Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 12.0 → 5.9

Time: 5.4s

Precision: binary64

Math

\[\frac{x \cdot \left(y - z\right)}{t - z} \]

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_1 \leq 1.710510294576776 \cdot 10^{+291}:\\ \;\;\;\;\frac{y \cdot x - z \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (<= t_1 (- INFINITY))
     x
     (if (<= t_1 1.710510294576776e+291) (/ (- (* y x) (* z x)) (- t z)) x))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x;
	} else if (t_1 <= 1.710510294576776e+291) {
		tmp = ((y * x) - (z * x)) / (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x;
	} else if (t_1 <= 1.710510294576776e+291) {
		tmp = ((y * x) - (z * x)) / (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x
	elif t_1 <= 1.710510294576776e+291:
		tmp = ((y * x) - (z * x)) / (t - z)
	else:
		tmp = x
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = x;
	elseif (t_1 <= 1.710510294576776e+291)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * x)) / Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x;
	elseif (t_1 <= 1.710510294576776e+291)
		tmp = ((y * x) - (z * x)) / (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], x, If[LessEqual[t$95$1, 1.710510294576776e+291], N[(N[(N[(y * x), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], x]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	12.0
Target	2.0
Herbie	5.9

\[\frac{x}{\frac{t - z}{y - z}} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -inf.0 or 1.710510294576776e291 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 63.3

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]

   2. Taylor expanded in z around inf 27.2

      \[\leadsto \color{blue}{x} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.710510294576776e291

   1. Initial program 1.5

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]

   2. Taylor expanded in y around 0 1.5

      \[\leadsto \frac{\color{blue}{y \cdot x - z \cdot x}}{t - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 5.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.710510294576776 \cdot 10^{+291}:\\ \;\;\;\;\frac{y \cdot x - z \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Reproduce

herbie shell --seed 2022152 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))