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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

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, 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 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x, \sin y, z \cdot \cos y\right) \]
6. 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: 75.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := x \cdot \sin y\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -80000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.039:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.58:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+182}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* x (sin y))))
   (if (<= y -4.1e+142)
     t_0
     (if (<= y -7.6e+35)
       t_1
       (if (<= y -80000000000000.0)
         t_0
         (if (<= y -0.039)
           t_1
           (if (<= y 0.58)
             (+
              z
              (*
               y
               (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y)))))))
             (if (<= y 2.2e+182) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = x * sin(y);
	double tmp;
	if (y <= -4.1e+142) {
		tmp = t_0;
	} else if (y <= -7.6e+35) {
		tmp = t_1;
	} else if (y <= -80000000000000.0) {
		tmp = t_0;
	} else if (y <= -0.039) {
		tmp = t_1;
	} else if (y <= 0.58) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	} else if (y <= 2.2e+182) {
		tmp = 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 = z * cos(y)
    t_1 = x * sin(y)
    if (y <= (-4.1d+142)) then
        tmp = t_0
    else if (y <= (-7.6d+35)) then
        tmp = t_1
    else if (y <= (-80000000000000.0d0)) then
        tmp = t_0
    else if (y <= (-0.039d0)) then
        tmp = t_1
    else if (y <= 0.58d0) then
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    else if (y <= 2.2d+182) then
        tmp = 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 = z * Math.cos(y);
	double t_1 = x * Math.sin(y);
	double tmp;
	if (y <= -4.1e+142) {
		tmp = t_0;
	} else if (y <= -7.6e+35) {
		tmp = t_1;
	} else if (y <= -80000000000000.0) {
		tmp = t_0;
	} else if (y <= -0.039) {
		tmp = t_1;
	} else if (y <= 0.58) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	} else if (y <= 2.2e+182) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = x * math.sin(y)
	tmp = 0
	if y <= -4.1e+142:
		tmp = t_0
	elif y <= -7.6e+35:
		tmp = t_1
	elif y <= -80000000000000.0:
		tmp = t_0
	elif y <= -0.039:
		tmp = t_1
	elif y <= 0.58:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	elif y <= 2.2e+182:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -4.1e+142)
		tmp = t_0;
	elseif (y <= -7.6e+35)
		tmp = t_1;
	elseif (y <= -80000000000000.0)
		tmp = t_0;
	elseif (y <= -0.039)
		tmp = t_1;
	elseif (y <= 0.58)
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	elseif (y <= 2.2e+182)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = x * sin(y);
	tmp = 0.0;
	if (y <= -4.1e+142)
		tmp = t_0;
	elseif (y <= -7.6e+35)
		tmp = t_1;
	elseif (y <= -80000000000000.0)
		tmp = t_0;
	elseif (y <= -0.039)
		tmp = t_1;
	elseif (y <= 0.58)
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	elseif (y <= 2.2e+182)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+142], t$95$0, If[LessEqual[y, -7.6e+35], t$95$1, If[LessEqual[y, -80000000000000.0], t$95$0, If[LessEqual[y, -0.039], t$95$1, If[LessEqual[y, 0.58], 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], If[LessEqual[y, 2.2e+182], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999982e142 or -7.5999999999999999e35 < y < -8e13 or 0.57999999999999996 < y < 2.19999999999999997e182

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 64.2%

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

   if -4.09999999999999982e142 < y < -7.5999999999999999e35 or -8e13 < y < -0.0389999999999999999 or 2.19999999999999997e182 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 68.3%

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

   if -0.0389999999999999999 < y < 0.57999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -80000000000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -0.039:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 0.58:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.017 \lor \neg \left(y \leq 0.0265\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + z \cdot \left(y \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.017) (not (<= y 0.0265)))
   (* x (sin y))
   (+ z (* y (+ x (* z (* y -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.017) || !(y <= 0.0265)) {
		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 <= (-0.017d0)) .or. (.not. (y <= 0.0265d0))) 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 <= -0.017) || !(y <= 0.0265)) {
		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 <= -0.017) or not (y <= 0.0265):
		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 <= -0.017) || !(y <= 0.0265))
		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 <= -0.017) || ~((y <= 0.0265)))
		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, -0.017], N[Not[LessEqual[y, 0.0265]], $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 < -0.017000000000000001 or 0.0264999999999999993 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 48.6%

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

   if -0.017000000000000001 < y < 0.0264999999999999993

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. associate-*r* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.017 \lor \neg \left(y \leq 0.0265\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + z \cdot \left(y \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-38} \lor \neg \left(z \leq 9 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e-38) (not (<= z 9e-164))) (* x (/ z x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-38) || !(z <= 9e-164)) {
		tmp = x * (z / x);
	} else {
		tmp = 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 ((z <= (-1.9d-38)) .or. (.not. (z <= 9d-164))) then
        tmp = x * (z / x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-38) || !(z <= 9e-164)) {
		tmp = x * (z / x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e-38) or not (z <= 9e-164):
		tmp = x * (z / x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e-38) || !(z <= 9e-164))
		tmp = Float64(x * Float64(z / x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e-38) || ~((z <= 9e-164)))
		tmp = x * (z / x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e-38], N[Not[LessEqual[z, 9e-164]], $MachinePrecision]], N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e-38 or 8.9999999999999995e-164 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 53.1%

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

      1. +-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 47.6%

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

   7. Taylor expanded in y around 0 40.0%

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

   if -1.9e-38 < z < 8.9999999999999995e-164

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 57.4%

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

      1. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x around inf 42.1%

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

      1. *-commutative 42.1%

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

   8. Simplified 42.1%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-38} \lor \neg \left(z \leq 9 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.2% 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 54.6%

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

   1. +-commutative 54.6%

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

5. Simplified 54.6%

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

6. Final simplification 54.6%

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

Alternative 7: 17.3% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * y), $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 54.6%

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

   1. +-commutative 54.6%

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

5. Simplified 54.6%

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

6. Taylor expanded in x around inf 21.6%

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

   1. *-commutative 21.6%

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

8. Simplified 21.6%

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

9. Final simplification 21.6%

   \[\leadsto x \cdot y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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))))