Details

Time bar (total: 9.5s)

sample51.0ms

Algorithm
intervals
Results
22.0ms736×body80nan
13.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
29×add-sqr-sqrt
27×times-frac
23×add-cube-cbrt
20×sqrt-prod
8×log-prod
7×associate-/l*
6×add-exp-log
5×pow1 add-cbrt-cube difference-of-squares
4×sqrt-div distribute-lft-out
3×expm1-log1p-u log-div associate-/r* log1p-expm1-u div-inv add-log-exp
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp rem-log-exp frac-add clear-num log-pow flip-+
Counts
3 → 87
Calls
3 calls:
6.0ms
(sqrt (- 1.0 (* x x)))
24.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series488.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(sqrt (- 1.0 (* x x)))
296.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
129.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify494.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
02211608
14921480
215781389
done50001389

prune439.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
292×sqrt-prod
208×add-sqr-sqrt
179×times-frac
112×add-cube-cbrt *-un-lft-identity
36×swap-sqr
28×associate-*r* associate-*l*
22×difference-of-squares
21×pow1
16×unswap-sqr
10×sqrt-pow1 pow1/2
8×add-exp-log sqrt-div add-cbrt-cube
7×div-inv associate-/l*
6×rem-sqrt-square
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down associate-/r* pow-sqr
2×associate-/l/
1×cbrt-undiv pow2 frac-times flip3-- frac-2neg pow-plus sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 265
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
47.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

series761.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (sqrt (- 1.0 (* x x))) x)
195.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
196.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
237.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

simplify970.0ms

Counts
277 → 277
Iterations

Useful iterations: done (954.0ms)

IterNodesCost
03336462
16274800
226574542
done50004537

prune728.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
0.5b
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
0.5b
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
0.5b
(* (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))) (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
319×sqrt-prod
252×cbrt-prod
224×add-sqr-sqrt
179×times-frac
117×add-cube-cbrt *-un-lft-identity
39×swap-sqr
31×associate-*r* associate-*l*
25×unswap-sqr
21×difference-of-squares
11×pow1
9×pow1/3
7×cbrt-div sqrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 266
Calls
4 calls:
4.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
4.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
5.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
55.0ms
(* (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))) (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))))

series2.1s

Counts
4 → 12
Calls
4 calls:
494.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
493.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
495.0ms
(cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x)))
608.0ms
(* (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))) (cbrt (sqrt (/ (sqrt (- 1.0 (* x x))) x))))

simplify789.0ms

Counts
278 → 278
Iterations

Useful iterations: 2 (292.0ms)

IterNodesCost
03928053
17377518
223677208
done50007208

prune987.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01447
11747
done1747

end0.0ms

sample1.4s

Algorithm
intervals
Results
720.0ms23884×body80nan
301.0ms8000×body80valid