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

Average Error: 18.92% → 2.8%

Time: 6.7s

Precision: binary64

Cost: 1481

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq -5 \cdot 10^{-163}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 (or (<= t_0 (- INFINITY)) (not (<= t_0 -5e-163)))
     (- x (/ x (/ y z)))
     t_0)))

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)) || !(t_0 <= -5e-163)) {
		tmp = x - (x / (y / z));
	} else {
		tmp = t_0;
	}
	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) || !(t_0 <= -5e-163)) {
		tmp = x - (x / (y / z));
	} else {
		tmp = t_0;
	}
	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) or not (t_0 <= -5e-163):
		tmp = x - (x / (y / z))
	else:
		tmp = t_0
	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)) || !(t_0 <= -5e-163))
		tmp = Float64(x - Float64(x / Float64(y / z)));
	else
		tmp = t_0;
	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) || ~((t_0 <= -5e-163)))
		tmp = x - (x / (y / z));
	else
		tmp = t_0;
	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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, -5e-163]], $MachinePrecision]], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Target

Original	18.92%
Target	4.73%
Herbie	2.8%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or -4.99999999999999977e-163 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 28.15

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

   2. Simplified 3.93

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

      [Start] 28.15	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      associate-*r/ [<=] 4.26	\[ \color{blue}{x \cdot \frac{y - z}{y}} \]
      div-sub [=>] 4.25	\[ x \cdot \color{blue}{\left(\frac{y}{y} - \frac{z}{y}\right)} \]
      distribute-rgt-out-- [<=] 4.25	\[ \color{blue}{\frac{y}{y} \cdot x - \frac{z}{y} \cdot x} \]
      *-inverses [=>] 4.25	\[ \color{blue}{1} \cdot x - \frac{z}{y} \cdot x \]
      *-lft-identity [=>] 4.25	\[ \color{blue}{x} - \frac{z}{y} \cdot x \]
      associate-*l/ [=>] 10.84	\[ x - \color{blue}{\frac{z \cdot x}{y}} \]
      *-commutative [<=] 10.84	\[ x - \frac{\color{blue}{x \cdot z}}{y} \]
      associate-/l* [=>] 3.93	\[ x - \color{blue}{\frac{x}{\frac{y}{z}}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -4.99999999999999977e-163

   1. Initial program 0.54

      \[\frac{x \cdot \left(y - z\right)}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq -5 \cdot 10^{-163}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \]

Alternatives

Alternative 1
Error	30.33%
Cost	914

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+35} \lor \neg \left(z \leq -30000000 \lor \neg \left(z \leq -1.7 \cdot 10^{-44}\right) \land z \leq 5.5 \cdot 10^{-35}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	31.73%
Cost	912

\[\begin{array}{l} t_0 := z \cdot \frac{-x}{y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -230000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \end{array} \]

Alternative 3
Error	31.68%
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq -102000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \end{array} \]

Alternative 4
Error	31.81%
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq -23500000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \end{array} \]

Alternative 5
Error	5.21%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-161} \lor \neg \left(y \leq 2.3 \cdot 10^{-158}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6
Error	12.34%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+193}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	5.23%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-158}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 8
Error	40.74%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(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))