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

Average Error: 12.8 → 2.2

Time: 2.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := x - \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;x \leq -2.5475090785488885 \cdot 10^{-183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.005781062679642 \cdot 10^{-122}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x (/ y z)))))
   (if (<= x -2.5475090785488885e-183)
     t_0
     (if (<= x 6.005781062679642e-122) (- x (* z (/ x y))) t_0))))

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 - (x / (y / z));
	double tmp;
	if (x <= -2.5475090785488885e-183) {
		tmp = t_0;
	} else if (x <= 6.005781062679642e-122) {
		tmp = x - (z * (x / y));
	} else {
		tmp = t_0;
	}
	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) :: tmp
    t_0 = x - (x / (y / z))
    if (x <= (-2.5475090785488885d-183)) then
        tmp = t_0
    else if (x <= 6.005781062679642d-122) then
        tmp = x - (z * (x / y))
    else
        tmp = t_0
    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 - (x / (y / z));
	double tmp;
	if (x <= -2.5475090785488885e-183) {
		tmp = t_0;
	} else if (x <= 6.005781062679642e-122) {
		tmp = x - (z * (x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x - (x / (y / z))
	tmp = 0
	if x <= -2.5475090785488885e-183:
		tmp = t_0
	elif x <= 6.005781062679642e-122:
		tmp = x - (z * (x / y))
	else:
		tmp = t_0
	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(x / Float64(y / z)))
	tmp = 0.0
	if (x <= -2.5475090785488885e-183)
		tmp = t_0;
	elseif (x <= 6.005781062679642e-122)
		tmp = Float64(x - Float64(z * Float64(x / y)));
	else
		tmp = t_0;
	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 - (x / (y / z));
	tmp = 0.0;
	if (x <= -2.5475090785488885e-183)
		tmp = t_0;
	elseif (x <= 6.005781062679642e-122)
		tmp = x - (z * (x / y));
	else
		tmp = t_0;
	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[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5475090785488885e-183], t$95$0, If[LessEqual[x, 6.005781062679642e-122], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	12.8
Target	3.0
Herbie	2.2

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

Derivation

1. Split input into 2 regimes

2. if x < -2.54750907854888853e-183 or 6.00578106267964183e-122 < x

   1. Initial program 14.4

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

   2. Simplified 4.9

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

   3. Taylor expanded in x around 0 1.5

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

   4. Taylor expanded in z around 0 4.5

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

   5. Simplified 1.3

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

   if -2.54750907854888853e-183 < x < 6.00578106267964183e-122

   1. Initial program 8.7

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

   2. Simplified 4.5

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

   3. Applied egg-rr 4.2

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

4. Final simplification 2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5475090785488885 \cdot 10^{-183}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;x \leq 6.005781062679642 \cdot 10^{-122}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022186 
(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))