Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.3s

Precision: binary64

Cost: 64

Math

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

↓

\[0.4691358024691358 \]

FPCore

(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)

C

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;
}

Fortran

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

Java

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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Target

Original	0
Target	0
Herbie	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 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. Simplified 0

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

   [Start] 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 [=>] 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 [=>] 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 [=>] 0	\[ 2 \cdot \left(\left(0.1111111111111111 + \color{blue}{0.1111111111111111} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \left(\left(0.1111111111111111 + 0.1111111111111111 \cdot \color{blue}{0.1111111111111111}\right) + \frac{1}{9} \cdot 1\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \left(\left(0.1111111111111111 + \color{blue}{0.012345679012345678}\right) + \frac{1}{9} \cdot 1\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \left(\color{blue}{0.12345679012345678} + \frac{1}{9} \cdot 1\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \left(0.12345679012345678 + \color{blue}{0.1111111111111111} \cdot 1\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \left(0.12345679012345678 + \color{blue}{0.1111111111111111}\right) \]
   metadata-eval [=>] 0	\[ 2 \cdot \color{blue}{0.2345679012345679} \]
   metadata-eval [=>] 0	\[ \color{blue}{0.4691358024691358} \]

3. Final simplification 0

   \[\leadsto 0.4691358024691358 \]

Reproduce

herbie shell --seed 2023104 
(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))))