Rectangular parallelepiped of dimension a×b×c

?

Percentage Accurate: 100.0% → 100.0%
Time: 931.0ms
Precision: binary64
Cost: 64

?

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]
↓
\[0.4691358024691358 \]
(FPCore ()
 :precision binary64
 (*
  2.0
  (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))
↓
(FPCore () :precision binary64 0.4691358024691358)
double code() {
	return 2.0 * (((1.0 * (1.0 / 9.0)) + ((1.0 / 9.0) * (1.0 / 9.0))) + ((1.0 / 9.0) * 1.0));
}
↓
double code() {
	return 0.4691358024691358;
}

real(8) function code()
    code = 2.0d0 * (((1.0d0 * (1.0d0 / 9.0d0)) + ((1.0d0 / 9.0d0) * (1.0d0 / 9.0d0))) + ((1.0d0 / 9.0d0) * 1.0d0))
end function
↓
real(8) function code()
    code = 0.4691358024691358d0
end function

public static double code() {
	return 2.0 * (((1.0 * (1.0 / 9.0)) + ((1.0 / 9.0) * (1.0 / 9.0))) + ((1.0 / 9.0) * 1.0));
}
↓
public static double code() {
	return 0.4691358024691358;
}

def code():
	return 2.0 * (((1.0 * (1.0 / 9.0)) + ((1.0 / 9.0) * (1.0 / 9.0))) + ((1.0 / 9.0) * 1.0))
↓
def code():
	return 0.4691358024691358

function code()
	return Float64(2.0 * Float64(Float64(Float64(1.0 * Float64(1.0 / 9.0)) + Float64(Float64(1.0 / 9.0) * Float64(1.0 / 9.0))) + Float64(Float64(1.0 / 9.0) * 1.0)))
end
↓
function code()
	return 0.4691358024691358
end

function tmp = code()
	tmp = 2.0 * (((1.0 * (1.0 / 9.0)) + ((1.0 / 9.0) * (1.0 / 9.0))) + ((1.0 / 9.0) * 1.0));
end
↓
function tmp = code()
	tmp = 0.4691358024691358;
end

code[] := N[(2.0 * N[(N[(N[(1.0 * N[(1.0 / 9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / 9.0), $MachinePrecision] * N[(1.0 / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / 9.0), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[] := 0.4691358024691358

2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)
↓
0.4691358024691358

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 1 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Target

    Original100.0%
    Target100.0%
    Herbie100.0%
    \[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right) \]

    Derivation?

    1. Initial program 100.0%

      \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]

    2. Simplified100.0%

      \[\leadsto \color{blue}{0.4691358024691358} \]
      Step-by-step derivation

      [Start]100.0%

      \[ 2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\left(1 \cdot \color{blue}{0.1111111111111111} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\left(\color{blue}{0.1111111111111111} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\left(0.1111111111111111 + \color{blue}{0.1111111111111111} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\left(0.1111111111111111 + 0.1111111111111111 \cdot \color{blue}{0.1111111111111111}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\left(0.1111111111111111 + \color{blue}{0.012345679012345678}\right) + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(\color{blue}{0.12345679012345678} + \frac{1}{9} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(0.12345679012345678 + \color{blue}{0.1111111111111111} \cdot 1\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \left(0.12345679012345678 + \color{blue}{0.1111111111111111}\right) \]

      metadata-eval [=>]100.0%

      \[ 2 \cdot \color{blue}{0.2345679012345679} \]

      metadata-eval [=>]100.0%

      \[ \color{blue}{0.4691358024691358} \]

    3. Final simplification100.0%

      \[\leadsto 0.4691358024691358 \]

    Reproduce?

    herbie shell --seed 2023178 
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"
  :precision binary64

  :herbie-target
  (+ (+ (* (* (/ 1.0 9.0) 1.0) 2.0) (* 2.0 (* (/ 1.0 9.0) (/ 1.0 9.0)))) (* 2.0 (* 1.0 (/ 1.0 9.0))))

  (* 2.0 (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))