Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.2% → 99.6%

Time: 9.9s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (sin(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 * (sin(y) / y)) / z
end function

Java

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

Python

def code(x, y, z):
	return (x * (math.sin(y) / y)) / z

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (sin(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 * (sin(y) / y)) / z
end function

Java

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

Python

def code(x, y, z):
	return (x * (math.sin(y) / y)) / z

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+78} \lor \neg \left(z \leq 0.012\right):\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (or (<= z -5e+78) (not (<= z 0.012))) (* t_0 (/ x z)) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if ((z <= -5e+78) || !(z <= 0.012)) {
		tmp = t_0 * (x / z);
	} else {
		tmp = x / (z / 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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if ((z <= (-5d+78)) .or. (.not. (z <= 0.012d0))) then
        tmp = t_0 * (x / z)
    else
        tmp = x / (z / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if ((z <= -5e+78) || !(z <= 0.012)) {
		tmp = t_0 * (x / z);
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if (z <= -5e+78) or not (z <= 0.012):
		tmp = t_0 * (x / z)
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if ((z <= -5e+78) || !(z <= 0.012))
		tmp = Float64(t_0 * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if ((z <= -5e+78) || ~((z <= 0.012)))
		tmp = t_0 * (x / z);
	else
		tmp = x / (z / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[z, -5e+78], N[Not[LessEqual[z, 0.012]], $MachinePrecision]], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999984e78 or 0.012 < z

   1. Initial program 99.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   if -4.99999999999999984e78 < z < 0.012

   1. Initial program 91.9%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+78} \lor \neg \left(z \leq 0.012\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+78} \lor \neg \left(z \leq 0.24\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+78) (not (<= z 0.24)))
   (* (/ (sin y) y) (/ x z))
   (/ x (* z (/ y (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+78) || !(z <= 0.24)) {
		tmp = (sin(y) / y) * (x / z);
	} else {
		tmp = x / (z * (y / sin(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 <= (-6d+78)) .or. (.not. (z <= 0.24d0))) then
        tmp = (sin(y) / y) * (x / z)
    else
        tmp = x / (z * (y / sin(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+78) || !(z <= 0.24)) {
		tmp = (Math.sin(y) / y) * (x / z);
	} else {
		tmp = x / (z * (y / Math.sin(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+78) or not (z <= 0.24):
		tmp = (math.sin(y) / y) * (x / z)
	else:
		tmp = x / (z * (y / math.sin(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+78) || !(z <= 0.24))
		tmp = Float64(Float64(sin(y) / y) * Float64(x / z));
	else
		tmp = Float64(x / Float64(z * Float64(y / sin(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e+78) || ~((z <= 0.24)))
		tmp = (sin(y) / y) * (x / z);
	else
		tmp = x / (z * (y / sin(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+78], N[Not[LessEqual[z, 0.24]], $MachinePrecision]], N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999964e78 or 0.23999999999999999 < z

   1. Initial program 99.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   if -5.99999999999999964e78 < z < 0.23999999999999999

   1. Initial program 91.9%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+78} \lor \neg \left(z \leq 0.24\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array} \]

Alternative 3: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.4e-8) (/ x z) (* (sin y) (/ x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-8) {
		tmp = x / z;
	} else {
		tmp = sin(y) * (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 (y <= 2.4d-8) then
        tmp = x / z
    else
        tmp = sin(y) * (x / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-8) {
		tmp = x / z;
	} else {
		tmp = Math.sin(y) * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.4e-8:
		tmp = x / z
	else:
		tmp = math.sin(y) * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.4e-8)
		tmp = Float64(x / z);
	else
		tmp = Float64(sin(y) * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.4e-8)
		tmp = x / z;
	else
		tmp = sin(y) * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.4e-8], N[(x / z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.39999999999999998e-8

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.39999999999999998e-8 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

      2. associate-/r/ 90.2%

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

      3. associate-/l/ 90.9%

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

      4. associate-/r/ 91.0%

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

      5. associate-/r* 90.3%

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

   3. Simplified 90.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 4: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (<= x -2.9e+64) (/ (* x t_0) z) (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (x <= -2.9e+64) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (x <= (-2.9d+64)) then
        tmp = (x * t_0) / z
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if (x <= -2.9e+64) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if x <= -2.9e+64:
		tmp = (x * t_0) / z
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (x <= -2.9e+64)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (x <= -2.9e+64)
		tmp = (x * t_0) / z;
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -2.9e+64], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999993e64

   1. Initial program 99.6%

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

   if -2.89999999999999993e64 < x

   1. Initial program 94.0%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. *-commutative 94.0%

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

      2. associate-*r/ 97.9%

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

   3. Simplified 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (sin(y) / y) * (x / 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 = (sin(y) / y) * (x / z)
end function

