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

Average Error: 0.0 → 0.0

Time: 9.4s

Precision: binary64

Cost: 576

Math

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

↓

\[y \cdot z + \left(1 - z\right) \cdot x \]

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ (* y z) (* (- 1.0 z) x)))

C

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

↓

double code(double x, double y, double z) {
	return (y * z) + ((1.0 - z) * x);
}

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 = (y * z) + ((1.0d0 - z) * x)
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 (y * z) + ((1.0 - z) * x);
}

Python

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

↓

def code(x, y, z):
	return (y * z) + ((1.0 - z) * x)

Julia

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

↓

function code(x, y, z)
	return Float64(Float64(y * z) + Float64(Float64(1.0 - z) * x))
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = (y * z) + ((1.0 - z) * x);
end

Wolfram

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

↓

code[x_, y_, z_] := N[(N[(y * z), $MachinePrecision] + N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{y \cdot z + \left(-1 \cdot z + 1\right) \cdot x} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{y \cdot z + \left(1 - z\right) \cdot x} \]
   Proof

   [Start] 0.0	\[ y \cdot z + \left(-1 \cdot z + 1\right) \cdot x \]
   rational.json-simplify-2 [=>] 0.0	\[ y \cdot z + \left(\color{blue}{z \cdot -1} + 1\right) \cdot x \]
   rational.json-simplify-9 [=>] 0.0	\[ y \cdot z + \left(\color{blue}{\left(-z\right)} + 1\right) \cdot x \]
   rational.json-simplify-12 [=>] 0.0	\[ y \cdot z + \left(\color{blue}{\left(0 - z\right)} + 1\right) \cdot x \]
   metadata-eval [<=] 0.0	\[ y \cdot z + \left(\left(0 - z\right) + \color{blue}{\left(1 - 0\right)}\right) \cdot x \]
   rational.json-simplify-27 [=>] 0.0	\[ y \cdot z + \color{blue}{\left(1 - z\right)} \cdot x \]

4. Final simplification 0.0

   \[\leadsto y \cdot z + \left(1 - z\right) \cdot x \]

Alternatives

Alternative 1
Error	16.3
Cost	848

\[\begin{array}{l} t_0 := \left(1 - z\right) \cdot x\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-137}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-184}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	24.1
Cost	652

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 13.2:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	12.0
Cost	584

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-10}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	23.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.0
Cost	448

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

Alternative 6
Error	34.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))