Details

Time bar (total: 15.9s)

sample15.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2128
done128

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (exp x) (exp (- x)))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 52
Calls
2 calls:
14.0ms
(+ (exp x) (exp (- x)))
35.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series101.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(+ (exp x) (exp (- x)))
52.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify4.0s

Counts
58 → 58
Iterations

Useful iterations: 3 (323.0ms)

IterNodesCost
094681
1199650
2469597
3950593
43863593
done5000593

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ 2.0 (+ (exp x) (exp (- x)))))
0.0b
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
134×*-un-lft-identity
116×sqrt-prod
103×times-frac
101×add-sqr-sqrt
70×add-cube-cbrt
29×swap-sqr distribute-lft-out
21×associate-*r* associate-*l*
20×pow1
14×associate-/r/
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
8×associate-/r*
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 212
Calls
4 calls:
24.0ms
(sqrt (/ 2.0 (+ (exp x) (exp (- x)))))
223.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
46.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
53.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(sqrt (/ 2.0 (+ (exp x) (exp (- x)))))
134.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
57.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
51.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify3.1s

Counts
224 → 224
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02344573
14283348
213293134
340413052
done50002989

prune822.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
0.5b
(sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))
0.5b
(* (* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (sqrt 2.0))) (sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x))))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
100×sqrt-prod
86×times-frac
66×add-sqr-sqrt
61×add-cube-cbrt
33×associate-*r*
23×distribute-lft-out
13×pow1 add-exp-log add-cbrt-cube
9×associate-/l*
8×associate-/r* associate-/r/
7×pow-prod-down
5×sqrt-div
4×expm1-log1p-u sqrt-pow1 flip3-+ pow1/2 flip-+ log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square associate-*l/ prod-exp cbrt-unprod
2×cbrt-undiv frac-2neg sqrt-unprod div-exp clear-num
1×frac-times associate-*r/ associate-*l* *-commutative
Counts
4 → 186
Calls
4 calls:
30.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
34.0ms
(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
32.0ms
(sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))
234.0ms
(* (* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (sqrt 2.0))) (sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x))))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
98.0ms
(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
160.0ms
(sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))
146.0ms
(* (* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (sqrt 2.0))) (sqrt (/ (sqrt 2.0) (+ (exp x) (exp (- x))))))

simplify1.7s

Counts
198 → 198
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02683842
15793486
218223287
done50013264

prune825.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3)))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3))

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
120×cbrt-prod sqrt-prod
116×*-un-lft-identity
99×times-frac
70×add-cube-cbrt
51×unpow-prod-down cube-prod associate-*r*
27×unswap-sqr
23×distribute-lft-out
21×associate-*l*
14×associate-/r/
10×add-exp-log
9×add-cbrt-cube
8×associate-/r*
7×flip3-+ flip-+ div-inv
6×pow1 associate-/l*
5×sqrt-div sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div cbrt-div
2×cbrt-undiv cube-mult frac-2neg unpow3 div-exp clear-num
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ prod-exp *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 245
Calls
4 calls:
214.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3)))
53.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
47.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
35.0ms
(cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3))

series442.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3)))
59.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
63.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
181.0ms
(cbrt (pow (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) 3))

simplify1.7s

Counts
257 → 257
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02926058
16314786
218714195
done50004154

prune914.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes1.0ms