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

Percentage Accurate: 99.8% → 99.8%

Time: 9.1s

Alternatives: 7

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, 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]

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 86.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-29} \lor \neg \left(z \leq 1.05 \cdot 10^{-54}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.25e-29) (not (<= z 1.05e-54)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.25e-29) || !(z <= 1.05e-54)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x * cos(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 <= (-2.25d-29)) .or. (.not. (z <= 1.05d-54))) then
        tmp = x - (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.25e-29) || !(z <= 1.05e-54)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.25e-29) or not (z <= 1.05e-54):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.25e-29) || !(z <= 1.05e-54))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.25e-29) || ~((z <= 1.05e-54)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.25e-29], N[Not[LessEqual[z, 1.05e-54]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e-29 or 1.05e-54 < z

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.5%

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

   if -2.2499999999999999e-29 < z < 1.05e-54

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-29} \lor \neg \left(z \leq 1.05 \cdot 10^{-54}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-115} \lor \neg \left(x \leq 2.25 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e-115) (not (<= x 2.25e-104)))
   (* x (cos y))
   (* z (- (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e-115) || !(x <= 2.25e-104)) {
		tmp = x * cos(y);
	} else {
		tmp = z * -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 ((x <= (-3.1d-115)) .or. (.not. (x <= 2.25d-104))) then
        tmp = x * cos(y)
    else
        tmp = z * -sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e-115) || !(x <= 2.25e-104)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = z * -Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.1e-115) or not (x <= 2.25e-104):
		tmp = x * math.cos(y)
	else:
		tmp = z * -math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.1e-115) || !(x <= 2.25e-104))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(z * Float64(-sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.1e-115) || ~((x <= 2.25e-104)))
		tmp = x * cos(y);
	else
		tmp = z * -sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.1e-115], N[Not[LessEqual[x, 2.25e-104]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.10000000000000007e-115 or 2.2499999999999999e-104 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.9%

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

   if -3.10000000000000007e-115 < x < 2.2499999999999999e-104

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. neg-mul-1 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-115} \lor \neg \left(x \leq 2.25 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.33 \lor \neg \left(y \leq 0.185\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.33) (not (<= y 0.185)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* y z)))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.33) || !(y <= 0.185)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - 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 <= (-0.33d0)) .or. (.not. (y <= 0.185d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (y * z)))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.33) || !(y <= 0.185)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.33) or not (y <= 0.185):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.33) || !(y <= 0.185))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.33) || ~((y <= 0.185)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.33], N[Not[LessEqual[y, 0.185]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.330000000000000016 or 0.185 < y

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 57.3%

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

   if -0.330000000000000016 < y < 0.185

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.7%

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(-0.5 \cdot x + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.33 \lor \neg \left(y \leq 0.185\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-93} \lor \neg \left(x \leq 1.25 \cdot 10^{-149}\right):\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.6e-93) (not (<= x 1.25e-149))) (* z (/ x z)) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-93) || !(x <= 1.25e-149)) {
		tmp = z * (x / z);
	} else {
		tmp = 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 ((x <= (-3.6d-93)) .or. (.not. (x <= 1.25d-149))) then
        tmp = z * (x / z)
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-93) || !(x <= 1.25e-149)) {
		tmp = z * (x / z);
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.6e-93) or not (x <= 1.25e-149):
		tmp = z * (x / z)
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.6e-93) || !(x <= 1.25e-149))
		tmp = Float64(z * Float64(x / z));
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.6e-93) || ~((x <= 1.25e-149)))
		tmp = z * (x / z);
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.6e-93], N[Not[LessEqual[x, 1.25e-149]], $MachinePrecision]], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6000000000000002e-93 or 1.24999999999999992e-149 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

   8. Simplified 44.1%

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

   9. Taylor expanded in x around inf 36.8%

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

   if -3.6000000000000002e-93 < x < 1.24999999999999992e-149

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in z around inf 36.2%

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

       1. mul-1-neg 36.2%

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

       2. distribute-lft-neg-out 36.2%

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

       3. *-commutative 36.2%

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

   11. Simplified 36.2%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-93} \lor \neg \left(x \leq 1.25 \cdot 10^{-149}\right):\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 50.7%

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

   1. mul-1-neg 50.7%

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

   2. unsub-neg 50.7%

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

5. Simplified 50.7%

   \[\leadsto \color{blue}{x - y \cdot z} \]
6. Add Preprocessing

Alternative 7: 16.6% accurate, 51.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in z around inf 87.6%

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

   1. associate-/l* 87.5%

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

5. Simplified 87.5%

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

6. Taylor expanded in y around 0 44.7%

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

   1. +-commutative 44.7%

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

   2. mul-1-neg 44.7%

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

   3. unsub-neg 44.7%

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

8. Simplified 44.7%

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

9. Taylor expanded in z around inf 18.2%

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

    1. mul-1-neg 18.2%

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

    2. distribute-lft-neg-out 18.2%

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

    3. *-commutative 18.2%

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

11. Simplified 18.2%

    \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(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))))