distribute-lft-out--
24×swap-sqr
21×add-cbrt-cube add-exp-log
18×associate-*r* associate-*l*
12×pow1
6×cbrt-undiv div-exp frac-add add-log-exp
5×difference-cubes
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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 div-sub pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 967
Calls
4 calls:
Slowest
495.0ms
(/ (- (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))))
168.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
57.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
22.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(/ (- (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))))
94.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
65.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
47.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))

simplify6.4m

Counts
1633 → 979
Calls
1633 calls:
Slowest
1.0s
(pow (/ 1 (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) 3)
1.0s
(fma (pow (/ (sqrt 2) 1) 3) (pow (/ (sqrt 2) (+ 1 (exp (* -2 x)))) 3) (- (* (pow 1 3) (pow 1 3))))
954.0ms
(fma (pow (/ (sqrt 2) 1) 3) (pow (/ (sqrt 2) (+ 1 (exp (* -2 x)))) 3) (- (* (pow 1 3) 1)))
947.0ms
(fma (pow (/ (* (cbrt 2) (cbrt 2)) 1) 3) (pow (/ (cbrt 2) (+ 1 (exp (* -2 x)))) 3) (- (* (pow 1 (/ 3 2)) (pow 1 (/ 3 2)))))
879.0ms
(/ (pow 1 3) (* (cbrt (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)))) (cbrt (+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1))))))

prune12.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize100.0ms

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)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
8247×unpow-prod-down cube-prod
7375×add-sqr-sqrt
7067×times-frac
5491×*-un-lft-identity
3371×add-cube-cbrt
2700×prod-diff
2548×difference-of-squares
1457×sqr-pow
693×associate-/l*
443×cube-mult
384×distribute-lft-out
365×unpow3
351×distribute-lft-out--
296×associate-/r/
148×flip3-+ flip-+
133×div-inv
90×fma-neg
34×cube-div
30×frac-add
15×add-cbrt-cube add-exp-log
13×difference-cubes
10×frac-times associate-*l/ associate-*r/
6×pow1 pow-unpow add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u pow-exp insert-posit16 log1p-expm1-u rem-cube-cbrt
3×associate-/r*
2×pow-to-exp pow-pow div-sub
1×clear-num sub-neg frac-2neg flip3-- diff-log flip-- associate-/l/
Counts
4 → 5949
Calls
4 calls:
Slowest
862.0ms
(/ (/ (- (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))))
417.0ms
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
19.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
17.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

series885.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
643.0ms
(/ (/ (- (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))))
148.0ms
(- (pow (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) 3) (pow (pow 1 3) 3))
57.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
37.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)