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

Average Error: 12.7 → 0.7

Time: 7.5s

Precision: binary64

Cost: 2512

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := x - \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -4 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+275}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (- x (/ x (/ y z)))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -4e-40)
       t_0
       (if (<= t_0 1e+82) t_1 (if (<= t_0 4e+275) t_0 (* (- y z) (/ x y))))))))

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 t_1 = x - (x / (y / z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -4e-40) {
		tmp = t_0;
	} else if (t_0 <= 1e+82) {
		tmp = t_1;
	} else if (t_0 <= 4e+275) {
		tmp = t_0;
	} else {
		tmp = (y - z) * (x / y);
	}
	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 t_1 = x - (x / (y / z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -4e-40) {
		tmp = t_0;
	} else if (t_0 <= 1e+82) {
		tmp = t_1;
	} else if (t_0 <= 4e+275) {
		tmp = t_0;
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	t_1 = x - (x / (y / z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -4e-40:
		tmp = t_0
	elif t_0 <= 1e+82:
		tmp = t_1
	elif t_0 <= 4e+275:
		tmp = t_0
	else:
		tmp = (y - z) * (x / y)
	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)
	t_1 = Float64(x - Float64(x / Float64(y / z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -4e-40)
		tmp = t_0;
	elseif (t_0 <= 1e+82)
		tmp = t_1;
	elseif (t_0 <= 4e+275)
		tmp = t_0;
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	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;
	t_1 = x - (x / (y / z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -4e-40)
		tmp = t_0;
	elseif (t_0 <= 1e+82)
		tmp = t_1;
	elseif (t_0 <= 4e+275)
		tmp = t_0;
	else
		tmp = (y - z) * (x / y);
	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]}, Block[{t$95$1 = N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -4e-40], t$95$0, If[LessEqual[t$95$0, 1e+82], t$95$1, If[LessEqual[t$95$0, 4e+275], t$95$0, N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	12.7
Target	3.3
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or -3.9999999999999997e-40 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.9999999999999996e81

   1. Initial program 14.5

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

   2. Simplified 0.4

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

      [Start] 14.5	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      associate-*r/ [<=] 0.5	\[ \color{blue}{x \cdot \frac{y - z}{y}} \]
      div-sub [=>] 0.4	\[ x \cdot \color{blue}{\left(\frac{y}{y} - \frac{z}{y}\right)} \]
      distribute-rgt-out-- [<=] 0.4	\[ \color{blue}{\frac{y}{y} \cdot x - \frac{z}{y} \cdot x} \]
      *-inverses [=>] 0.4	\[ \color{blue}{1} \cdot x - \frac{z}{y} \cdot x \]
      *-lft-identity [=>] 0.4	\[ \color{blue}{x} - \frac{z}{y} \cdot x \]
      associate-*l/ [=>] 6.1	\[ x - \color{blue}{\frac{z \cdot x}{y}} \]
      *-commutative [<=] 6.1	\[ x - \frac{\color{blue}{x \cdot z}}{y} \]
      associate-/l* [=>] 0.4	\[ x - \color{blue}{\frac{x}{\frac{y}{z}}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -3.9999999999999997e-40 or 9.9999999999999996e81 < (/.f64 (*.f64 x (-.f64 y z)) y) < 3.99999999999999984e275

   1. Initial program 0.2

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

   if 3.99999999999999984e275 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 52.5

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

   2. Simplified 5.0

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

      [Start] 52.5	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      *-commutative [=>] 52.5	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]
      associate-*r/ [<=] 5.0	\[ \color{blue}{\left(y - z\right) \cdot \frac{x}{y}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+82}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 4 \cdot 10^{+275}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternatives

Alternative 1
Error	19.6
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00086:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 2
Error	8.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+106}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	19.4
Cost	649

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+44} \lor \neg \left(z \leq 1.25 \cdot 10^{-36}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	19.5
Cost	648

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+42}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 5
Error	5.1
Cost	580

\[\begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+83}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 6
Error	25.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023055 
(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))