Details

Time bar (total: 3.6s)

sample36.0ms

Algorithm
intervals
Results
13.0ms775×body80nan
6.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
194
294
done94

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(log (- (/ 1.0 x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×log-prod
4×*-un-lft-identity
2×pow1 add-exp-log add-cube-cbrt log-div difference-of-squares
1×expm1-log1p-u flip3-- times-frac rem-log-exp log-pow add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- add-log-exp
Counts
1 → 19
Calls
1 calls:
14.0ms
(log (- (/ 1.0 x) 1.0))

series62.0ms

Counts
1 → 3
Calls
1 calls:
62.0ms
(log (- (/ 1.0 x) 1.0))

simplify61.0ms

Counts
22 → 22
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0161151
1452138
21918137
35003137
done5003137

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt (- (/ 1.0 x) 1.0)))
0.0b
(log (sqrt (- (/ 1.0 x) 1.0)))
0.1b
(sqrt (- (/ 1.0 x) 1.0))
0.1b
(sqrt (- (/ 1.0 x) 1.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×sqrt-prod
18×log-prod *-un-lft-identity
10×pow1 add-cube-cbrt
8×sqrt-div difference-of-squares
6×add-exp-log log-pow
4×expm1-log1p-u log-div flip3-- sqrt-pow1 times-frac pow1/2 add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- add-log-exp
2×rem-sqrt-square rem-log-exp
Counts
4 → 88
Calls
4 calls:
12.0ms
(log (sqrt (- (/ 1.0 x) 1.0)))
12.0ms
(log (sqrt (- (/ 1.0 x) 1.0)))
26.0ms
(sqrt (- (/ 1.0 x) 1.0))
28.0ms
(sqrt (- (/ 1.0 x) 1.0))

series337.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(log (sqrt (- (/ 1.0 x) 1.0)))
117.0ms
(log (sqrt (- (/ 1.0 x) 1.0)))
54.0ms
(sqrt (- (/ 1.0 x) 1.0))
51.0ms
(sqrt (- (/ 1.0 x) 1.0))

simplify86.0ms

Counts
100 → 100
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0223764
1608714
22651696
35001682
done5001682

prune255.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (/ 1.0 x) 1.0))
0.2b
(sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0)))
0.2b
(sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0)))
0.6b
(* (sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0))) (sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0))))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
71×sqrt-prod
69×add-sqr-sqrt
29×*-un-lft-identity
18×sqrt-div
14×associate-*r* difference-of-squares
11×pow1 add-cube-cbrt
8×associate-*l*
7×times-frac
6×add-exp-log add-cbrt-cube hypot-def
5×flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out--
4×expm1-log1p-u frac-times flip3-+ flip-+ log1p-expm1-u distribute-lft-out add-log-exp unswap-sqr
3×rem-sqrt-square pow-prod-down
2×associate-*r/ associate-*l/
1×sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 120
Calls
4 calls:
27.0ms
(sqrt (- (/ 1.0 x) 1.0))
33.0ms
(sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0)))
44.0ms
(sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0)))
136.0ms
(* (sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0))) (sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0))))

series785.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (- (/ 1.0 x) 1.0))
144.0ms
(sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0)))
191.0ms
(sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0)))
395.0ms
(* (sqrt (+ (sqrt (/ 1.0 x)) (sqrt 1.0))) (sqrt (- (sqrt (/ 1.0 x)) (sqrt 1.0))))

simplify65.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
07041521
125691402
250021382
done50021382

prune455.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02218
12318
22318
done2318

end0.0ms

sample1.1s

Algorithm
intervals
Results
423.0ms24216×body80nan
195.0ms8000×body80valid