Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Error: 0.0 → 0.2

Time: 12.3s

Precision: binary64

Cost: 960

Math

\[x + \left(y - x\right) \cdot z \]

↓

\[x + \frac{z \cdot \left(x \cdot 8 - 4 \cdot \left(x + y\right)\right)}{-4} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))

↓

(FPCore (x y z)
 :precision binary64
 (+ x (/ (* z (- (* x 8.0) (* 4.0 (+ x y)))) -4.0)))

C

double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

↓

double code(double x, double y, double z) {
	return x + ((z * ((x * 8.0) - (4.0 * (x + y)))) / -4.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * z)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((z * ((x * 8.0d0) - (4.0d0 * (x + y)))) / (-4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

↓

public static double code(double x, double y, double z) {
	return x + ((z * ((x * 8.0) - (4.0 * (x + y)))) / -4.0);
}

Python

def code(x, y, z):
	return x + ((y - x) * z)

↓

def code(x, y, z):
	return x + ((z * ((x * 8.0) - (4.0 * (x + y)))) / -4.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * z))
end

↓

function code(x, y, z)
	return Float64(x + Float64(Float64(z * Float64(Float64(x * 8.0) - Float64(4.0 * Float64(x + y)))) / -4.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * z);
end

↓

function tmp = code(x, y, z)
	tmp = x + ((z * ((x * 8.0) - (4.0 * (x + y)))) / -4.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x + N[(N[(z * N[(N[(x * 8.0), $MachinePrecision] - N[(4.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x + \left(y - x\right) \cdot z \]

2. Applied egg-rr 0.2

   \[\leadsto x + \color{blue}{\frac{z \cdot \left(\left(x + x\right) \cdot 4 - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4}} \]

3. Simplified 0.2

   \[\leadsto x + \color{blue}{\frac{z \cdot \left(x \cdot 8 - 4 \cdot \left(x + y\right)\right)}{-4}} \]
   Proof

   [Start] 0.2	\[ x + \frac{z \cdot \left(\left(x + x\right) \cdot 4 - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-1 [=>] 0.2	\[ x + \frac{z \cdot \left(\color{blue}{4 \cdot \left(x + x\right)} - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-63 [<=] 0.2	\[ x + \frac{z \cdot \left(\color{blue}{\left(x \cdot 4 + x \cdot 4\right)} - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-1 [=>] 0.2	\[ x + \frac{z \cdot \left(\left(\color{blue}{4 \cdot x} + x \cdot 4\right) - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-1 [=>] 0.2	\[ x + \frac{z \cdot \left(\left(4 \cdot x + \color{blue}{4 \cdot x}\right) - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-63 [=>] 0.2	\[ x + \frac{z \cdot \left(\color{blue}{x \cdot \left(4 + 4\right)} - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   metadata-eval [=>] 0.2	\[ x + \frac{z \cdot \left(x \cdot \color{blue}{8} - 2 \cdot \left(2 \cdot \left(y + x\right)\right)\right)}{-4} \]
   rational_best-simplify-50 [=>] 0.2	\[ x + \frac{z \cdot \left(x \cdot 8 - \color{blue}{\left(y + x\right) \cdot \left(2 \cdot 2\right)}\right)}{-4} \]
   metadata-eval [=>] 0.2	\[ x + \frac{z \cdot \left(x \cdot 8 - \left(y + x\right) \cdot \color{blue}{4}\right)}{-4} \]
   rational_best-simplify-1 [=>] 0.2	\[ x + \frac{z \cdot \left(x \cdot 8 - \color{blue}{4 \cdot \left(y + x\right)}\right)}{-4} \]
   rational_best-simplify-3 [=>] 0.2	\[ x + \frac{z \cdot \left(x \cdot 8 - 4 \cdot \color{blue}{\left(x + y\right)}\right)}{-4} \]

4. Final simplification 0.2

   \[\leadsto x + \frac{z \cdot \left(x \cdot 8 - 4 \cdot \left(x + y\right)\right)}{-4} \]

Alternatives

Alternative 1
Error	8.8
Cost	648

\[\begin{array}{l} t_0 := x + z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[x + \left(y - x\right) \cdot z \]

Alternative 3
Error	11.9
Cost	320

\[x + z \cdot y \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))