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

Average Error: 0.0 → 0.0

Time: 10.6s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

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

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	23.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+135}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-89}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 2
Error	15.2
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-89}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.9
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))