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

Average Error: 14.2 → 1.2

Time: 3.1s

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 5 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= (/ y z) -1e+278)
     (* y (/ x z))
     (if (<= (/ y z) -1e-146)
       t_1
       (if (<= (/ y z) 2e-318)
         (/ (* y x) z)
         (if (<= (/ y z) 5e+86) t_1 (/ y (/ z x))))))))

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 t_1 = x / (z / y);
	double tmp;
	if ((y / z) <= -1e+278) {
		tmp = y * (x / z);
	} else if ((y / z) <= -1e-146) {
		tmp = t_1;
	} else if ((y / z) <= 2e-318) {
		tmp = (y * x) / z;
	} else if ((y / z) <= 5e+86) {
		tmp = t_1;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (((y / z) * t) / t)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / y)
    if ((y / z) <= (-1d+278)) then
        tmp = y * (x / z)
    else if ((y / z) <= (-1d-146)) then
        tmp = t_1
    else if ((y / z) <= 2d-318) then
        tmp = (y * x) / z
    else if ((y / z) <= 5d+86) then
        tmp = t_1
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

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 t_1 = x / (z / y);
	double tmp;
	if ((y / z) <= -1e+278) {
		tmp = y * (x / z);
	} else if ((y / z) <= -1e-146) {
		tmp = t_1;
	} else if ((y / z) <= 2e-318) {
		tmp = (y * x) / z;
	} else if ((y / z) <= 5e+86) {
		tmp = t_1;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = x / (z / y)
	tmp = 0
	if (y / z) <= -1e+278:
		tmp = y * (x / z)
	elif (y / z) <= -1e-146:
		tmp = t_1
	elif (y / z) <= 2e-318:
		tmp = (y * x) / z
	elif (y / z) <= 5e+86:
		tmp = t_1
	else:
		tmp = y / (z / x)
	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)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (Float64(y / z) <= -1e+278)
		tmp = Float64(y * Float64(x / z));
	elseif (Float64(y / z) <= -1e-146)
		tmp = t_1;
	elseif (Float64(y / z) <= 2e-318)
		tmp = Float64(Float64(y * x) / z);
	elseif (Float64(y / z) <= 5e+86)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(z / x));
	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)
	t_1 = x / (z / y);
	tmp = 0.0;
	if ((y / z) <= -1e+278)
		tmp = y * (x / z);
	elseif ((y / z) <= -1e-146)
		tmp = t_1;
	elseif ((y / z) <= 2e-318)
		tmp = (y * x) / z;
	elseif ((y / z) <= 5e+86)
		tmp = t_1;
	else
		tmp = y / (z / x);
	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_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y / z), $MachinePrecision], -1e+278], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], -1e-146], t$95$1, If[LessEqual[N[(y / z), $MachinePrecision], 2e-318], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 5e+86], t$95$1, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.2
Target	1.3
Herbie	1.2

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 y z) < -9.99999999999999964e277

   1. Initial program 57.3

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

   2. Simplified 46.1

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

   3. Taylor expanded in x around 0 0.3

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

   4. Simplified 0.3

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

   if -9.99999999999999964e277 < (/.f64 y z) < -1.00000000000000003e-146 or 2.0000024e-318 < (/.f64 y z) < 4.9999999999999998e86

   1. Initial program 8.6

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

   2. Simplified 0.4

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

   if -1.00000000000000003e-146 < (/.f64 y z) < 2.0000024e-318

   1. Initial program 15.7

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

   2. Simplified 10.9

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

   3. Taylor expanded in x around 0 1.1

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

   if 4.9999999999999998e86 < (/.f64 y z)

   1. Initial program 27.1

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

   2. Simplified 11.8

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

   3. Taylor expanded in x around 0 4.5

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

   4. Simplified 5.1

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

   5. Applied egg-rr 5.1

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -1 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022160 
(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)))