Details

Time bar (total: 12.5s)

sample125.0ms

Algorithm
intervals
Results
59.0ms813×body80nan
22.0ms256×body80valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 1 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
4×distribute-lft-out
3×div-inv add-log-exp
1×pow1 add-exp-log +-commutative expm1-log1p-u distribute-rgt-out flip3-+ frac-add sum-log add-cbrt-cube flip-+ log1p-expm1-u
Counts
1 → 32
Calls
1 calls:
91.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series208.0ms

Counts
1 → 3
Calls
1 calls:
208.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify839.0ms

Counts
35 → 35
Iterations

Useful iterations: done (837.0ms)

IterNodesCost
071402
1187387
2702354
done5001344

prune298.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.4b
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite960.0ms

Algorithm
rewrite-expression-head
Rules
97×*-un-lft-identity
87×add-sqr-sqrt
65×times-frac
62×sqrt-prod
35×add-cube-cbrt
30×sqrt-div distribute-lft-out
21×pow1
15×swap-sqr div-inv
13×fma-def
12×hypot-def
11×flip3-+ associate-*r* associate-*l* frac-add flip-+
10×sqrt-pow1 pow1/2
9×frac-times
7×distribute-rgt-out
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*r/ pow-prod-down associate-*l/ pow-sqr
2×rem-sqrt-square
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 173
Calls
4 calls:
79.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
146.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
151.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
564.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
190.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
367.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
371.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
317.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify2.3s

Counts
185 → 185
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02424691
15813518
226673263
done50013116

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01128
11228
done1228

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.5s24078×body80nan
1.3s8000×body80valid