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

Percentage Accurate: 84.4% → 96.7%

Time: 5.7s

Alternatives: 7

Speedup: 1.0×

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: 84.4% 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: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{y}{y - z}} \end{array} \]

FPCore

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

C

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

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 / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

   1. associate-/l* 96.5%

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

   2. add-sqr-sqrt 44.3%

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

   3. associate-*l* 44.3%

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

4. Applied egg-rr 44.3%

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

   1. associate-*r* 44.3%

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

   2. add-sqr-sqrt 96.5%

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

   3. clear-num 96.5%

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

   4. un-div-inv 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

   \[\leadsto \frac{x}{\frac{y}{y - z}} \]
8. Add Preprocessing

Alternative 2: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -320000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{-105}\right) \land \left(z \leq 1.85 \cdot 10^{-78} \lor \neg \left(z \leq 0.00022\right)\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -320000000000.0)
         (and (not (<= z 5.2e-105)) (or (<= z 1.85e-78) (not (<= z 0.00022)))))
   (* x (/ z (- y)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -320000000000.0) || (!(z <= 5.2e-105) && ((z <= 1.85e-78) || !(z <= 0.00022)))) {
		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 <= (-320000000000.0d0)) .or. (.not. (z <= 5.2d-105)) .and. (z <= 1.85d-78) .or. (.not. (z <= 0.00022d0))) 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 <= -320000000000.0) || (!(z <= 5.2e-105) && ((z <= 1.85e-78) || !(z <= 0.00022)))) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -320000000000.0) or (not (z <= 5.2e-105) and ((z <= 1.85e-78) or not (z <= 0.00022))):
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -320000000000.0) || (!(z <= 5.2e-105) && ((z <= 1.85e-78) || !(z <= 0.00022))))
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -320000000000.0) || (~((z <= 5.2e-105)) && ((z <= 1.85e-78) || ~((z <= 0.00022)))))
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -320000000000.0], And[N[Not[LessEqual[z, 5.2e-105]], $MachinePrecision], Or[LessEqual[z, 1.85e-78], N[Not[LessEqual[z, 0.00022]], $MachinePrecision]]]], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e11 or 5.1999999999999997e-105 < z < 1.85000000000000003e-78 or 2.20000000000000008e-4 < z

   1. Initial program 89.2%

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

      1. associate-/l* 93.3%

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

      2. add-sqr-sqrt 42.8%

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

      3. associate-*l* 42.8%

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

   4. Applied egg-rr 42.8%

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

   5. Taylor expanded in y around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-frac-neg 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

      4. associate-*r/ 75.7%

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

   7. Simplified 75.7%

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

   if -3.2e11 < z < 5.1999999999999997e-105 or 1.85000000000000003e-78 < z < 2.20000000000000008e-4

   1. Initial program 80.6%

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

      1. remove-double-neg 80.6%

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

      2. distribute-frac-neg2 80.6%

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

      3. distribute-frac-neg 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{-105}\right) \land \left(z \leq 1.85 \cdot 10^{-78} \lor \neg \left(z \leq 0.00022\right)\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-103} \lor \neg \left(z \leq 2 \cdot 10^{-80}\right) \land z \leq 0.011:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -12500000000000.0)
   (* z (/ x (- y)))
   (if (or (<= z 5e-103) (and (not (<= z 2e-80)) (<= z 0.011)))
     x
     (* x (/ z (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -12500000000000.0) {
		tmp = z * (x / -y);
	} else if ((z <= 5e-103) || (!(z <= 2e-80) && (z <= 0.011))) {
		tmp = x;
	} else {
		tmp = x * (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 <= (-12500000000000.0d0)) then
        tmp = z * (x / -y)
    else if ((z <= 5d-103) .or. (.not. (z <= 2d-80)) .and. (z <= 0.011d0)) then
        tmp = x
    else
        tmp = x * (z / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -12500000000000.0) {
		tmp = z * (x / -y);
	} else if ((z <= 5e-103) || (!(z <= 2e-80) && (z <= 0.011))) {
		tmp = x;
	} else {
		tmp = x * (z / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -12500000000000.0:
		tmp = z * (x / -y)
	elif (z <= 5e-103) or (not (z <= 2e-80) and (z <= 0.011)):
		tmp = x
	else:
		tmp = x * (z / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -12500000000000.0)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif ((z <= 5e-103) || (!(z <= 2e-80) && (z <= 0.011)))
		tmp = x;
	else
		tmp = Float64(x * Float64(z / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -12500000000000.0)
		tmp = z * (x / -y);
	elseif ((z <= 5e-103) || (~((z <= 2e-80)) && (z <= 0.011)))
		tmp = x;
	else
		tmp = x * (z / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -12500000000000.0], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 5e-103], And[N[Not[LessEqual[z, 2e-80]], $MachinePrecision], LessEqual[z, 0.011]]], x, N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e13

