Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A

Percentage Accurate: 99.8% → 99.8%

Time: 8.5s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (sin y) (- z) (* x (cos y))))

C

double code(double x, double y, double z) {
	return fma(sin(y), -z, (x * cos(y)));
}

Julia

function code(x, y, z)
	return fma(sin(y), Float64(-z), Float64(x * cos(y)))
end

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]
2. Step-by-step derivation

   1. sub-neg 99.8%

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

   2. +-commutative 99.8%

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

   3. *-commutative 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right) \]

Alternative 2: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, x, \sin y \cdot \left(-z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) x (* (sin y) (- z))))

C

double code(double x, double y, double z) {
	return fma(cos(y), x, (sin(y) * -z));
}

Julia

function code(x, y, z)
	return fma(cos(y), x, Float64(sin(y) * Float64(-z)))
end

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]

2. Taylor expanded in x around 0 99.8%

   \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right) + \cos y \cdot x} \]
3. Step-by-step derivation

   1. mul-1-neg 99.8%

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

   2. distribute-rgt-neg-out 99.8%

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

   3. +-commutative 99.8%

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

   4. fma-udef 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, x, z \cdot \left(-\sin y\right)\right)} \]

   5. distribute-rgt-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(\cos y, x, \color{blue}{-z \cdot \sin y}\right) \]

   6. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(\cos y, x, -\color{blue}{\sin y \cdot z}\right) \]

   7. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(\cos y, x, \color{blue}{\sin y \cdot \left(-z\right)}\right) \]

4. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, x, \sin y \cdot \left(-z\right)\right)} \]

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(\cos y, x, \sin y \cdot \left(-z\right)\right) \]

Alternative 3: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+140} \lor \neg \left(x \leq 2.2 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+140) (not (<= x 2.2e+112)))
   (* x (cos y))
   (fma (sin y) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+140) || !(x <= 2.2e+112)) {
		tmp = x * cos(y);
	} else {
		tmp = fma(sin(y), -z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+140) || !(x <= 2.2e+112))
		tmp = Float64(x * cos(y));
	else
		tmp = fma(sin(y), Float64(-z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+140], N[Not[LessEqual[x, 2.2e+112]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e140 or 2.1999999999999999e112 < x

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Step-by-step derivation

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   4. Taylor expanded in z around 0 90.8%

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

   if -5.5e140 < x < 2.1999999999999999e112

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   4. Taylor expanded in y around 0 88.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+140} \lor \neg \left(x \leq 2.2 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* (sin y) z)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]

2. Final simplification 99.8%

   \[\leadsto x \cdot \cos y - \sin y \cdot z \]

Alternative 5: 85.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+140} \lor \neg \left(x \leq 8.5 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+140) (not (<= x 8.5e+113)))
   (* x (cos y))
   (- x (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+140) || !(x <= 8.5e+113)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (sin(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 ((x <= (-5.5d+140)) .or. (.not. (x <= 8.5d+113))) then
        tmp = x * cos(y)
    else
        tmp = x - (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+140) || !(x <= 8.5e+113)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+140) or not (x <= 8.5e+113):
		tmp = x * math.cos(y)
	else:
		tmp = x - (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+140) || !(x <= 8.5e+113))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e+140) || ~((x <= 8.5e+113)))
		tmp = x * cos(y);
	else
		tmp = x - (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+140], N[Not[LessEqual[x, 8.5e+113]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e140 or 8.5000000000000001e113 < x

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Step-by-step derivation

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   4. Taylor expanded in z around 0 90.8%

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

   if -5.5e140 < x < 8.5000000000000001e113

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 87.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+140} \lor \neg \left(x \leq 8.5 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \]

Alternative 6: 74.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -65:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 0.000235:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -65.0)
   (* x (cos y))
   (if (<= y 0.000235) (- x (* y z)) (* (sin y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -65.0) {
		tmp = x * cos(y);
	} else if (y <= 0.000235) {
		tmp = x - (y * z);
	} else {
		tmp = sin(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 <= (-65.0d0)) then
        tmp = x * cos(y)
    else if (y <= 0.000235d0) then
        tmp = x - (y * z)
    else
        tmp = sin(y) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -65.0) {
		tmp = x * Math.cos(y);
	} else if (y <= 0.000235) {
		tmp = x - (y * z);
	} else {
		tmp = Math.sin(y) * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -65.0:
		tmp = x * math.cos(y)
	elif y <= 0.000235:
		tmp = x - (y * z)
	else:
		tmp = math.sin(y) * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -65.0)
		tmp = Float64(x * cos(y));
	elseif (y <= 0.000235)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = Float64(sin(y) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -65.0)
		tmp = x * cos(y);
	elseif (y <= 0.000235)
		tmp = x - (y * z);
	else
		tmp = sin(y) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -65.0], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.000235], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -65

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   4. Taylor expanded in z around 0 57.4%

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

   if -65 < y < 2.34999999999999993e-4

   1. Initial program 99.9%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 97.4%

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

      1. +-commutative 97.4%

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

      2. mul-1-neg 97.4%

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

      3. unsub-neg 97.4%

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

   4. Simplified 97.4%

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

   if 2.34999999999999993e-4 < y

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. *-commutative 63.3%

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

      3. distribute-rgt-neg-in 63.3%

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

   4. Simplified 63.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 0.000235:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 7: 74.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -65 \lor \neg \left(y \leq 1250000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -65.0) (not (<= y 1250000.0))) (* x (cos y)) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -65.0) || !(y <= 1250000.0)) {
		tmp = x * cos(y);
	} 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 ((y <= (-65.0d0)) .or. (.not. (y <= 1250000.0d0))) then
        tmp = x * cos(y)
    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 ((y <= -65.0) || !(y <= 1250000.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -65.0) or not (y <= 1250000.0):
		tmp = x * math.cos(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -65.0) || !(y <= 1250000.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -65.0) || ~((y <= 1250000.0)))
		tmp = x * cos(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -65.0], N[Not[LessEqual[y, 1250000.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -65 or 1.25e6 < y

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

   4. Taylor expanded in z around 0 47.7%

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

   if -65 < y < 1.25e6

   1. Initial program 99.9%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. mul-1-neg 95.6%

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

      3. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65 \lor \neg \left(y \leq 1250000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 8: 51.5% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]

2. Taylor expanded in y around 0 50.9%

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

   1. +-commutative 50.9%

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

   2. mul-1-neg 50.9%

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

   3. unsub-neg 50.9%

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

4. Simplified 50.9%

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

5. Final simplification 50.9%

   \[\leadsto x - y \cdot z \]

Alternative 9: 38.5% accurate, 207.0× 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 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]
2. Step-by-step derivation

   1. sub-neg 99.8%

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

   2. +-commutative 99.8%

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

   3. *-commutative 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)} \]

4. Taylor expanded in y around 0 32.8%

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

5. Final simplification 32.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))