Java

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

Python

def code(x, y, z):
	return (math.sin(y) / y) * (x / z)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
2. Step-by-step derivation

   1. *-commutative 95.3%

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

   2. associate-*r/ 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

   \[\leadsto \frac{\sin y}{y} \cdot \frac{x}{z} \]

Alternative 6: 62.8% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5) (/ x z) (* 6.0 (/ (/ x y) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / y) / (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 (y <= 2.5d0) then
        tmp = x / z
    else
        tmp = 6.0d0 * ((x / y) / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / y) / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5:
		tmp = x / z
	else:
		tmp = 6.0 * ((x / y) / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z);
	else
		tmp = Float64(6.0 * Float64(Float64(x / y) / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z;
	else
		tmp = 6.0 * ((x / y) / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5], N[(x / z), $MachinePrecision], N[(6.0 * N[(N[(x / y), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.5 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left({y}^{2} \cdot z\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}} \]

      2. unpow2 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]

   6. Simplified 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left(z \cdot \left(y \cdot y\right)\right)}} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   8. Step-by-step derivation

      1. unpow2 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. associate-*r* 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot \left(y \cdot z\right)}} \]

      3. associate-/r* 32.4%

         \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{y}}{y \cdot z}} \]

      4. *-commutative 32.4%

         \[\leadsto 6 \cdot \frac{\frac{x}{y}}{\color{blue}{z \cdot y}} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{\frac{x}{y}}{z \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y \cdot z}\\ \end{array} \]

Alternative 7: 62.8% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{\frac{x}{y}}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5) (/ x z) (* 6.0 (/ (/ (/ x y) y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = 6.0 * (((x / y) / 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 (y <= 2.5d0) then
        tmp = x / z
    else
        tmp = 6.0d0 * (((x / y) / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = 6.0 * (((x / y) / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5:
		tmp = x / z
	else:
		tmp = 6.0 * (((x / y) / y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z);
	else
		tmp = Float64(6.0 * Float64(Float64(Float64(x / y) / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z;
	else
		tmp = 6.0 * (((x / y) / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5], N[(x / z), $MachinePrecision], N[(6.0 * N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.5 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left({y}^{2} \cdot z\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}} \]

      2. unpow2 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]

   6. Simplified 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left(z \cdot \left(y \cdot y\right)\right)}} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   8. Step-by-step derivation

      1. unpow2 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. associate-*r* 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot \left(y \cdot z\right)}} \]

      3. associate-*r/ 32.4%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{y \cdot \left(y \cdot z\right)}} \]

      4. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(y \cdot z\right) \cdot y}} \]

      5. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right)} \cdot y} \]

      6. associate-*r* 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{6 \cdot x}{z \cdot \left(y \cdot y\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 32.4%

          \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right) \cdot y}} \]

       2. times-frac 32.4%

          \[\leadsto \color{blue}{\frac{6}{z \cdot y} \cdot \frac{x}{y}} \]

       3. *-commutative 32.4%

          \[\leadsto \frac{6}{\color{blue}{y \cdot z}} \cdot \frac{x}{y} \]

   11. Applied egg-rr 32.4%

       \[\leadsto \color{blue}{\frac{6}{y \cdot z} \cdot \frac{x}{y}} \]

   12. Taylor expanded in y around 0 32.4%

       \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   13. Step-by-step derivation

       1. associate-/r* 32.5%

          \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{{y}^{2}}}{z}} \]

       2. unpow2 32.5%

          \[\leadsto 6 \cdot \frac{\frac{x}{\color{blue}{y \cdot y}}}{z} \]

       3. associate-/r* 32.4%

          \[\leadsto 6 \cdot \frac{\color{blue}{\frac{\frac{x}{y}}{y}}}{z} \]

   14. Simplified 32.4%

       \[\leadsto \color{blue}{6 \cdot \frac{\frac{\frac{x}{y}}{y}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{\frac{x}{y}}{y}}{z}\\ \end{array} \]

Alternative 8: 62.9% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{6}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5) (/ x z) (* (/ x z) (/ 6.0 (* y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (x / z) * (6.0 / (y * 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 (y <= 2.5d0) then
        tmp = x / z
    else
        tmp = (x / z) * (6.0d0 / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (x / z) * (6.0 / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5:
		tmp = x / z
	else:
		tmp = (x / z) * (6.0 / (y * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / z) * Float64(6.0 / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z;
	else
		tmp = (x / z) * (6.0 / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5], N[(x / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(6.0 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.5 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left({y}^{2} \cdot z\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}} \]

