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

Average Error: 12.6 → 2.1

Time: 4.9s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t_0 \leq -4 \cdot 10^{+158}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 (- INFINITY))
     (* (- y z) (/ x y))
     (if (<= t_0 -4e+158) t_0 (/ x (/ y (- y z)))))))

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 * (y - z)) / y;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (y - z) * (x / y);
	} else if (t_0 <= -4e+158) {
		tmp = t_0;
	} else {
		tmp = x / (y / (y - z));
	}
	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 * (y - z)) / y;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = (y - z) * (x / y);
	} else if (t_0 <= -4e+158) {
		tmp = t_0;
	} else {
		tmp = x / (y / (y - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (y - z) * (x / y)
	elif t_0 <= -4e+158:
		tmp = t_0
	else:
		tmp = x / (y / (y - z))
	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(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(Float64(y - z) * Float64(x / y));
	elseif (t_0 <= -4e+158)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(y / Float64(y - z)));
	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 * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (y - z) * (x / y);
	elseif (t_0 <= -4e+158)
		tmp = t_0;
	else
		tmp = x / (y / (y - z));
	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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -4e+158], t$95$0, N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	12.6
Target	2.9
Herbie	2.1

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

Derivation

1. Split input into 3 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 0.2

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

      [Start] 64.0	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      *-commutative [=>] 64.0	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]
      associate-*r/ [<=] 0.2	\[ \color{blue}{\left(y - z\right) \cdot \frac{x}{y}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -3.99999999999999981e158

   1. Initial program 0.2

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

   if -3.99999999999999981e158 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 9.4

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

   2. Simplified 2.4

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

      [Start] 9.4	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      associate-/l* [=>] 2.4	\[ \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+192}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	18.3
Cost	649

\[\begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+109} \lor \neg \left(z \leq 1.2 \cdot 10^{+95}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	19.1
Cost	648

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 4
Error	3.1
Cost	448

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

Alternative 5
Error	25.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))