Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Average Accuracy: 63.7% → 80.5%

Time: 13.6s

Precision: binary64

Cost: 1101

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-265} \lor \neg \left(\frac{y}{z} \leq 0\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) (- INFINITY))
   (/ 1.0 (/ z (* y x)))
   (if (or (<= (/ y z) -1e-265) (not (<= (/ y z) 0.0)))
     (* (/ y z) x)
     (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	return x * (((y / z) * t) / t);
}

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -((double) INFINITY)) {
		tmp = 1.0 / (z / (y * x));
	} else if (((y / z) <= -1e-265) || !((y / z) <= 0.0)) {
		tmp = (y / z) * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	return x * (((y / z) * t) / t);
}

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / (z / (y * x));
	} else if (((y / z) <= -1e-265) || !((y / z) <= 0.0)) {
		tmp = (y / z) * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -math.inf:
		tmp = 1.0 / (z / (y * x))
	elif ((y / z) <= -1e-265) or not ((y / z) <= 0.0):
		tmp = (y / z) * x
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(Float64(y / z) * t) / t))
end

↓

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y / z) <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(z / Float64(y * x)));
	elseif ((Float64(y / z) <= -1e-265) || !(Float64(y / z) <= 0.0))
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (((y / z) * t) / t);
end

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y / z) <= -Inf)
		tmp = 1.0 / (z / (y * x));
	elseif (((y / z) <= -1e-265) || ~(((y / z) <= 0.0)))
		tmp = (y / z) * x;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := If[LessEqual[N[(y / z), $MachinePrecision], (-Infinity)], N[(1.0 / N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], -1e-265], N[Not[LessEqual[N[(y / z), $MachinePrecision], 0.0]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Target

Original	63.7%
Target	81.3%
Herbie	80.5%

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -inf.0

   1. Initial program 0.0%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

   2. Simplified 54.8%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
      Step-by-step derivation

      [Start] 0.0	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
      *-commutative [=>] 0.0	\[ \color{blue}{\frac{\frac{y}{z} \cdot t}{t} \cdot x} \]
      associate-/l* [=>] 0.0	\[ \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \cdot x \]
      *-inverses [=>] 0.0	\[ \frac{\frac{y}{z}}{\color{blue}{1}} \cdot x \]
      /-rgt-identity [=>] 0.0	\[ \color{blue}{\frac{y}{z}} \cdot x \]
      associate-*l/ [=>] 54.9	\[ \color{blue}{\frac{y \cdot x}{z}} \]
      associate-*r/ [<=] 54.8	\[ \color{blue}{y \cdot \frac{x}{z}} \]

   3. Applied egg-rr 54.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot x}}} \]
      Step-by-step derivation

      [Start] 54.8	\[ y \cdot \frac{x}{z} \]
      associate-*r/ [=>] 54.9	\[ \color{blue}{\frac{y \cdot x}{z}} \]
      clear-num [=>] 54.9	\[ \color{blue}{\frac{1}{\frac{z}{y \cdot x}}} \]

   if -inf.0 < (/.f64 y z) < -9.99999999999999985e-266 or 0.0 < (/.f64 y z)

   1. Initial program 69.1%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

   2. Simplified 81.0%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
      Step-by-step derivation

      [Start] 69.1	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
      associate-/l* [=>] 81.0	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
      *-inverses [=>] 81.0	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
      /-rgt-identity [=>] 81.0	\[ x \cdot \color{blue}{\frac{y}{z}} \]

   if -9.99999999999999985e-266 < (/.f64 y z) < 0.0

   1. Initial program 75.2%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

   2. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
      Step-by-step derivation

      [Start] 75.2	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
      associate-/l* [=>] 77.6	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
      *-inverses [=>] 77.6	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
      /-rgt-identity [=>] 77.6	\[ x \cdot \color{blue}{\frac{y}{z}} \]

   3. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-265} \lor \neg \left(\frac{y}{z} \leq 0\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	80.5%
Cost	1101

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty \lor \neg \left(\frac{y}{z} \leq -1 \cdot 10^{-265}\right) \land \frac{y}{z} \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 2
Accuracy	80.5%
Cost	1101

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-265} \lor \neg \left(\frac{y}{z} \leq 0\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 3
Accuracy	80.5%
Cost	1101

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-265} \lor \neg \left(\frac{y}{z} \leq 0\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 4
Accuracy	74.8%
Cost	320

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

Alternative 5
Accuracy	19.1%
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))