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

Average Error: 12.6 → 0.2

Time: 6.6s

Precision: binary64

Cost: 2513

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{+31} \lor \neg \left(t_0 \leq 5 \cdot 10^{-8}\right) \land t_0 \leq 10^{+297}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

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 (or (<= t_0 -5e+31) (and (not (<= t_0 5e-8)) (<= t_0 1e+297)))
       t_0
       (- x (/ x (/ 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 <= -5e+31) || (!(t_0 <= 5e-8) && (t_0 <= 1e+297))) {
		tmp = t_0;
	} else {
		tmp = x - (x / (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 <= -5e+31) || (!(t_0 <= 5e-8) && (t_0 <= 1e+297))) {
		tmp = t_0;
	} else {
		tmp = x - (x / (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 <= -5e+31) or (not (t_0 <= 5e-8) and (t_0 <= 1e+297)):
		tmp = t_0
	else:
		tmp = x - (x / (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 <= -5e+31) || (!(t_0 <= 5e-8) && (t_0 <= 1e+297)))
		tmp = t_0;
	else
		tmp = Float64(x - Float64(x / 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 <= -5e+31) || (~((t_0 <= 5e-8)) && (t_0 <= 1e+297)))
		tmp = t_0;
	else
		tmp = x - (x / (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[Or[LessEqual[t$95$0, -5e+31], And[N[Not[LessEqual[t$95$0, 5e-8]], $MachinePrecision], LessEqual[t$95$0, 1e+297]]], t$95$0, N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	12.6
Target	3.0
Herbie	0.2

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

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 0.1

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{y}} \]
      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/ [<=] 0.1	\[ \color{blue}{\left(y - z\right) \cdot \frac{x}{y}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -5.00000000000000027e31 or 4.9999999999999998e-8 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1e297

   1. Initial program 0.2

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

   if -5.00000000000000027e31 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.9999999999999998e-8 or 1e297 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 14.9

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

   2. Simplified 0.2

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

      [Start] 14.9	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      associate-*r/ [<=] 0.3	\[ \color{blue}{x \cdot \frac{y - z}{y}} \]
      div-sub [=>] 0.3	\[ x \cdot \color{blue}{\left(\frac{y}{y} - \frac{z}{y}\right)} \]
      distribute-rgt-out-- [<=] 0.3	\[ \color{blue}{\frac{y}{y} \cdot x - \frac{z}{y} \cdot x} \]
      *-inverses [=>] 0.3	\[ \color{blue}{1} \cdot x - \frac{z}{y} \cdot x \]
      *-lft-identity [=>] 0.3	\[ \color{blue}{x} - \frac{z}{y} \cdot x \]
      associate-*l/ [=>] 6.2	\[ x - \color{blue}{\frac{z \cdot x}{y}} \]
      *-commutative [<=] 6.2	\[ x - \frac{\color{blue}{x \cdot z}}{y} \]
      associate-/l* [=>] 0.2	\[ x - \color{blue}{\frac{x}{\frac{y}{z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -5 \cdot 10^{+31} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{-8}\right) \land \frac{x \cdot \left(y - z\right)}{y} \leq 10^{+297}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.6
Cost	7300

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{z}{y}, x\right)\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{-8}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \end{array} \]

Alternative 2
Error	1.5
Cost	1996

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{-8}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \end{array} \]

Alternative 3
Error	19.9
Cost	1178

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-26} \lor \neg \left(y \leq -8.5 \cdot 10^{-95}\right) \land \left(y \leq 5.8 \cdot 10^{-115} \lor \neg \left(y \leq 2.55 \cdot 10^{-81}\right) \land y \leq 4.5 \cdot 10^{-35}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	19.9
Cost	1177

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-115} \lor \neg \left(y \leq 1.4 \cdot 10^{-79}\right) \land y \leq 1.26 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	19.2
Cost	912

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	3.3
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-165} \lor \neg \left(y \leq 3 \cdot 10^{-41}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7
Error	7.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+183}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	26.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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))