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

Percentage Accurate: 84.3% → 96.1%

Time: 4.7s

Alternatives: 8

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

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

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

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

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.2e+160) (- x (/ x (/ y z))) (/ (* x (- y z)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.2e+160) {
		tmp = x - (x / (y / z));
	} else {
		tmp = (x * (y - z)) / y;
	}
	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
    real(8) :: tmp
    if (z <= 2.2d+160) then
        tmp = x - (x / (y / z))
    else
        tmp = (x * (y - z)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.2e+160) {
		tmp = x - (x / (y / z));
	} else {
		tmp = (x * (y - z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.2e+160:
		tmp = x - (x / (y / z))
	else:
		tmp = (x * (y - z)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.2e+160)
		tmp = Float64(x - Float64(x / Float64(y / z)));
	else
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.2e+160)
		tmp = x - (x / (y / z));
	else
		tmp = (x * (y - z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.2e+160], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.19999999999999992e160

   1. Initial program 81.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. --rgt-identity 81.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y} - 0} \]

      2. associate-*l/ 84.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} - 0 \]

      3. sub-neg 84.5%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(-z\right)\right)} - 0 \]

      4. distribute-rgt-in 81.4%

         \[\leadsto \color{blue}{\left(y \cdot \frac{x}{y} + \left(-z\right) \cdot \frac{x}{y}\right)} - 0 \]

      5. *-commutative 81.4%

         \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot y} + \left(-z\right) \cdot \frac{x}{y}\right) - 0 \]

      6. distribute-lft-neg-out 81.4%

         \[\leadsto \left(\frac{x}{y} \cdot y + \color{blue}{\left(-z \cdot \frac{x}{y}\right)}\right) - 0 \]

      7. unsub-neg 81.4%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot y - z \cdot \frac{x}{y}\right)} - 0 \]

      8. associate--r+ 81.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot y - \left(z \cdot \frac{x}{y} + 0\right)} \]

      9. associate-*l/ 77.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{y}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      10. associate-/l* 93.9%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{y}}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      11. *-inverses 93.9%

          \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      12. /-rgt-identity 93.9%

          \[\leadsto \color{blue}{x} - \left(z \cdot \frac{x}{y} + 0\right) \]

      13. +-rgt-identity 93.9%

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

      14. *-commutative 93.9%

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

      15. associate-/r/ 96.5%

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

   3. Simplified 96.5%

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

   if 2.19999999999999992e160 < z

   1. Initial program 94.9%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \]

Alternative 2: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+86} \lor \neg \left(z \leq -1.2 \cdot 10^{+15}\right) \land \left(z \leq -9.5 \cdot 10^{-88} \lor \neg \left(z \leq 1.9 \cdot 10^{-116}\right) \land \left(z \leq 6.6 \cdot 10^{-92} \lor \neg \left(z \leq 2.55 \cdot 10^{+69}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+86)
         (and (not (<= z -1.2e+15))
              (or (<= z -9.5e-88)
                  (and (not (<= z 1.9e-116))
                       (or (<= z 6.6e-92) (not (<= z 2.55e+69)))))))
   (* x (/ (- z) y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+86) || (!(z <= -1.2e+15) && ((z <= -9.5e-88) || (!(z <= 1.9e-116) && ((z <= 6.6e-92) || !(z <= 2.55e+69)))))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if ((z <= (-1.5d+86)) .or. (.not. (z <= (-1.2d+15))) .and. (z <= (-9.5d-88)) .or. (.not. (z <= 1.9d-116)) .and. (z <= 6.6d-92) .or. (.not. (z <= 2.55d+69))) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+86) || (!(z <= -1.2e+15) && ((z <= -9.5e-88) || (!(z <= 1.9e-116) && ((z <= 6.6e-92) || !(z <= 2.55e+69)))))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+86) or (not (z <= -1.2e+15) and ((z <= -9.5e-88) or (not (z <= 1.9e-116) and ((z <= 6.6e-92) or not (z <= 2.55e+69))))):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+86) || (!(z <= -1.2e+15) && ((z <= -9.5e-88) || (!(z <= 1.9e-116) && ((z <= 6.6e-92) || !(z <= 2.55e+69))))))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+86) || (~((z <= -1.2e+15)) && ((z <= -9.5e-88) || (~((z <= 1.9e-116)) && ((z <= 6.6e-92) || ~((z <= 2.55e+69)))))))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+86], And[N[Not[LessEqual[z, -1.2e+15]], $MachinePrecision], Or[LessEqual[z, -9.5e-88], And[N[Not[LessEqual[z, 1.9e-116]], $MachinePrecision], Or[LessEqual[z, 6.6e-92], N[Not[LessEqual[z, 2.55e+69]], $MachinePrecision]]]]]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999988e86 or -1.2e15 < z < -9.5e-88 or 1.9000000000000001e-116 < z < 6.59999999999999996e-92 or 2.54999999999999999e69 < z