   1. Initial program 91.4%

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

      1. remove-double-neg 91.4%

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

      2. distribute-frac-neg2 91.4%

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

      3. distribute-frac-neg 91.4%

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

      4. distribute-rgt-neg-in 91.4%

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

      5. associate-/l* 91.3%

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

      6. distribute-frac-neg 91.3%

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

      7. distribute-frac-neg2 91.3%

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

      8. remove-double-neg 91.3%

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

      9. div-sub 91.4%

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

      10. *-inverses 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around inf 76.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-*l* 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*r/ 73.5%

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

      5. mul-1-neg 73.5%

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

   7. Simplified 73.5%

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

   if -1.25e13 < z < 4.99999999999999966e-103 or 1.99999999999999992e-80 < z < 0.010999999999999999

   1. Initial program 80.6%

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

      1. remove-double-neg 80.6%

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

      2. distribute-frac-neg2 80.6%

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

      3. distribute-frac-neg 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.0%

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

   if 4.99999999999999966e-103 < z < 1.99999999999999992e-80 or 0.010999999999999999 < z

   1. Initial program 87.6%

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

      1. associate-/l* 94.8%

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

      2. add-sqr-sqrt 44.0%

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

      3. associate-*l* 44.0%

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

   4. Applied egg-rr 44.0%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-frac-neg 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

      4. associate-*r/ 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-103} \lor \neg \left(z \leq 2 \cdot 10^{-80}\right) \land z \leq 0.011:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-103} \lor \neg \left(z \leq 1.2 \cdot 10^{-80}\right) \land z \leq 0.0085:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -150000000000.0)
   (* z (/ x (- y)))
   (if (or (<= z 6e-103) (and (not (<= z 1.2e-80)) (<= z 0.0085)))
     x
     (/ x (/ y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -150000000000.0) {
		tmp = z * (x / -y);
	} else if ((z <= 6e-103) || (!(z <= 1.2e-80) && (z <= 0.0085))) {
		tmp = x;
	} else {
		tmp = x / (y / -z);
	}
	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 <= (-150000000000.0d0)) then
        tmp = z * (x / -y)
    else if ((z <= 6d-103) .or. (.not. (z <= 1.2d-80)) .and. (z <= 0.0085d0)) then
        tmp = x
    else
        tmp = x / (y / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -150000000000.0) {
		tmp = z * (x / -y);
	} else if ((z <= 6e-103) || (!(z <= 1.2e-80) && (z <= 0.0085))) {
		tmp = x;
	} else {
		tmp = x / (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -150000000000.0:
		tmp = z * (x / -y)
	elif (z <= 6e-103) or (not (z <= 1.2e-80) and (z <= 0.0085)):
		tmp = x
	else:
		tmp = x / (y / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -150000000000.0)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif ((z <= 6e-103) || (!(z <= 1.2e-80) && (z <= 0.0085)))
		tmp = x;
	else
		tmp = Float64(x / Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -150000000000.0)
		tmp = z * (x / -y);
	elseif ((z <= 6e-103) || (~((z <= 1.2e-80)) && (z <= 0.0085)))
		tmp = x;
	else
		tmp = x / (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -150000000000.0], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6e-103], And[N[Not[LessEqual[z, 1.2e-80]], $MachinePrecision], LessEqual[z, 0.0085]]], x, N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e11

   1. Initial program 91.4%

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

      1. remove-double-neg 91.4%

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

      2. distribute-frac-neg2 91.4%

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

      3. distribute-frac-neg 91.4%

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

      4. distribute-rgt-neg-in 91.4%

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

      5. associate-/l* 91.3%

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

      6. distribute-frac-neg 91.3%

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

      7. distribute-frac-neg2 91.3%

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

      8. remove-double-neg 91.3%

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

      9. div-sub 91.4%

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

      10. *-inverses 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around inf 76.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-*l* 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*r/ 73.5%

