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

Percentage Accurate: 99.8% → 99.8%

Time: 10.1s

Alternatives: 8

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-define 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 86.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-12} \lor \neg \left(x \leq 2.25 \cdot 10^{-63}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.6e-12) (not (<= x 2.25e-63)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-12) || !(x <= 2.25e-63)) {
		tmp = z + (x * sin(y));
	} 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 <= (-3.6d-12)) .or. (.not. (x <= 2.25d-63))) then
        tmp = z + (x * sin(y))
    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 <= -3.6e-12) || !(x <= 2.25e-63)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.6e-12) or not (x <= 2.25e-63):
		tmp = z + (x * math.sin(y))
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.6e-12) || !(x <= 2.25e-63))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.6e-12) || ~((x <= 2.25e-63)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.6e-12], N[Not[LessEqual[x, 2.25e-63]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e-12 or 2.25e-63 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 87.5%

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

   if -3.6e-12 < x < 2.25e-63

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 90.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-12} \lor \neg \left(x \leq 2.25 \cdot 10^{-63}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.008 \lor \neg \left(y \leq 0.0062\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(-0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.008) (not (<= y 0.0062)))
   (* z (cos y))
   (+ z (* y (+ x (* y (* -0.16666666666666666 (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.008) || !(y <= 0.0062)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (y * (x + (y * (-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 <= (-0.008d0)) .or. (.not. (y <= 0.0062d0))) then
        tmp = z * cos(y)
    else
        tmp = z + (y * (x + (y * ((-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 <= -0.008) || !(y <= 0.0062)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (y * (x + (y * (-0.16666666666666666 * (x * y)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.008) or not (y <= 0.0062):
		tmp = z * math.cos(y)
	else:
		tmp = z + (y * (x + (y * (-0.16666666666666666 * (x * y)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.008) || !(y <= 0.0062))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(-0.16666666666666666 * Float64(x * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.008) || ~((y <= 0.0062)))
		tmp = z * cos(y);
	else
		tmp = z + (y * (x + (y * (-0.16666666666666666 * (x * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.008], N[Not[LessEqual[y, 0.0062]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0080000000000000002 or 0.00619999999999999978 < y

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 59.1%

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

   if -0.0080000000000000002 < y < 0.00619999999999999978

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.008 \lor \neg \left(y \leq 0.0062\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(-0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-8} \lor \neg \left(y \leq 3.3\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + z \cdot \left(y \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.9e-8) (not (<= y 3.3)))
   (* x (sin y))
   (+ z (* y (+ x (* z (* y -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e-8) || !(y <= 3.3)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (z * (y * -0.5))));
	}
	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 <= (-3.9d-8)) .or. (.not. (y <= 3.3d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (z * (y * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e-8) || !(y <= 3.3)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (z * (y * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.9e-8) or not (y <= 3.3):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (z * (y * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.9e-8) || !(y <= 3.3))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(z * Float64(y * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.9e-8) || ~((y <= 3.3)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (z * (y * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.9e-8], N[Not[LessEqual[y, 3.3]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.89999999999999985e-8 or 3.2999999999999998 < y

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 43.5%

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

   if -3.89999999999999985e-8 < y < 3.2999999999999998

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 99.4%

         \[\leadsto z + y \cdot \left(x + \color{blue}{\left(-0.5 \cdot y\right) \cdot z}\right) \]

   7. Simplified 99.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-8} \lor \neg \left(y \leq 3.3\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + z \cdot \left(y \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.7% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+219} \lor \neg \left(x \leq 6.6 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e+219) (not (<= x 6.6e+165))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e+219) || !(x <= 6.6e+165)) {
		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 <= (-4.3d+219)) .or. (.not. (x <= 6.6d+165))) 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 <= -4.3e+219) || !(x <= 6.6e+165)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e+219) or not (x <= 6.6e+165):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e+219) || !(x <= 6.6e+165))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.3e+219) || ~((x <= 6.6e+165)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e+219], N[Not[LessEqual[x, 6.6e+165]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999997e219 or 6.5999999999999997e165 < x

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 58.6%

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

      1. +-commutative 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in y around inf 51.4%

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

   9. Taylor expanded in x around inf 45.2%

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

   if -4.2999999999999997e219 < x < 6.5999999999999997e165

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.8%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   4. Applied egg-rr 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   5. Taylor expanded in y around 0 50.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+219} \lor \neg \left(x \leq 6.6 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.0% 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. Step-by-step derivation

   1. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 56.2%

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

   1. +-commutative 56.2%

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

7. Simplified 56.2%

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

8. Final simplification 56.2%

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

Alternative 8: 39.8% 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. Step-by-step derivation

   1. expm1-log1p-u 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

4. Applied egg-rr 99.8%

   \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

5. Taylor expanded in y around 0 44.8%

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

Reproduce

herbie shell --seed 2024163 
(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))))