Details

Time bar (total: 11.2s)

sample103.0ms

Algorithm
intervals
Results
37.0ms772×body80nan
14.0ms256×body80valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done18
318
216
112
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
27×times-frac
25×add-sqr-sqrt
21×add-cube-cbrt
16×sqrt-prod
8×log-prod
7×associate-/l*
5×add-exp-log
4×add-cbrt-cube distribute-lft-out difference-of-squares
3×pow1 log-div associate-/r* div-inv
2×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ distribute-rgt-out flip3-- div-exp rem-log-exp frac-add log-pow flip-+ flip--
Counts
2 → 69
Calls
2 calls:
18.0ms
(/ (sqrt (- 1.0 (* x x))) x)
48.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series601.0ms

Counts
2 → 6
Calls
2 calls:
184.0ms
(/ (sqrt (- 1.0 (* x x))) x)
417.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.1s

Counts
75 → 75
Iterations
IterNodes
done5001
21907
1463
0205

prune410.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
50×*-un-lft-identity
38×times-frac
36×sqrt-prod
22×log-prod
18×add-cube-cbrt
16×distribute-lft-out
12×sqrt-div hypot-def
10×pow1
8×div-inv
6×log-div add-exp-log log-pow
4×expm1-log1p-u sqrt-pow1 flip3-+ distribute-rgt-out add-cbrt-cube pow1/2 frac-add flip-+ log1p-expm1-u add-log-exp
2×rem-sqrt-square rem-log-exp
Counts
4 → 112
Calls
4 calls:
28.0ms
(log (sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x))))
33.0ms
(log (sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x))))
92.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x)))
57.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x)))

series2.3s

Counts
4 → 12
Calls
4 calls:
916.0ms
(log (sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x))))
857.0ms
(log (sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x))))
271.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x)))
274.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (fma x (- x) 1.0)) x)))

simplify1.5s

Counts
124 → 124
Iterations
IterNodes
done5001
22815
1653
0256

prune801.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done12
112
011

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.0s23776×body80nan
1.2s8000×body80valid