   1. Initial program 87.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around 0 69.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 69.6%

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

      2. distribute-neg-frac 69.6%

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

   6. Simplified 69.6%

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

   if -1.49999999999999988e86 < z < -1.2e15 or -9.5e-88 < z < 1.9000000000000001e-116 or 6.59999999999999996e-92 < z < 2.54999999999999999e69

   1. Initial program 80.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 79.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+86} \lor \neg \left(z \leq -1.2 \cdot 10^{+15}\right) \land \left(z \leq -9.5 \cdot 10^{-88} \lor \neg \left(z \leq 1.9 \cdot 10^{-116}\right) \land \left(z \leq 6.6 \cdot 10^{-92} \lor \neg \left(z \leq 2.55 \cdot 10^{+69}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-z}{y}\\ t_1 := z \cdot \frac{-x}{y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- z) y))) (t_1 (* z (/ (- x) y))))
   (if (<= z -2.2e+39)
     t_1
     (if (<= z -1.02e+15)
       x
       (if (<= z -8e-88)
         t_0
         (if (<= z 1.9e-116)
           x
           (if (<= z 2.5e-92) t_0 (if (<= z 2e+69) x t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double t_1 = z * (-x / y);
	double tmp;
	if (z <= -2.2e+39) {
		tmp = t_1;
	} else if (z <= -1.02e+15) {
		tmp = x;
	} else if (z <= -8e-88) {
		tmp = t_0;
	} else if (z <= 1.9e-116) {
		tmp = x;
	} else if (z <= 2.5e-92) {
		tmp = t_0;
	} else if (z <= 2e+69) {
		tmp = x;
	} 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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (-z / y)
    t_1 = z * (-x / y)
    if (z <= (-2.2d+39)) then
        tmp = t_1
    else if (z <= (-1.02d+15)) then
        tmp = x
    else if (z <= (-8d-88)) then
        tmp = t_0
    else if (z <= 1.9d-116) then
        tmp = x
    else if (z <= 2.5d-92) then
        tmp = t_0
    else if (z <= 2d+69) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double t_1 = z * (-x / y);
	double tmp;
	if (z <= -2.2e+39) {
		tmp = t_1;
	} else if (z <= -1.02e+15) {
		tmp = x;
	} else if (z <= -8e-88) {
		tmp = t_0;
	} else if (z <= 1.9e-116) {
		tmp = x;
	} else if (z <= 2.5e-92) {
		tmp = t_0;
	} else if (z <= 2e+69) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-z / y)
	t_1 = z * (-x / y)
	tmp = 0
	if z <= -2.2e+39:
		tmp = t_1
	elif z <= -1.02e+15:
		tmp = x
	elif z <= -8e-88:
		tmp = t_0
	elif z <= 1.9e-116:
		tmp = x
	elif z <= 2.5e-92:
		tmp = t_0
	elif z <= 2e+69:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-z) / y))
	t_1 = Float64(z * Float64(Float64(-x) / y))
	tmp = 0.0
	if (z <= -2.2e+39)
		tmp = t_1;
	elseif (z <= -1.02e+15)
		tmp = x;
	elseif (z <= -8e-88)
		tmp = t_0;
	elseif (z <= 1.9e-116)
		tmp = x;
	elseif (z <= 2.5e-92)
		tmp = t_0;
	elseif (z <= 2e+69)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-z / y);
	t_1 = z * (-x / y);
	tmp = 0.0;
	if (z <= -2.2e+39)
		tmp = t_1;
	elseif (z <= -1.02e+15)
		tmp = x;
	elseif (z <= -8e-88)
		tmp = t_0;
	elseif (z <= 1.9e-116)
		tmp = x;
	elseif (z <= 2.5e-92)
		tmp = t_0;
	elseif (z <= 2e+69)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+39], t$95$1, If[LessEqual[z, -1.02e+15], x, If[LessEqual[z, -8e-88], t$95$0, If[LessEqual[z, 1.9e-116], x, If[LessEqual[z, 2.5e-92], t$95$0, If[LessEqual[z, 2e+69], x, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e39 or 2.0000000000000001e69 < z

   1. Initial program 89.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around 0 80.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 81.4%

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

      2. associate-*r* 81.4%

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

      3. neg-mul-1 81.4%

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

      4. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if -2.2000000000000001e39 < z < -1.02e15 or -7.99999999999999947e-88 < z < 1.9000000000000001e-116 or 2.50000000000000006e-92 < z < 2.0000000000000001e69

   1. Initial program 78.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.7%

      \[\leadsto \color{blue}{x} \]

   if -1.02e15 < z < -7.99999999999999947e-88 or 1.9000000000000001e-116 < z < 2.50000000000000006e-92

   1. Initial program 82.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 63.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 63.7%

