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

Average Error: 11.7 → 1.3

Time: 4.4s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+206}:\\ \;\;\;\;\frac{x \cdot y}{t - z} - \frac{x \cdot z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

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 (* (- t z) (/ 1.0 (- y z))))
     (if (<= t_1 2e+206)
       (- (/ (* x y) (- t z)) (/ (* x z) (- t z)))
       (* x (/ (- y z) (- t z)))))))

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 / ((t - z) * (1.0 / (y - z)));
	} else if (t_1 <= 2e+206) {
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	} else {
		tmp = x * ((y - z) / (t - z));
	}
	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 / ((t - z) * (1.0 / (y - z)));
	} else if (t_1 <= 2e+206) {
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	} else {
		tmp = x * ((y - z) / (t - z));
	}
	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 / ((t - z) * (1.0 / (y - z)))
	elif t_1 <= 2e+206:
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z))
	else:
		tmp = x * ((y - z) / (t - z))
	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 = Float64(x / Float64(Float64(t - z) * Float64(1.0 / Float64(y - z))));
	elseif (t_1 <= 2e+206)
		tmp = Float64(Float64(Float64(x * y) / Float64(t - z)) - Float64(Float64(x * z) / Float64(t - z)));
	else
		tmp = Float64(x * Float64(Float64(y - z) / Float64(t - z)));
	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 / ((t - z) * (1.0 / (y - z)));
	elseif (t_1 <= 2e+206)
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	else
		tmp = x * ((y - z) / (t - z));
	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)], N[(x / N[(N[(t - z), $MachinePrecision] * N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+206], N[(N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	11.7
Target	2.1
Herbie	1.3

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 0.1

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Applied egg-rr 0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   4. Applied egg-rr 0.3

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2.0000000000000001e206

   1. Initial program 1.3

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

   2. Simplified 2.4

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Taylor expanded in y around 0 1.3

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{t - z} + \frac{y \cdot x}{t - z}} \]

   if 2.0000000000000001e206 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 47.8

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

   2. Simplified 2.3

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+206}:\\ \;\;\;\;\frac{x \cdot y}{t - z} - \frac{x \cdot z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022192 
(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)))