Details

Time bar (total: 10.0s)

sample46.0ms

Algorithm
intervals
Results
21.0ms680×body80nan
10.0ms256×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

localize9.0ms

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))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u sqrt-div log1p-expm1-u
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 → 119
Calls
4 calls:
3.0ms
(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)
30.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series594.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (- 1.0 (* x x)))
293.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
130.0ms
(/ (sqrt (- 1.0 (* x x))) x)
108.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify521.0ms

Counts
131 → 131
Iterations

Useful iterations: 2 (211.0ms)

IterNodesCost
02342010
15351867
215841735
done50001735

prune355.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

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))))

rewrite342.0ms

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:
27.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
52.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
52.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
199.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series693.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
212.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
206.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
169.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify564.0ms

Counts
185 → 185
Iterations

Useful iterations: done (558.0ms)

IterNodesCost
02424691
15323503
216343263
done50003253

prune737.0ms

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

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
144×sqrt-prod
112×add-sqr-sqrt
108×times-frac
103×*-un-lft-identity
76×sqrt-div
73×add-cube-cbrt
41×associate-*r*
36×frac-times
22×associate-*l/
18×pow1 flip3-+ frac-add flip-+
17×add-exp-log
15×add-cbrt-cube
13×distribute-lft-out
12×associate-*l* associate-/r* unswap-sqr
10×pow-prod-down associate-/l*
8×associate-*r/
7×div-inv difference-of-squares
6×sqrt-pow1 pow1/2
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-flip sqrt-unprod div-exp
2×cbrt-undiv distribute-rgt-out frac-2neg clear-num *-commutative associate-/l/
1×rec-exp sqrt-undiv flip3-- 1-exp flip-- inv-pow
Counts
4 → 257
Calls
4 calls:
3.0ms
(/ 1 (sqrt x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
117.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (/ 1 (sqrt x))))
292.0ms
(* (* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (/ 1 (sqrt x)))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (sqrt x))
72.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
352.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (/ 1 (sqrt x))))
874.0ms
(* (* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (/ 1 (sqrt x)))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))

simplify1.8s

Counts
269 → 269
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
06228019
115687170
247426736
done50006736

prune970.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02036
12636
done2636

end0.0ms

sample1.4s

Algorithm
intervals
Results
746.0ms24232×body80nan
300.0ms8000×body80valid