      2. unpow2 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]

   6. Simplified 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left(z \cdot \left(y \cdot y\right)\right)}} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   8. Step-by-step derivation

      1. unpow2 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. associate-*r* 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot \left(y \cdot z\right)}} \]

      3. associate-*r/ 32.4%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{y \cdot \left(y \cdot z\right)}} \]

      4. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(y \cdot z\right) \cdot y}} \]

      5. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right)} \cdot y} \]

      6. associate-*r* 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{6 \cdot x}{z \cdot \left(y \cdot y\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 32.4%

          \[\leadsto \frac{\color{blue}{x \cdot 6}}{z \cdot \left(y \cdot y\right)} \]

       2. times-frac 33.7%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{6}{y \cdot y}} \]

   11. Applied egg-rr 33.7%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{6}{y \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{6}{y \cdot y}\\ \end{array} \]

Alternative 9: 63.0% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5) (/ x z) (* (/ x (* y z)) (/ 6.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (x / (y * z)) * (6.0 / 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 (y <= 2.5d0) then
        tmp = x / z
    else
        tmp = (x / (y * z)) * (6.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (x / (y * z)) * (6.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5:
		tmp = x / z
	else:
		tmp = (x / (y * z)) * (6.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / Float64(y * z)) * Float64(6.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z;
	else
		tmp = (x / (y * z)) * (6.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5], N[(x / z), $MachinePrecision], N[(N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(6.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.5 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left({y}^{2} \cdot z\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}} \]

      2. unpow2 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]

   6. Simplified 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left(z \cdot \left(y \cdot y\right)\right)}} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   8. Step-by-step derivation

      1. unpow2 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. associate-*r* 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot \left(y \cdot z\right)}} \]

      3. associate-*r/ 32.4%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{y \cdot \left(y \cdot z\right)}} \]

      4. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(y \cdot z\right) \cdot y}} \]

      5. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right)} \cdot y} \]

      6. associate-*r* 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{6 \cdot x}{z \cdot \left(y \cdot y\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 32.4%

          \[\leadsto \frac{\color{blue}{x \cdot 6}}{z \cdot \left(y \cdot y\right)} \]

       2. associate-*r* 32.4%

          \[\leadsto \frac{x \cdot 6}{\color{blue}{\left(z \cdot y\right) \cdot y}} \]

       3. times-frac 33.8%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y} \cdot \frac{6}{y}} \]

       4. *-commutative 33.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot z}} \cdot \frac{6}{y} \]

   11. Applied egg-rr 33.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z} \cdot \frac{6}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \end{array} \]

Alternative 10: 63.0% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{6}{y}}{z \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5) (/ x z) (/ (/ 6.0 y) (* z (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (6.0 / y) / (z * (y / 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 (y <= 2.5d0) then
        tmp = x / z
    else
        tmp = (6.0d0 / y) / (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z;
	} else {
		tmp = (6.0 / y) / (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5:
		tmp = x / z
	else:
		tmp = (6.0 / y) / (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(6.0 / y) / Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z;
	else
		tmp = (6.0 / y) / (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5], N[(x / z), $MachinePrecision], N[(N[(6.0 / y), $MachinePrecision] / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 96.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

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

      2. associate-/r/ 85.4%

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

      3. associate-/l/ 79.5%

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

      4. associate-/r/ 81.3%

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

      5. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.7%

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

   if 2.5 < y

   1. Initial program 90.8%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left({y}^{2} \cdot z\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}} \]

      2. unpow2 32.4%

         \[\leadsto \frac{x}{z + 0.16666666666666666 \cdot \left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]

   6. Simplified 32.4%

      \[\leadsto \frac{x}{\color{blue}{z + 0.16666666666666666 \cdot \left(z \cdot \left(y \cdot y\right)\right)}} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   8. Step-by-step derivation

      1. unpow2 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. associate-*r* 32.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot \left(y \cdot z\right)}} \]

      3. associate-*r/ 32.4%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{y \cdot \left(y \cdot z\right)}} \]

      4. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(y \cdot z\right) \cdot y}} \]

      5. *-commutative 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right)} \cdot y} \]

      6. associate-*r* 32.4%

         \[\leadsto \frac{6 \cdot x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{6 \cdot x}{z \cdot \left(y \cdot y\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 32.4%

          \[\leadsto \frac{6 \cdot x}{\color{blue}{\left(z \cdot y\right) \cdot y}} \]

       2. times-frac 32.4%

          \[\leadsto \color{blue}{\frac{6}{z \cdot y} \cdot \frac{x}{y}} \]

