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

Average Error: 0.0 → 0.0

Time: 5.7s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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 - (x * (z - y));
}

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 - (x * (z - y))
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 - (x * (z - y));
}

Python

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

↓

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

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(x * Float64(z - y)))
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = z - (x * (z - y));
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[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ x \cdot y + \left(1 - x\right) \cdot z \]
   rational_best-simplify-1 [=>] 0.0	\[ x \cdot y + \color{blue}{z \cdot \left(1 - x\right)} \]
   rational_best-simplify-68 [=>] 0.0	\[ x \cdot y + \color{blue}{\left(x - 1\right) \cdot \left(-z\right)} \]
   rational_best-simplify-1 [=>] 0.0	\[ x \cdot y + \color{blue}{\left(-z\right) \cdot \left(x - 1\right)} \]
   rational_best-simplify-18 [=>] 0.0	\[ x \cdot y + \left(-z\right) \cdot \color{blue}{\left(x + -1\right)} \]
   rational_best-simplify-74 [<=] 0.0	\[ x \cdot y + \color{blue}{\left(x \cdot \left(-z\right) + -1 \cdot \left(-z\right)\right)} \]
   rational_best-simplify-11 [=>] 0.0	\[ x \cdot y + \left(x \cdot \left(-z\right) + -1 \cdot \color{blue}{\left(z \cdot -1\right)}\right) \]
   rational_best-simplify-1 [=>] 0.0	\[ x \cdot y + \left(x \cdot \left(-z\right) + -1 \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]
   rational_best-simplify-53 [=>] 0.0	\[ x \cdot y + \left(x \cdot \left(-z\right) + \color{blue}{z \cdot \left(-1 \cdot -1\right)}\right) \]
   metadata-eval [=>] 0.0	\[ x \cdot y + \left(x \cdot \left(-z\right) + z \cdot \color{blue}{1}\right) \]
   rational_best-simplify-7 [=>] 0.0	\[ x \cdot y + \left(x \cdot \left(-z\right) + \color{blue}{z}\right) \]
   rational_best-simplify-47 [=>] 0.0	\[ \color{blue}{z + \left(x \cdot \left(-z\right) + x \cdot y\right)} \]
   rational_best-simplify-1 [=>] 0.0	\[ z + \left(\color{blue}{\left(-z\right) \cdot x} + x \cdot y\right) \]
   rational_best-simplify-1 [=>] 0.0	\[ z + \left(\left(-z\right) \cdot x + \color{blue}{y \cdot x}\right) \]
   rational_best-simplify-74 [=>] 0.0	\[ z + \color{blue}{x \cdot \left(\left(-z\right) + y\right)} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	12.7
Cost	848

\[\begin{array}{l} t_0 := \left(y - z\right) \cdot x\\ t_1 := z \cdot \left(1 - x\right)\\ \mathbf{if}\;x \leq -0.38:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	23.8
Cost	784

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -65000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-43}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	15.7
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(1 - x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := \left(y - z\right) \cdot x\\ \mathbf{if}\;x \leq -59000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	23.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-53}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6
Error	34.8
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023101 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))