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

Percentage Accurate: 99.8% → 99.8%

Time: 11.4s

Alternatives: 6

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: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(0 - z\right)\\ \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right) + z \cdot \left(0.3333333333333333 \cdot \left(y \cdot \left(y \cdot y\right)\right) - y \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- 0.0 z))))
   (if (<= y -0.054)
     t_0
     (if (<= y 0.13)
       (+
        (* x (+ 1.0 (* -0.5 (* y y))))
        (*
         z
         (-
          (* 0.3333333333333333 (* y (* y y)))
          (* y (+ 1.0 (* (* y y) 0.16666666666666666))))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * (0.0 - z);
	double tmp;
	if (y <= -0.054) {
		tmp = t_0;
	} else if (y <= 0.13) {
		tmp = (x * (1.0 + (-0.5 * (y * y)))) + (z * ((0.3333333333333333 * (y * (y * y))) - (y * (1.0 + ((y * y) * 0.16666666666666666)))));
	} else {
		tmp = t_0;
	}
	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 = sin(y) * (0.0d0 - z)
    if (y <= (-0.054d0)) then
        tmp = t_0
    else if (y <= 0.13d0) then
        tmp = (x * (1.0d0 + ((-0.5d0) * (y * y)))) + (z * ((0.3333333333333333d0 * (y * (y * y))) - (y * (1.0d0 + ((y * y) * 0.16666666666666666d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * (0.0 - z);
	double tmp;
	if (y <= -0.054) {
		tmp = t_0;
	} else if (y <= 0.13) {
		tmp = (x * (1.0 + (-0.5 * (y * y)))) + (z * ((0.3333333333333333 * (y * (y * y))) - (y * (1.0 + ((y * y) * 0.16666666666666666)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * (0.0 - z)
	tmp = 0
	if y <= -0.054:
		tmp = t_0
	elif y <= 0.13:
		tmp = (x * (1.0 + (-0.5 * (y * y)))) + (z * ((0.3333333333333333 * (y * (y * y))) - (y * (1.0 + ((y * y) * 0.16666666666666666)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(0.0 - z))
	tmp = 0.0
	if (y <= -0.054)
		tmp = t_0;
	elseif (y <= 0.13)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.5 * Float64(y * y)))) + Float64(z * Float64(Float64(0.3333333333333333 * Float64(y * Float64(y * y))) - Float64(y * Float64(1.0 + Float64(Float64(y * y) * 0.16666666666666666))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * (0.0 - z);
	tmp = 0.0;
	if (y <= -0.054)
		tmp = t_0;
	elseif (y <= 0.13)
		tmp = (x * (1.0 + (-0.5 * (y * y)))) + (z * ((0.3333333333333333 * (y * (y * y))) - (y * (1.0 + ((y * y) * 0.16666666666666666)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * N[(0.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.054], t$95$0, If[LessEqual[y, 0.13], N[(N[(x * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(0.3333333333333333 * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 0.13 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \sin y\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \sin y} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \sin y\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\sin y}\right)\right) \]

      5. sin-lowering-sin.f64 57.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{sin.f64}\left(y\right)\right)\right) \]

   5. Simplified 57.1%

      \[\leadsto \color{blue}{0 - z \cdot \sin y} \]

   if -0.0539999999999999994 < y < 0.13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), \color{blue}{z}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot x\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\left(\frac{1}{6} \cdot y\right) \cdot z\right)\right)\right), z\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(z \cdot \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(y \cdot \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

      12. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(x \cdot -0.5 + z \cdot \left(y \cdot 0.16666666666666666\right)\right) - z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right) - z\right) \cdot \color{blue}{y}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) \cdot \left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) - z \cdot z}{y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right) + z} \cdot y\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(\left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) \cdot \left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) - z \cdot z\right) \cdot y}{\color{blue}{y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right) + z}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) \cdot \left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right)\right) - z \cdot z\right) \cdot y\right), \color{blue}{\left(y \cdot \left(x \cdot \frac{-1}{2} + z \cdot \left(y \cdot \frac{1}{6}\right)\right) + z\right)}\right)\right) \]

   7. Applied egg-rr 73.3%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{-1}{2} \cdot \left(x \cdot {y}^{2}\right) + z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + \frac{-1}{2} \cdot \left(x \cdot {y}^{2}\right)\right) + \color{blue}{z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{-1}{2} \cdot \left(x \cdot {y}^{2}\right)\right), \color{blue}{\left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)}\right) \]

      3. *-lft-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\left(1 \cdot x + \frac{-1}{2} \cdot \left(x \cdot {y}^{2}\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(1 \cdot x + \frac{-1}{2} \cdot \left({y}^{2} \cdot x\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(1 \cdot x + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot x\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(1 + \frac{-1}{2} \cdot {y}^{2}\right)\right), \left(\color{blue}{z} \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(1 + \frac{-1}{2} \cdot {y}^{2}\right)\right), \left(\color{blue}{z} \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot {y}^{2}\right)\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \left({y}^{2}\right)\right)\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \left(y \cdot y\right)\right)\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right), \left(z \cdot \left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{3} \cdot {y}^{3} - y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)}\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot {y}^{3}\right), \color{blue}{\left(y \cdot \left(1 + \frac{1}{6} \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

