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

Average Error: 15.0 → 1.0

Time: 3.7s

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ t_2 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{y}{z} \leq -1.1302820992287937 \cdot 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{y}{z} \leq -3.3661765824879353 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{y}{z} \leq 6.72368 \cdot 10^{-318}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{y}{z} \leq 1.3164353627601914 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))) (t_2 (/ y (/ z x))))
   (if (<= (/ y z) -1.1302820992287937e+282)
     t_2
     (if (<= (/ y z) -3.3661765824879353e-113)
       t_1
       (if (<= (/ y z) 6.72368e-318)
         t_2
         (if (<= (/ y z) 1.3164353627601914e+143) t_1 (/ (* 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 t_1 = x / (z / y);
	double t_2 = y / (z / x);
	double tmp;
	if ((y / z) <= -1.1302820992287937e+282) {
		tmp = t_2;
	} else if ((y / z) <= -3.3661765824879353e-113) {
		tmp = t_1;
	} else if ((y / z) <= 6.72368e-318) {
		tmp = t_2;
	} else if ((y / z) <= 1.3164353627601914e+143) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x / (z / y)
    t_2 = y / (z / x)
    if ((y / z) <= (-1.1302820992287937d+282)) then
        tmp = t_2
    else if ((y / z) <= (-3.3661765824879353d-113)) then
        tmp = t_1
    else if ((y / z) <= 6.72368d-318) then
        tmp = t_2
    else if ((y / z) <= 1.3164353627601914d+143) then
        tmp = t_1
    else
        tmp = (y * x) / z
    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 t_2 = y / (z / x);
	double tmp;
	if ((y / z) <= -1.1302820992287937e+282) {
		tmp = t_2;
	} else if ((y / z) <= -3.3661765824879353e-113) {
		tmp = t_1;
	} else if ((y / z) <= 6.72368e-318) {
		tmp = t_2;
	} else if ((y / z) <= 1.3164353627601914e+143) {
		tmp = t_1;
	} 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):
	t_1 = x / (z / y)
	t_2 = y / (z / x)
	tmp = 0
	if (y / z) <= -1.1302820992287937e+282:
		tmp = t_2
	elif (y / z) <= -3.3661765824879353e-113:
		tmp = t_1
	elif (y / z) <= 6.72368e-318:
		tmp = t_2
	elif (y / z) <= 1.3164353627601914e+143:
		tmp = t_1
	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)
	t_1 = Float64(x / Float64(z / y))
	t_2 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (Float64(y / z) <= -1.1302820992287937e+282)
		tmp = t_2;
	elseif (Float64(y / z) <= -3.3661765824879353e-113)
		tmp = t_1;
	elseif (Float64(y / z) <= 6.72368e-318)
		tmp = t_2;
	elseif (Float64(y / z) <= 1.3164353627601914e+143)
		tmp = t_1;
	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)
	t_1 = x / (z / y);
	t_2 = y / (z / x);
	tmp = 0.0;
	if ((y / z) <= -1.1302820992287937e+282)
		tmp = t_2;
	elseif ((y / z) <= -3.3661765824879353e-113)
		tmp = t_1;
	elseif ((y / z) <= 6.72368e-318)
		tmp = t_2;
	elseif ((y / z) <= 1.3164353627601914e+143)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y / z), $MachinePrecision], -1.1302820992287937e+282], t$95$2, If[LessEqual[N[(y / z), $MachinePrecision], -3.3661765824879353e-113], t$95$1, If[LessEqual[N[(y / z), $MachinePrecision], 6.72368e-318], t$95$2, If[LessEqual[N[(y / z), $MachinePrecision], 1.3164353627601914e+143], t$95$1, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	15.0
Target	1.5
Herbie	1.0

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -1.1302820992287937e282 or -3.36617658248793534e-113 < (/.f64 y z) < 6.7236801e-318

   1. Initial program 21.0

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

   2. Simplified 14.4

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

   3. Taylor expanded in x around 0 1.5

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

   4. Simplified 1.6

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

   5. Applied egg-rr 1.7

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

   if -1.1302820992287937e282 < (/.f64 y z) < -3.36617658248793534e-113 or 6.7236801e-318 < (/.f64 y z) < 1.3164353627601914e143

   1. Initial program 9.0

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

   2. Simplified 0.5

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

   if 1.3164353627601914e143 < (/.f64 y z)

   1. Initial program 34.2

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

   2. Simplified 16.2

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

   3. Taylor expanded in x around 0 2.3

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

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1.1302820992287937 \cdot 10^{+282}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq -3.3661765824879353 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 6.72368 \cdot 10^{-318}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq 1.3164353627601914 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022153 
(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)))