Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Average Error: 12.6 → 1.1

Time: 3.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := x - \frac{x \cdot z}{y}\\ t_1 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{1}{\frac{-y}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ (* x z) y))) (t_1 (/ (* x (- y z)) y)))
   (if (<= t_1 (- INFINITY))
     (- x (* z (/ x y)))
     (if (<= t_1 -4e-76)
       t_0
       (if (<= t_1 0.0)
         (- x (/ z (/ y x)))
         (if (<= t_1 5e+298) t_0 (+ x (* z (/ 1.0 (/ (- y) x))))))))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = x - ((x * z) / y);
	double t_1 = (x * (y - z)) / y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (z * (x / y));
	} else if (t_1 <= -4e-76) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = x - (z / (y / x));
	} else if (t_1 <= 5e+298) {
		tmp = t_0;
	} else {
		tmp = x + (z * (1.0 / (-y / x)));
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = x - ((x * z) / y);
	double t_1 = (x * (y - z)) / y;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (z * (x / y));
	} else if (t_1 <= -4e-76) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = x - (z / (y / x));
	} else if (t_1 <= 5e+298) {
		tmp = t_0;
	} else {
		tmp = x + (z * (1.0 / (-y / x)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x - ((x * z) / y)
	t_1 = (x * (y - z)) / y
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (z * (x / y))
	elif t_1 <= -4e-76:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = x - (z / (y / x))
	elif t_1 <= 5e+298:
		tmp = t_0
	else:
		tmp = x + (z * (1.0 / (-y / x)))
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(x - Float64(Float64(x * z) / y))
	t_1 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(z * Float64(x / y)));
	elseif (t_1 <= -4e-76)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(z / Float64(y / x)));
	elseif (t_1 <= 5e+298)
		tmp = t_0;
	else
		tmp = Float64(x + Float64(z * Float64(1.0 / Float64(Float64(-y) / x))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = x - ((x * z) / y);
	t_1 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (z * (x / y));
	elseif (t_1 <= -4e-76)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = x - (z / (y / x));
	elseif (t_1 <= 5e+298)
		tmp = t_0;
	else
		tmp = x + (z * (1.0 / (-y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-76], t$95$0, If[LessEqual[t$95$1, 0.0], N[(x - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], t$95$0, N[(x + N[(z * N[(1.0 / N[((-y) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	12.6
Target	3.3
Herbie	1.1

\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.0

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

   2. Simplified 0.0

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

   3. Applied egg-rr 0.0

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -3.99999999999999971e-76 or 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000003e298

   1. Initial program 0.3

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

   2. Simplified 5.5

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

   3. Taylor expanded in z around 0 0.2

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

   if -3.99999999999999971e-76 < (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0

   1. Initial program 15.5

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

   2. Simplified 4.5

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

   if 5.0000000000000003e298 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 60.8

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

   2. Simplified 1.7

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

   3. Applied egg-rr 2.0

      \[\leadsto x - \color{blue}{\left(-z\right) \cdot \frac{1}{\frac{-y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{-76}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{1}{\frac{-y}{x}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022185 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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