Details

Time bar (total: 10.3s)

sample44.0ms

Algorithm
intervals
Results
19.0ms680×body80nan
9.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
done1613

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 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)
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×times-frac
32×add-sqr-sqrt
26×add-cube-cbrt
20×sqrt-prod
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube add-log-exp
5×div-inv difference-of-squares
4×sqrt-div
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 98
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* x x)))
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
29.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series713.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (- 1.0 (* x x)))
324.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
193.0ms
(/ (sqrt (- 1.0 (* x x))) x)
135.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify640.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (177.0ms)

IterNodesCost
02261924
15131800
217061665
done50011665

prune383.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.5b
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
90×*-un-lft-identity
58×sqrt-prod
42×add-sqr-sqrt times-frac
30×sqrt-div distribute-lft-out
28×add-cube-cbrt
21×pow1
15×swap-sqr
14×div-inv
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×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 → 140
Calls
4 calls:
24.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
46.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
46.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
210.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series761.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
210.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
239.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
198.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify776.0ms

Counts
152 → 152
Iterations

Useful iterations: done (771.0ms)

IterNodesCost
02364553
15083433
219863177
done50003175

prune415.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b
(* (sqrt (/ 1 (sqrt x))) (* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
0.4b
(* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite587.0ms

Algorithm
rewrite-expression-head
Rules
128×sqrt-prod
100×times-frac
99×*-un-lft-identity
92×add-sqr-sqrt
90×sqrt-div
73×add-cube-cbrt
42×frac-times
41×associate-*l*
24×flip3-+ associate-*r/ frac-add flip-+
16×pow1
15×add-exp-log add-cbrt-cube
13×distribute-lft-out
12×associate-*r* associate-/r*
10×pow-prod-down associate-*l/ associate-/l*
7×div-inv difference-of-squares
5×sqrt-pow1 pow1/2
4×prod-exp cbrt-unprod add-log-exp unswap-sqr
3×sqrt-unprod
2×cbrt-undiv distribute-rgt-out frac-2neg div-exp clear-num *-commutative associate-/l/
1×sqrt-undiv flip3-- flip--
Counts
4 → 243
Calls
4 calls:
3.0ms
(/ 1.0 (sqrt x))
8.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
245.0ms
(* (sqrt (/ 1 (sqrt x))) (* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
318.0ms
(* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series2.3s

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1.0 (sqrt x))
79.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
1.1s
(* (sqrt (/ 1 (sqrt x))) (* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
1.1s
(* (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify584.0ms

Counts
255 → 255
Iterations

Useful iterations: done (570.0ms)

IterNodesCost
06618788
116408138
done50007674

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02036
12636
done2636

end0.0ms

sample1.5s

Algorithm
intervals
Results
770.0ms24232×body80nan
319.0ms8000×body80valid