   10. Simplified 99.7%

       \[\leadsto \color{blue}{x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right) + z \cdot \left(0.3333333333333333 \cdot \left(y \cdot \left(y \cdot y\right)\right) - y \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;\sin y \cdot \left(0 - z\right)\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right) + z \cdot \left(0.3333333333333333 \cdot \left(y \cdot \left(y \cdot y\right)\right) - y \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(0 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -48:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0115:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + z \cdot \left(y \cdot 0.16666666666666666\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= y -48.0)
     t_0
     (if (<= y 0.0115)
       (+ x (* y (- (* y (+ (* x -0.5) (* z (* y 0.16666666666666666)))) z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (y <= -48.0) {
		tmp = t_0;
	} else if (y <= 0.0115) {
		tmp = x + (y * ((y * ((x * -0.5) + (z * (y * 0.16666666666666666)))) - z));
	} else {
		tmp = t_0;
	}
	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 * cos(y)
    if (y <= (-48.0d0)) then
        tmp = t_0
    else if (y <= 0.0115d0) then
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (z * (y * 0.16666666666666666d0)))) - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double tmp;
	if (y <= -48.0) {
		tmp = t_0;
	} else if (y <= 0.0115) {
		tmp = x + (y * ((y * ((x * -0.5) + (z * (y * 0.16666666666666666)))) - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if y <= -48.0:
		tmp = t_0
	elif y <= 0.0115:
		tmp = x + (y * ((y * ((x * -0.5) + (z * (y * 0.16666666666666666)))) - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -48.0)
		tmp = t_0;
	elseif (y <= 0.0115)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(z * Float64(y * 0.16666666666666666)))) - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (y <= -48.0)
		tmp = t_0;
	elseif (y <= 0.0115)
		tmp = x + (y * ((y * ((x * -0.5) + (z * (y * 0.16666666666666666)))) - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -48.0], t$95$0, If[LessEqual[y, 0.0115], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(z * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -48 or 0.0115 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 45.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 45.7%

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

   if -48 < y < 0.0115

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), \color{blue}{z}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot x\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\left(\frac{1}{6} \cdot y\right) \cdot z\right)\right)\right), z\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(z \cdot \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(y \cdot \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

      12. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

   5. Simplified 99.3%

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

Alternative 4: 41.5% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-137) x (if (<= x 3e-141) (* y (- 0.0 z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-137) {
		tmp = x;
	} else if (x <= 3e-141) {
		tmp = y * (0.0 - z);
	} else {
		tmp = x;
	}
	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 <= (-2.1d-137)) then
        tmp = x
    else if (x <= 3d-141) then
        tmp = y * (0.0d0 - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-137) {
		tmp = x;
	} else if (x <= 3e-141) {
		tmp = y * (0.0 - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-137:
		tmp = x
	elif x <= 3e-141:
		tmp = y * (0.0 - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-137)
		tmp = x;
	elseif (x <= 3e-141)
		tmp = Float64(y * Float64(0.0 - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-137)
		tmp = x;
	elseif (x <= 3e-141)
		tmp = y * (0.0 - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-137], x, If[LessEqual[x, 3e-141], N[(y * N[(0.0 - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999992e-137 or 2.99999999999999983e-141 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 49.9%

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

   if -2.09999999999999992e-137 < x < 2.99999999999999983e-141

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), \color{blue}{z}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot x\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(\left(\frac{1}{6} \cdot y\right) \cdot z\right)\right)\right), z\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \left(z \cdot \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(\frac{1}{6} \cdot y\right)\right)\right)\right), z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \left(y \cdot \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

      12. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-1}{2}\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), z\right)\right)\right) \]

   5. Simplified 51.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right)\right), \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({y}^{2} \cdot z\right)\right), z\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(z \cdot {y}^{2}\right)\right), z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(z, \left({y}^{2}\right)\right)\right), z\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(z, \left(y \cdot y\right)\right)\right), z\right)\right) \]

      7. *-lowering-*.f64 34.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, y\right)\right)\right), z\right)\right) \]

   8. Simplified 34.9%

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

   9. Taylor expanded in y around 0

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

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(y \cdot z\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{y \cdot z} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot z\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(z \cdot \color{blue}{y}\right)\right) \]

       5. *-lowering-*.f64 34.3%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   11. Simplified 34.3%

       \[\leadsto \color{blue}{0 - z \cdot y} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{neg}\left(z \cdot y\right) \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(z \cdot y\right)\right) \]

       3. *-lowering-*.f64 34.3%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, y\right)\right) \]

   13. Applied egg-rr 34.3%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.8% 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

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

   1. mul-1-neg N/A

      \[\leadsto x + \left(\mathsf{neg}\left(y \cdot z\right)\right) \]

   2. unsub-neg N/A

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

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

   5. *-lowering-*.f64 52.4%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

5. Simplified 52.4%

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

6. Final simplification 52.4%

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

Alternative 6: 39.4% 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. Add Preprocessing

3. Taylor expanded in y around 0

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

5. Simplified 41.0%

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

Reproduce

herbie shell --seed 2024158 
(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))))