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

      5. mul-1-neg 73.5%

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

   7. Simplified 73.5%

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

   if -1.5e11 < z < 6e-103 or 1.2e-80 < z < 0.0085000000000000006

   1. Initial program 80.6%

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

      1. remove-double-neg 80.6%

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

      2. distribute-frac-neg2 80.6%

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

      3. distribute-frac-neg 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.0%

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

   if 6e-103 < z < 1.2e-80 or 0.0085000000000000006 < z

   1. Initial program 87.6%

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

      1. associate-/l* 94.8%

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

      2. add-sqr-sqrt 44.0%

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

      3. associate-*l* 44.0%

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

   4. Applied egg-rr 44.0%

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

      1. associate-*r* 44.0%

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

      2. add-sqr-sqrt 94.8%

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

      3. clear-num 94.7%

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

      4. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-*l/ 78.7%

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

      3. associate-/r/ 80.9%

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

      4. distribute-neg-frac 80.9%

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

   9. Simplified 80.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-103} \lor \neg \left(z \leq 1.2 \cdot 10^{-80}\right) \land z \leq 0.0085:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -340000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-103} \lor \neg \left(z \leq 8.8 \cdot 10^{-79}\right) \land z \leq 0.00145:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -340000000.0)
   (/ (* x (- z)) y)
   (if (or (<= z 2e-103) (and (not (<= z 8.8e-79)) (<= z 0.00145)))
     x
     (/ x (/ y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -340000000.0) {
		tmp = (x * -z) / y;
	} else if ((z <= 2e-103) || (!(z <= 8.8e-79) && (z <= 0.00145))) {
		tmp = x;
	} else {
		tmp = x / (y / -z);
	}
	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 <= (-340000000.0d0)) then
        tmp = (x * -z) / y
    else if ((z <= 2d-103) .or. (.not. (z <= 8.8d-79)) .and. (z <= 0.00145d0)) then
        tmp = x
    else
        tmp = x / (y / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -340000000.0) {
		tmp = (x * -z) / y;
	} else if ((z <= 2e-103) || (!(z <= 8.8e-79) && (z <= 0.00145))) {
		tmp = x;
	} else {
		tmp = x / (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -340000000.0:
		tmp = (x * -z) / y
	elif (z <= 2e-103) or (not (z <= 8.8e-79) and (z <= 0.00145)):
		tmp = x
	else:
		tmp = x / (y / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -340000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif ((z <= 2e-103) || (!(z <= 8.8e-79) && (z <= 0.00145)))
		tmp = x;
	else
		tmp = Float64(x / Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -340000000.0)
		tmp = (x * -z) / y;
	elseif ((z <= 2e-103) || (~((z <= 8.8e-79)) && (z <= 0.00145)))
		tmp = x;
	else
		tmp = x / (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -340000000.0], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 2e-103], And[N[Not[LessEqual[z, 8.8e-79]], $MachinePrecision], LessEqual[z, 0.00145]]], x, N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e8

   1. Initial program 91.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.8%

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

      1. associate-*r* 76.8%

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

      2. *-commutative 76.8%

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

      3. mul-1-neg 76.8%

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

   5. Simplified 76.8%

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

   if -3.4e8 < z < 1.99999999999999992e-103 or 8.7999999999999995e-79 < z < 0.00145

   1. Initial program 80.6%

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

      1. remove-double-neg 80.6%

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

      2. distribute-frac-neg2 80.6%

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

      3. distribute-frac-neg 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.0%

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

   if 1.99999999999999992e-103 < z < 8.7999999999999995e-79 or 0.00145 < z

   1. Initial program 87.6%

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

      1. associate-/l* 94.8%

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

      2. add-sqr-sqrt 44.0%

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

      3. associate-*l* 44.0%

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

   4. Applied egg-rr 44.0%

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

      1. associate-*r* 44.0%

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

      2. add-sqr-sqrt 94.8%

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

      3. clear-num 94.7%

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

      4. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-*l/ 78.7%

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

      3. associate-/r/ 80.9%

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

      4. distribute-neg-frac 80.9%

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

   9. Simplified 80.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -340000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-103} \lor \neg \left(z \leq 8.8 \cdot 10^{-79}\right) \land z \leq 0.00145:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{y}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (/ z y))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (z / y));
}

Python

def code(x, y, z):
	return x * (1.0 - (z / y))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (z / y));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.0%

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

   1. remove-double-neg 85.0%

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

   2. distribute-frac-neg2 85.0%

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

   3. distribute-frac-neg 85.0%

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

   4. distribute-rgt-neg-in 85.0%

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

   5. associate-/l* 96.5%

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

   6. distribute-frac-neg 96.5%

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

   7. distribute-frac-neg2 96.5%

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

   8. remove-double-neg 96.5%

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

   9. div-sub 96.5%

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

   10. *-inverses 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

   \[\leadsto x \cdot \left(1 - \frac{z}{y}\right) \]
6. Add Preprocessing

Alternative 7: 50.4% 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 85.0%

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

   1. remove-double-neg 85.0%

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

   2. distribute-frac-neg2 85.0%

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

   3. distribute-frac-neg 85.0%

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

   4. distribute-rgt-neg-in 85.0%

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

   5. associate-/l* 96.5%

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

   6. distribute-frac-neg 96.5%

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

   7. distribute-frac-neg2 96.5%

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

   8. remove-double-neg 96.5%

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

   9. div-sub 96.5%

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

   10. *-inverses 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in z around 0 49.6%

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

6. Final simplification 49.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.2% accurate, 0.4× 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 2024050 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (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))