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

Average Error: 12.4 → 1.8

Time: 5.9s

Precision: binary64

Cost: 1996

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := \frac{x}{\frac{y}{y - z}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{+117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (/ x (/ y (- y z)))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -1e+117) t_0 (if (<= t_0 5e-25) t_1 (/ (- y z) (/ 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 * (y - z)) / y;
	double t_1 = x / (y / (y - z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -1e+117) {
		tmp = t_0;
	} else if (t_0 <= 5e-25) {
		tmp = t_1;
	} else {
		tmp = (y - z) / (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 * (y - z)) / y;
	double t_1 = x / (y / (y - z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -1e+117) {
		tmp = t_0;
	} else if (t_0 <= 5e-25) {
		tmp = t_1;
	} else {
		tmp = (y - z) / (y / x);
	}
	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 / (y / (y - z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -1e+117:
		tmp = t_0
	elif t_0 <= 5e-25:
		tmp = t_1
	else:
		tmp = (y - z) / (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(Float64(x * Float64(y - z)) / y)
	t_1 = Float64(x / Float64(y / Float64(y - z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -1e+117)
		tmp = t_0;
	elseif (t_0 <= 5e-25)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) / 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 * (y - z)) / y;
	t_1 = x / (y / (y - z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -1e+117)
		tmp = t_0;
	elseif (t_0 <= 5e-25)
		tmp = t_1;
	else
		tmp = (y - z) / (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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -1e+117], t$95$0, If[LessEqual[t$95$0, 5e-25], t$95$1, N[(N[(y - z), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	12.4
Target	3.0
Herbie	1.8

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or -1.00000000000000005e117 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.99999999999999962e-25

   1. Initial program 13.0

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

   2. Simplified 0.4

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

      [Start] 13.0	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      associate-/l* [=>] 0.4	\[ \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -1.00000000000000005e117

   1. Initial program 0.2

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

   if 4.99999999999999962e-25 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 15.9

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

   2. Simplified 4.8

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

      [Start] 15.9	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      *-commutative [=>] 15.9	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]
      associate-/l* [=>] 4.8	\[ \color{blue}{\frac{y - z}{\frac{y}{x}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1 \cdot 10^{+117}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	2.0
Cost	1996

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := \frac{x}{\frac{y}{y - z}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{+117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2
Error	20.6
Cost	913

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-151} \lor \neg \left(y \leq -1.65 \cdot 10^{-227}\right) \land y \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	20.7
Cost	912

\[\begin{array}{l} t_0 := \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 0.0006:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	20.6
Cost	912

\[\begin{array}{l} t_0 := \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	20.7
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \]

Alternative 6
Error	3.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+210} \lor \neg \left(z \leq 0.0002\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

Alternative 7
Error	7.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+193}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	25.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023046 
(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))