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

Percentage Accurate: 99.8% → 99.8%

Time: 7.0s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 74.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -3850000 \lor \neg \left(y \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= y -5.2e+103)
     t_0
     (if (<= y -6e+85)
       (* z (cos y))
       (if (or (<= y -3850000.0) (not (<= y 1.4e-18)))
         t_0
         (+
          z
          (*
           y
           (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (y <= -5.2e+103) {
		tmp = t_0;
	} else if (y <= -6e+85) {
		tmp = z * cos(y);
	} else if ((y <= -3850000.0) || !(y <= 1.4e-18)) {
		tmp = t_0;
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * sin(y)
    if (y <= (-5.2d+103)) then
        tmp = t_0
    else if (y <= (-6d+85)) then
        tmp = z * cos(y)
    else if ((y <= (-3850000.0d0)) .or. (.not. (y <= 1.4d-18))) then
        tmp = t_0
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.sin(y);
	double tmp;
	if (y <= -5.2e+103) {
		tmp = t_0;
	} else if (y <= -6e+85) {
		tmp = z * Math.cos(y);
	} else if ((y <= -3850000.0) || !(y <= 1.4e-18)) {
		tmp = t_0;
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if y <= -5.2e+103:
		tmp = t_0
	elif y <= -6e+85:
		tmp = z * math.cos(y)
	elif (y <= -3850000.0) or not (y <= 1.4e-18):
		tmp = t_0
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -5.2e+103)
		tmp = t_0;
	elseif (y <= -6e+85)
		tmp = Float64(z * cos(y));
	elseif ((y <= -3850000.0) || !(y <= 1.4e-18))
		tmp = t_0;
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (y <= -5.2e+103)
		tmp = t_0;
	elseif (y <= -6e+85)
		tmp = z * cos(y);
	elseif ((y <= -3850000.0) || ~((y <= 1.4e-18)))
		tmp = t_0;
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+103], t$95$0, If[LessEqual[y, -6e+85], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3850000.0], N[Not[LessEqual[y, 1.4e-18]], $MachinePrecision]], t$95$0, N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000003e103 or -6.0000000000000001e85 < y < -3.85e6 or 1.40000000000000006e-18 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.3%

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

   if -5.2000000000000003e103 < y < -6.0000000000000001e85

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 88.5%

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

   if -3.85e6 < y < 1.40000000000000006e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -3850000 \lor \neg \left(y \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-119} \lor \neg \left(x \leq 1.25 \cdot 10^{-207}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.4e-119) (not (<= x 1.25e-207)))
   (+ (* x (sin y)) z)
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.4e-119) || !(x <= 1.25e-207)) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = z * 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 ((x <= (-9.4d-119)) .or. (.not. (x <= 1.25d-207))) then
        tmp = (x * sin(y)) + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.4e-119) || !(x <= 1.25e-207)) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.4e-119) or not (x <= 1.25e-207):
		tmp = (x * math.sin(y)) + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.4e-119) || !(x <= 1.25e-207))
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.4e-119) || ~((x <= 1.25e-207)))
		tmp = (x * sin(y)) + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.4e-119], N[Not[LessEqual[x, 1.25e-207]], $MachinePrecision]], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.40000000000000004e-119 or 1.25000000000000004e-207 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.9%

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

   if -9.40000000000000004e-119 < x < 1.25000000000000004e-207

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-119} \lor \neg \left(x \leq 1.25 \cdot 10^{-207}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3850000 \lor \neg \left(y \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3850000.0) (not (<= y 1.4e-18)))
   (* x (sin y))
   (+ z (* y (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3850000.0) || !(y <= 1.4e-18)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3850000.0d0)) .or. (.not. (y <= 1.4d-18))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3850000.0) || !(y <= 1.4e-18)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3850000.0) or not (y <= 1.4e-18):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3850000.0) || !(y <= 1.4e-18))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3850000.0) || ~((y <= 1.4e-18)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3850000.0], N[Not[LessEqual[y, 1.4e-18]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.85e6 or 1.40000000000000006e-18 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 61.9%

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

   if -3.85e6 < y < 1.40000000000000006e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3850000 \lor \neg \left(y \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+35} \lor \neg \left(x \leq 7.1 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+35) (not (<= x 7.1e-6))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+35) || !(x <= 7.1e-6)) {
		tmp = x * y;
	} else {
		tmp = 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 <= (-5.8d+35)) .or. (.not. (x <= 7.1d-6))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+35) || !(x <= 7.1e-6)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+35) or not (x <= 7.1e-6):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+35) || !(x <= 7.1e-6))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e+35) || ~((x <= 7.1e-6)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+35], N[Not[LessEqual[x, 7.1e-6]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999989e35 or 7.0999999999999998e-6 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 46.9%

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

      1. *-commutative 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in z around 0 32.3%

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

      1. *-commutative 32.3%

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

   8. Simplified 32.3%

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

   if -5.79999999999999989e35 < x < 7.0999999999999998e-6

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 78.2%

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

   4. Taylor expanded in y around 0 53.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+35} \lor \neg \left(x \leq 7.1 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 51.5%

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

   1. *-commutative 51.5%

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

5. Simplified 51.5%

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

6. Final simplification 51.5%

   \[\leadsto z + x \cdot y \]
7. Add Preprocessing

Alternative 7: 39.2% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 50.8%

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

4. Taylor expanded in y around 0 35.0%

   \[\leadsto \color{blue}{z} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))