Details

Time bar (total: 20.9s)

sample17.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify28.0ms

Calls
1 calls:
Slowest
27.0ms
(/ 2 (+ (exp x) (exp (- x))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(+ (exp x) (exp (- x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt times-frac add-cube-cbrt
5×distribute-lft-out
4×associate-/r* add-cbrt-cube add-exp-log add-log-exp
3×fma-def associate-/l*
2×expm1-log1p-u pow1 flip3-+ associate-/r/ flip-+ insert-posit16 log1p-expm1-u
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Calls
2 calls:
Slowest
25.0ms
(/ 2 (+ (exp x) (exp (- x))))
10.0ms
(+ (exp x) (exp (- x)))

series97.0ms

Calls
2 calls:
Slowest
56.0ms
(/ 2 (+ (exp x) (exp (- x))))
40.0ms
(+ (exp x) (exp (- x)))

simplify1.7s

Calls
44 calls:
Slowest
233.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
165.0ms
(/ (* (* 2 2) 2) (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))))
155.0ms
(/ 2 (+ (exp (* -1 x)) (exp x)))
130.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
72.0ms
(+ (exp (* -1 x)) (exp x))

prune447.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x))))))
0.0b
(+ (exp x) (exp (- x)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
98×sqrt-prod
91×add-sqr-sqrt
90×times-frac
63×add-cube-cbrt
29×swap-sqr
27×distribute-lft-out
21×associate-*r* associate-*l*
19×pow1
12×associate-/r/
10×add-cbrt-cube add-exp-log
9×unswap-sqr
8×associate-/r* sqrt-pow1 pow1/2
7×flip3-+ flip-+
6×div-inv associate-/l* add-log-exp
5×pow-prod-up
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×fma-def pow-prod-down pow-sqr
2×cbrt-undiv clear-num frac-2neg div-exp
1×pow2 frac-times +-commutative sum-log rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
106.0ms
(* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x))))))
38.0ms
(/ 2 (+ (exp x) (exp (- x))))
33.0ms
(/ 2 (+ (exp x) (exp (- x))))
20.0ms
(+ (exp x) (exp (- x)))

series285.0ms

Calls
4 calls:
Slowest
121.0ms
(* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x))))))
63.0ms
(/ 2 (+ (exp x) (exp (- x))))
60.0ms
(/ 2 (+ (exp x) (exp (- x))))
41.0ms
(+ (exp x) (exp (- x)))

simplify9.0s

Calls
230 calls:
Slowest
288.0ms
(sqrt (/ 2 (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))))
239.0ms
(* (* (* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))) (* (* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))))
221.0ms
(* (sqrt (/ 2 (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))))) (sqrt (/ 2 (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))))))
221.0ms
(sqrt (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
218.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))

prune2.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))))
0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(+ (exp x) (exp (- x)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
24×times-frac
23×add-sqr-sqrt add-cube-cbrt
9×distribute-lft-out
8×associate-/r* add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u pow1 associate-/r/ insert-posit16
3×fma-def flip3-+ flip-+
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×+-commutative expm1-log1p sum-log expm1-udef
Calls
4 calls:
Slowest
21.0ms
(/ 2 (+ (exp x) (exp (- x))))
15.0ms
(/ 2 (+ (exp x) (exp (- x))))
13.0ms
(+ (exp x) (exp (- x)))
0.0ms
(expm1 (* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))))

series389.0ms

Calls
4 calls:
Slowest
267.0ms
(expm1 (* (sqrt (/ 2 (+ (exp x) (exp (- x))))) (sqrt (/ 2 (+ (exp x) (exp (- x)))))))
49.0ms
(/ 2 (+ (exp x) (exp (- x))))
38.0ms
(/ 2 (+ (exp x) (exp (- x))))
35.0ms
(+ (exp x) (exp (- x)))

simplify3.8s

Calls
85 calls:
Slowest
300.0ms
(- (+ (exp (* 1/2 (pow (sqrt 2) 2))) (+ (* 1/32 (* (exp (* 1/2 (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 4)))) (* 5/48 (* (exp (* 1/2 (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2)))))) (+ (* 1/4 (* (exp (* 1/2 (pow (sqrt 2) 2))) (* (pow (sqrt 2) 2) (pow x 2)))) 1))
257.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
227.0ms
(- (exp (/ (pow (sqrt 2) 2) (+ (exp (* -1 x)) (exp x)))) 1)
213.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
167.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.1s

Algorithm
intervals
Results
1.0s8000×body80valid