Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

Average Error: 0.1 → 0.1

Time: 8.5s

Precision: binary64

Cost: 448

Math

\[x + \frac{x - y}{2} \]

↓

\[-0.5 \cdot y + 1.5 \cdot x \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))

↓

(FPCore (x y) :precision binary64 (+ (* -0.5 y) (* 1.5 x)))

C

double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

↓

double code(double x, double y) {
	return (-0.5 * y) + (1.5 * x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((x - y) / 2.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-0.5d0) * y) + (1.5d0 * x)
end function

Java

public static double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

↓

public static double code(double x, double y) {
	return (-0.5 * y) + (1.5 * x);
}

Python

def code(x, y):
	return x + ((x - y) / 2.0)

↓

def code(x, y):
	return (-0.5 * y) + (1.5 * x)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(x - y) / 2.0))
end

↓

function code(x, y)
	return Float64(Float64(-0.5 * y) + Float64(1.5 * x))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((x - y) / 2.0);
end

↓

function tmp = code(x, y)
	tmp = (-0.5 * y) + (1.5 * x);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(-0.5 * y), $MachinePrecision] + N[(1.5 * x), $MachinePrecision]), $MachinePrecision]

Target

Original	0.1
Target	0.1
Herbie	0.1

\[1.5 \cdot x - 0.5 \cdot y \]

Derivation

1. Initial program 0.1

   \[x + \frac{x - y}{2} \]

2. Taylor expanded in x around 0 0.1

   \[\leadsto \color{blue}{-0.5 \cdot y + 1.5 \cdot x} \]

3. Final simplification 0.1

   \[\leadsto -0.5 \cdot y + 1.5 \cdot x \]

Alternatives

Alternative 1
Error	15.4
Cost	912

\[\begin{array}{l} t_0 := \left(-y\right) + x \cdot 1.5\\ \mathbf{if}\;y \leq -1 \cdot 10^{+48}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot y\\ \end{array} \]

Alternative 2
Error	16.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+48}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-11}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot y\\ \end{array} \]

Alternative 3
Error	0.1
Cost	448

\[x + \frac{x - y}{2} \]

Alternative 4
Error	31.6
Cost	192

\[-0.5 \cdot y \]

Alternative 5
Error	56.9
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2.0)))