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

Average Error: 13.0 → 3.1

Time: 3.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := x - \frac{z \cdot x}{y}\\ t_1 := \frac{x}{\frac{y}{y - z}}\\ \mathbf{if}\;z \leq -7.372894544810212 \cdot 10^{+234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.267723067807247 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6281276401897885 \cdot 10^{+257}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ (* z x) y))) (t_1 (/ x (/ y (- y z)))))
   (if (<= z -7.372894544810212e+234)
     t_0
     (if (<= z 5.267723067807247e+137)
       t_1
       (if (<= z 3.6281276401897885e+257) t_0 t_1)))))

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 - ((z * x) / y);
	double t_1 = x / (y / (y - z));
	double tmp;
	if (z <= -7.372894544810212e+234) {
		tmp = t_0;
	} else if (z <= 5.267723067807247e+137) {
		tmp = t_1;
	} else if (z <= 3.6281276401897885e+257) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - ((z * x) / y)
    t_1 = x / (y / (y - z))
    if (z <= (-7.372894544810212d+234)) then
        tmp = t_0
    else if (z <= 5.267723067807247d+137) then
        tmp = t_1
    else if (z <= 3.6281276401897885d+257) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

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 - ((z * x) / y);
	double t_1 = x / (y / (y - z));
	double tmp;
	if (z <= -7.372894544810212e+234) {
		tmp = t_0;
	} else if (z <= 5.267723067807247e+137) {
		tmp = t_1;
	} else if (z <= 3.6281276401897885e+257) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x - ((z * x) / y)
	t_1 = x / (y / (y - z))
	tmp = 0
	if z <= -7.372894544810212e+234:
		tmp = t_0
	elif z <= 5.267723067807247e+137:
		tmp = t_1
	elif z <= 3.6281276401897885e+257:
		tmp = t_0
	else:
		tmp = t_1
	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(x - Float64(Float64(z * x) / y))
	t_1 = Float64(x / Float64(y / Float64(y - z)))
	tmp = 0.0
	if (z <= -7.372894544810212e+234)
		tmp = t_0;
	elseif (z <= 5.267723067807247e+137)
		tmp = t_1;
	elseif (z <= 3.6281276401897885e+257)
		tmp = t_0;
	else
		tmp = t_1;
	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 - ((z * x) / y);
	t_1 = x / (y / (y - z));
	tmp = 0.0;
	if (z <= -7.372894544810212e+234)
		tmp = t_0;
	elseif (z <= 5.267723067807247e+137)
		tmp = t_1;
	elseif (z <= 3.6281276401897885e+257)
		tmp = t_0;
	else
		tmp = t_1;
	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[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.372894544810212e+234], t$95$0, If[LessEqual[z, 5.267723067807247e+137], t$95$1, If[LessEqual[z, 3.6281276401897885e+257], t$95$0, t$95$1]]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.0
Target	2.9
Herbie	3.1

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

Derivation

1. Split input into 2 regimes

2. if z < -7.3728945448102116e234 or 5.2677230678072466e137 < z < 3.62812764018978853e257

   1. Initial program 13.7

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

   2. Taylor expanded in y around 0 11.8

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

   if -7.3728945448102116e234 < z < 5.2677230678072466e137 or 3.62812764018978853e257 < z

   1. Initial program 12.9

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

   2. Applied egg-rr 2.1

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}} \]

   3. Applied egg-rr 1.9

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.372894544810212 \cdot 10^{+234}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 5.267723067807247 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;z \leq 3.6281276401897885 \cdot 10^{+257}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022133 
(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))