Details

Time bar (total: 24.5s)

sample341.0ms

Algorithm
intervals
Results
110.0ms199×body10240exit
78.0ms371×body80nan
21.0ms236×body80valid
4.0ms21×body160valid

simplify6.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
010343
119343
227343
337343
465343
5133343
6332343
71069343
84148343
done5043343

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.9b
(- (exp (* 2.0 x)) 1.0)
4.1b
(- (exp x) 1.0)

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×sqrt-prod
27×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 associate-/r* flip3-- flip-- associate-/l*
4×associate-/r/
2×rem-sqrt-square sub-neg diff-log div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp
Counts
4 → 123
Calls
4 calls:
26.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
19.0ms
(- (exp (* 2.0 x)) 1.0)
30.0ms
(- (exp x) 1.0)

series282.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
91.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
47.0ms
(- (exp (* 2.0 x)) 1.0)
40.0ms
(- (exp x) 1.0)

simplify3.1s

Counts
135 → 135
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
018964260
139660394
299960114
3313359955
done500159955

prune738.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
0.0b
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.1b
(- (exp x) 1.0)
4.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
535×*-un-lft-identity
520×sqrt-prod
483×times-frac
437×add-sqr-sqrt
150×difference-of-squares
131×add-cube-cbrt
104×distribute-lft-out
98×distribute-lft-out--
11×associate-/r/
10×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×add-cbrt-cube add-exp-log
3×rem-sqrt-square
2×sub-neg diff-log
1×+-commutative sum-log sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 318
Calls
4 calls:
124.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
11.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
8.0ms
(- (exp x) 1.0)
20.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series702.0ms

Counts
4 → 12
Calls
4 calls:
514.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
76.0ms
(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
26.0ms
(- (exp x) 1.0)
85.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify5.8s

Counts
330 → 330
Iterations

Useful iterations: done (5.8s)

IterNodesCost
0542316854
11142292335
23142289661
done5001286963

prune970.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (* 1.0 (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (exp (* 2.0 x)))) (+ (exp (* 2.0 x)) (- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
4.1b
(- (exp x) 1.0)
4.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.1b
(- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
30×*-un-lft-identity
16×times-frac
14×add-cube-cbrt
10×add-log-exp
6×add-cbrt-cube add-exp-log sqrt-prod
5×cube-unmult pow3 sum-cubes distribute-lft-out difference-of-squares
4×pow1 associate-/r* associate-/l*
3×sub-neg flip3-- diff-log flip-- distribute-lft-out--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv clear-num frac-2neg distribute-rgt-out-- div-exp div-inv
Counts
4 → 85
Calls
4 calls:
71.0ms
(/ (+ (* 1.0 (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (exp (* 2.0 x)))) (+ (exp (* 2.0 x)) (- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
12.0ms
(- (exp x) 1.0)
23.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
9.0ms
(- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
452.0ms
(/ (+ (* 1.0 (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (exp (* 2.0 x)))) (+ (exp (* 2.0 x)) (- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
15.0ms
(- (exp x) 1.0)
74.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
104.0ms
(- 1.0 (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

simplify3.3s

Counts
97 → 97
Iterations

Useful iterations: done (3.3s)

IterNodesCost
023451257
158046807
2228746567
done500146327

prune732.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 1.0 (* 0.5 x)))
28.1b
(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log
3×associate-*r* associate-*l* sqrt-prod
2×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 37
Calls
2 calls:
12.0ms
(* x (+ 1.0 (* 0.5 x)))
4.0ms
(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

series232.0ms

Counts
2 → 6
Calls
2 calls:
113.0ms
(* x (+ 1.0 (* 0.5 x)))
119.0ms
(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

simplify90.0ms

Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
010612377