Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Average Error: 0.0 → 0.0

Time: 5.0s

Precision: binary64

Cost: 512

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y, double z) {
	return z + ((-z + y) * 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) + ((1.0d0 - 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 + ((-z + y) * x)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ \left(-1 \cdot z + y\right) \cdot x + z \]
   rational_best-simplify-1 [=>] 0.0	\[ \color{blue}{z + \left(-1 \cdot z + y\right) \cdot x} \]
   rational_best-simplify-2 [=>] 0.0	\[ z + \left(\color{blue}{z \cdot -1} + y\right) \cdot x \]
   rational_best-simplify-12 [=>] 0.0	\[ z + \left(\color{blue}{\left(-z\right)} + y\right) \cdot x \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	23.8
Cost	1312

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+239}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-18}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+191}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.2
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(1 - x\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.3
Cost	584

\[\begin{array}{l} t_0 := \left(y - z\right) \cdot x\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := \left(y - z\right) \cdot x\\ \mathbf{if}\;x \leq -110000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	23.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-72}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6
Error	35.0
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023092 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))