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

Percentage Accurate: 99.8% → 99.8%

Time: 10.3s

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: 85.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -5.8e+53) t_0 (if (<= z 1.62e+74) (+ (* x (sin y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5.8e+53) {
		tmp = t_0;
	} else if (z <= 1.62e+74) {
		tmp = (x * sin(y)) + 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 = z * cos(y)
    if (z <= (-5.8d+53)) then
        tmp = t_0
    else if (z <= 1.62d+74) then
        tmp = (x * sin(y)) + 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 = z * Math.cos(y);
	double tmp;
	if (z <= -5.8e+53) {
		tmp = t_0;
	} else if (z <= 1.62e+74) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -5.8e+53:
		tmp = t_0
	elif z <= 1.62e+74:
		tmp = (x * math.sin(y)) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -5.8e+53)
		tmp = t_0;
	elseif (z <= 1.62e+74)
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -5.8e+53)
		tmp = t_0;
	elseif (z <= 1.62e+74)
		tmp = (x * sin(y)) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+53], t$95$0, If[LessEqual[z, 1.62e+74], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000004e53 or 1.62e74 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. cos-lowering-cos.f64 89.7%

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

   5. Simplified 89.7%

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

   if -5.8000000000000004e53 < z < 1.62e74

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 87.4%

      \[\leadsto x \cdot \sin y + \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= x -2.4e+123) t_0 (if (<= x 9.5e+74) (* z (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (x <= -2.4e+123) {
		tmp = t_0;
	} else if (x <= 9.5e+74) {
		tmp = z * cos(y);
	} 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 * sin(y)
    if (x <= (-2.4d+123)) then
        tmp = t_0
    else if (x <= 9.5d+74) then
        tmp = z * cos(y)
    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.sin(y);
	double tmp;
	if (x <= -2.4e+123) {
		tmp = t_0;
	} else if (x <= 9.5e+74) {
		tmp = z * Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if x <= -2.4e+123:
		tmp = t_0
	elif x <= 9.5e+74:
		tmp = z * math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (x <= -2.4e+123)
		tmp = t_0;
	elseif (x <= 9.5e+74)
		tmp = Float64(z * cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (x <= -2.4e+123)
		tmp = t_0;
	elseif (x <= 9.5e+74)
		tmp = z * cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+123], t$95$0, If[LessEqual[x, 9.5e+74], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999989e123 or 9.5000000000000006e74 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. sin-lowering-sin.f64 73.4%

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

   5. Simplified 73.4%

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

   if -2.39999999999999989e123 < x < 9.5000000000000006e74

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. cos-lowering-cos.f64 80.2%

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

   5. Simplified 80.2%

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

Alternative 4: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -0.037:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.112:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= y -0.037)
     t_0
     (if (<= y 0.112) (+ z (* y (+ x (* y (* z -0.5))))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (y <= -0.037) {
		tmp = t_0;
	} else if (y <= 0.112) {
		tmp = z + (y * (x + (y * (z * -0.5))));
	} 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 * sin(y)
    if (y <= (-0.037d0)) then
        tmp = t_0
    else if (y <= 0.112d0) then
        tmp = z + (y * (x + (y * (z * (-0.5d0)))))
    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.sin(y);
	double tmp;
	if (y <= -0.037) {
		tmp = t_0;
	} else if (y <= 0.112) {
		tmp = z + (y * (x + (y * (z * -0.5))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if y <= -0.037:
		tmp = t_0
	elif y <= 0.112:
		tmp = z + (y * (x + (y * (z * -0.5))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -0.037)
		tmp = t_0;
	elseif (y <= 0.112)
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(z * -0.5)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (y <= -0.037)
		tmp = t_0;
	elseif (y <= 0.112)
		tmp = z + (y * (x + (y * (z * -0.5))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.037], t$95$0, If[LessEqual[y, 0.112], N[(z + N[(y * N[(x + N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0369999999999999982 or 0.112000000000000002 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. sin-lowering-sin.f64 50.0%

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

   5. Simplified 50.0%

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

   if -0.0369999999999999982 < y < 0.112000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 99.7%

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

   5. Simplified 99.7%

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

Alternative 5: 41.3% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-230}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e-230) z (if (<= z 1.65e-151) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e-230) {
		tmp = z;
	} else if (z <= 1.65e-151) {
		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 (z <= (-2.5d-230)) then
        tmp = z
    else if (z <= 1.65d-151) 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 (z <= -2.5e-230) {
		tmp = z;
	} else if (z <= 1.65e-151) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e-230:
		tmp = z
	elif z <= 1.65e-151:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e-230)
		tmp = z;
	elseif (z <= 1.65e-151)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e-230)
		tmp = z;
	elseif (z <= 1.65e-151)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e-230], z, If[LessEqual[z, 1.65e-151], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000017e-230 or 1.6499999999999999e-151 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 45.8%

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

   if -2.50000000000000017e-230 < z < 1.6499999999999999e-151

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 95.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, z\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 44.8%

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

   11. Simplified 44.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-230}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.6% 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

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

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

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 52.8%

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

5. Simplified 52.8%

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

6. Final simplification 52.8%

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

Alternative 7: 38.5% 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 y around 0

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

5. Simplified 39.9%

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

Reproduce

herbie shell --seed 2024155 
(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))))