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

Average Error: 14.5 → 0.4

Time: 3.5s

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;{\left(\frac{z}{y \cdot x}\right)}^{-1}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{-258}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) (- INFINITY))
   (pow (/ z (* y x)) -1.0)
   (if (<= (/ y z) -1e-153)
     (* (/ y z) x)
     (if (<= (/ y z) 2e-258)
       (/ y (/ z x))
       (if (<= (/ y z) 2e+261) (/ x (/ z y)) (* 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 = pow((z / (y * x)), -1.0);
	} else if ((y / z) <= -1e-153) {
		tmp = (y / z) * x;
	} else if ((y / z) <= 2e-258) {
		tmp = y / (z / x);
	} else if ((y / z) <= 2e+261) {
		tmp = x / (z / y);
	} 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 = Math.pow((z / (y * x)), -1.0);
	} else if ((y / z) <= -1e-153) {
		tmp = (y / z) * x;
	} else if ((y / z) <= 2e-258) {
		tmp = y / (z / x);
	} else if ((y / z) <= 2e+261) {
		tmp = x / (z / y);
	} 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 = math.pow((z / (y * x)), -1.0)
	elif (y / z) <= -1e-153:
		tmp = (y / z) * x
	elif (y / z) <= 2e-258:
		tmp = y / (z / x)
	elif (y / z) <= 2e+261:
		tmp = x / (z / y)
	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(z / Float64(y * x)) ^ -1.0;
	elseif (Float64(y / z) <= -1e-153)
		tmp = Float64(Float64(y / z) * x);
	elseif (Float64(y / z) <= 2e-258)
		tmp = Float64(y / Float64(z / x));
	elseif (Float64(y / z) <= 2e+261)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y * Float64(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 = (z / (y * x)) ^ -1.0;
	elseif ((y / z) <= -1e-153)
		tmp = (y / z) * x;
	elseif ((y / z) <= 2e-258)
		tmp = y / (z / x);
	elseif ((y / z) <= 2e+261)
		tmp = x / (z / y);
	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[Power[N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], -1e-153], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 2e-258], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 2e+261], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	14.5
Target	1.6
Herbie	0.4

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

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.0

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

   2. Simplified 59.2

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

   3. Applied egg-rr 0.3

      \[\leadsto \color{blue}{{\left(\frac{z}{x \cdot y}\right)}^{-1}} \]

   if -inf.0 < (/.f64 y z) < -1.00000000000000004e-153

   1. Initial program 9.9

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

   2. Simplified 0.3

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

   3. Taylor expanded in x around 0 9.3

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

   4. Simplified 9.4

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

   5. Applied egg-rr 9.6

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

   6. Applied egg-rr 0.3

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

   if -1.00000000000000004e-153 < (/.f64 y z) < 1.99999999999999991e-258

   1. Initial program 16.0

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

   2. Simplified 10.9

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

   3. Taylor expanded in x around 0 0.9

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

   4. Simplified 0.8

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

   5. Applied egg-rr 0.9

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

   if 1.99999999999999991e-258 < (/.f64 y z) < 1.9999999999999999e261

   1. Initial program 9.7

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

   2. Simplified 0.2

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

   if 1.9999999999999999e261 < (/.f64 y z)

   1. Initial program 54.9

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

   2. Simplified 42.0

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

   3. Taylor expanded in x around 0 0.5

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

   4. Simplified 0.3

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;{\left(\frac{z}{y \cdot x}\right)}^{-1}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{-258}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022192 
(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)))