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

      2. distribute-neg-frac 63.7%

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

   6. Simplified 63.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 4: 95.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.36 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.36e+178) (* x (/ (- y z) y)) (* z (/ (- x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.36e+178) {
		tmp = x * ((y - z) / y);
	} else {
		tmp = z * (-x / y);
	}
	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
    real(8) :: tmp
    if (z <= 1.36d+178) then
        tmp = x * ((y - z) / y)
    else
        tmp = z * (-x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.36e+178) {
		tmp = x * ((y - z) / y);
	} else {
		tmp = z * (-x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.36e+178:
		tmp = x * ((y - z) / y)
	else:
		tmp = z * (-x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.36e+178)
		tmp = Float64(x * Float64(Float64(y - z) / y));
	else
		tmp = Float64(z * Float64(Float64(-x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.36e+178)
		tmp = x * ((y - z) / y);
	else
		tmp = z * (-x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.36e+178], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35999999999999992e178

   1. Initial program 82.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 96.1%

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

   3. Simplified 96.1%

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

   if 1.35999999999999992e178 < z

   1. Initial program 94.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in y around 0 91.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 92.3%

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

      2. associate-*r* 92.3%

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

      3. neg-mul-1 92.3%

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

      4. *-commutative 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.36 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 5: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.3e+119) (* x (/ (- y z) y)) (* (- y z) (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.3e+119) {
		tmp = x * ((y - z) / y);
	} else {
		tmp = (y - z) * (x / y);
	}
	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
    real(8) :: tmp
    if (z <= 2.3d+119) then
        tmp = x * ((y - z) / y)
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.3e+119) {
		tmp = x * ((y - z) / y);
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.3e+119:
		tmp = x * ((y - z) / y)
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.3e+119)
		tmp = Float64(x * Float64(Float64(y - z) / y));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.3e+119)
		tmp = x * ((y - z) / y);
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.3e+119], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.3000000000000001e119

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   if 2.3000000000000001e119 < z

   1. Initial program 85.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

      2. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7e+118) (- x (/ x (/ y z))) (* (- y z) (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e+118) {
		tmp = x - (x / (y / z));
	} else {
		tmp = (y - z) * (x / y);
	}
	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
    real(8) :: tmp
    if (z <= 7d+118) then
        tmp = x - (x / (y / z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e+118) {
		tmp = x - (x / (y / z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7e+118:
		tmp = x - (x / (y / z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7e+118)
		tmp = Float64(x - Float64(x / Float64(y / z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7e+118)
		tmp = x - (x / (y / z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7e+118], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.00000000000000033e118

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. --rgt-identity 83.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y} - 0} \]

      2. associate-*l/ 83.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} - 0 \]

      3. sub-neg 83.9%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(-z\right)\right)} - 0 \]

      4. distribute-rgt-in 80.7%

         \[\leadsto \color{blue}{\left(y \cdot \frac{x}{y} + \left(-z\right) \cdot \frac{x}{y}\right)} - 0 \]

      5. *-commutative 80.7%

         \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot y} + \left(-z\right) \cdot \frac{x}{y}\right) - 0 \]

      6. distribute-lft-neg-out 80.7%

         \[\leadsto \left(\frac{x}{y} \cdot y + \color{blue}{\left(-z \cdot \frac{x}{y}\right)}\right) - 0 \]

      7. unsub-neg 80.7%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot y - z \cdot \frac{x}{y}\right)} - 0 \]

      8. associate--r+ 80.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot y - \left(z \cdot \frac{x}{y} + 0\right)} \]

      9. associate-*l/ 78.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{y}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      10. associate-/l* 93.6%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{y}}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      11. *-inverses 93.6%

          \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      12. /-rgt-identity 93.6%

          \[\leadsto \color{blue}{x} - \left(z \cdot \frac{x}{y} + 0\right) \]

      13. +-rgt-identity 93.6%

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

      14. *-commutative 93.6%

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

      15. associate-/r/ 96.8%

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

   3. Simplified 96.8%

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

   if 7.00000000000000033e118 < z

   1. Initial program 85.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

      2. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.8e+211) (* y (/ x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e+211) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if (x <= (-2.8d+211)) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e+211) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e+211:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e+211)
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8e+211)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e+211], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e211

   1. Initial program 76.7%

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

   2. Taylor expanded in y around inf 18.1%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{y} \]
   3. Step-by-step derivation

      1. associate-/l* 61.8%

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

      2. div-inv 66.1%

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

      3. clear-num 66.2%

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

   4. Applied egg-rr 66.2%

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

   if -2.8e211 < x

   1. Initial program 84.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 49.6%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.7%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*r/ 92.9%

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

3. Simplified 92.9%

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

4. Taylor expanded in y around inf 48.5%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 48.5%

   \[\leadsto x \]

Developer target: 96.1% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	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
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023268 
(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))