       3. *-commutative 32.4%

          \[\leadsto \frac{6}{\color{blue}{y \cdot z}} \cdot \frac{x}{y} \]

   11. Applied egg-rr 32.4%

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

       1. *-commutative 32.4%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{6}{y \cdot z}} \]

       2. clear-num 32.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \cdot \frac{6}{y \cdot z} \]

       3. associate-/r* 32.4%

          \[\leadsto \frac{1}{\frac{y}{x}} \cdot \color{blue}{\frac{\frac{6}{y}}{z}} \]

       4. frac-times 33.8%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{6}{y}}{\frac{y}{x} \cdot z}} \]

       5. *-un-lft-identity 33.8%

          \[\leadsto \frac{\color{blue}{\frac{6}{y}}}{\frac{y}{x} \cdot z} \]

   13. Applied egg-rr 33.8%

       \[\leadsto \color{blue}{\frac{\frac{6}{y}}{\frac{y}{x} \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{6}{y}}{z \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 11: 66.9% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{z \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/ x (* z (+ 1.0 (* (* y y) 0.16666666666666666)))))

C

double code(double x, double y, double z) {
	return x / (z * (1.0 + ((y * y) * 0.16666666666666666)));
}

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 / (z * (1.0d0 + ((y * y) * 0.16666666666666666d0)))
end function

Java

public static double code(double x, double y, double z) {
	return x / (z * (1.0 + ((y * y) * 0.16666666666666666)));
}

Python

def code(x, y, z):
	return x / (z * (1.0 + ((y * y) * 0.16666666666666666)))

Julia

function code(x, y, z)
	return Float64(x / Float64(z * Float64(1.0 + Float64(Float64(y * y) * 0.16666666666666666))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x / (z * (1.0 + ((y * y) * 0.16666666666666666)));
end

Wolfram

code[x_, y_, z_] := N[(x / N[(z * N[(1.0 + N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.3%

   \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
2. Step-by-step derivation

   1. associate-/l* 94.9%

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

3. Simplified 94.9%

   \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}} \]
4. Step-by-step derivation

   1. clear-num 94.8%

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

   2. associate-/r/ 94.8%

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

   3. clear-num 94.9%

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

5. Applied egg-rr 94.9%

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

6. Taylor expanded in y around 0 66.0%

   \[\leadsto \frac{x}{\color{blue}{\left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \cdot z} \]
7. Step-by-step derivation

   1. *-commutative 66.0%

      \[\leadsto \frac{x}{\left(1 + \color{blue}{{y}^{2} \cdot 0.16666666666666666}\right) \cdot z} \]

   2. unpow2 66.0%

      \[\leadsto \frac{x}{\left(1 + \color{blue}{\left(y \cdot y\right)} \cdot 0.16666666666666666\right) \cdot z} \]

8. Simplified 66.0%

   \[\leadsto \frac{x}{\color{blue}{\left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)} \cdot z} \]

9. Final simplification 66.0%

   \[\leadsto \frac{x}{z \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)} \]

Alternative 12: 59.0% accurate, 35.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x / 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 / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
2. Step-by-step derivation

   1. associate-/l* 94.9%

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

   2. associate-/r/ 86.6%

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

   3. associate-/l/ 82.4%

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

   4. associate-/r/ 83.7%

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

   5. associate-/r* 84.3%

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

3. Simplified 84.3%

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

4. Taylor expanded in y around 0 60.5%

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

5. Final simplification 60.5%

   \[\leadsto \frac{x}{z} \]

Developer target: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\sin y}\\ t_1 := \frac{x \cdot \frac{1}{t_0}}{z}\\ \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (sin y))) (t_1 (/ (* x (/ 1.0 t_0)) z)))
   (if (< z -4.2173720203427147e-29)
     t_1
     (if (< z 4.446702369113811e+64) (/ x (* z t_0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y / sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * 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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / sin(y)
    t_1 = (x * (1.0d0 / t_0)) / z
    if (z < (-4.2173720203427147d-29)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x / (z * t_0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / Math.sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / math.sin(y)
	t_1 = (x * (1.0 / t_0)) / z
	tmp = 0
	if z < -4.2173720203427147e-29:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x / (z * t_0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / sin(y))
	t_1 = Float64(Float64(x * Float64(1.0 / t_0)) / z)
	tmp = 0.0
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x / Float64(z * t_0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / sin(y);
	t_1 = (x * (1.0 / t_0)) / z;
	tmp = 0.0;
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x / (z * t_0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[Less[z, -4.2173720203427147e-29], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x / N[(z * t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))