Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 8

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]

2. Final simplification 99.8%

   \[\leadsto z \cdot \sin y + x \cdot \cos y \]

Alternative 3: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-25} \lor \neg \left(z \leq 1.55 \cdot 10^{-25}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-25) (not (<= z 1.55e-25)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-25) || !(z <= 1.55e-25)) {
		tmp = x + (z * sin(y));
	} else {
		tmp = x * 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 ((z <= (-1.35d-25)) .or. (.not. (z <= 1.55d-25))) then
        tmp = x + (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-25) || !(z <= 1.55e-25)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-25) or not (z <= 1.55e-25):
		tmp = x + (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-25) || !(z <= 1.55e-25))
		tmp = Float64(x + Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-25) || ~((z <= 1.55e-25)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-25], N[Not[LessEqual[z, 1.55e-25]], $MachinePrecision]], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000008e-25 or 1.54999999999999997e-25 < z

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 94.6%

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

   if -1.35000000000000008e-25 < z < 1.54999999999999997e-25

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 52.4%

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

      3. associate-*r* 52.4%

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

      4. fma-def 52.4%

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

   3. Applied egg-rr 52.4%

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

   4. Taylor expanded in z around 0 86.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-25} \lor \neg \left(z \leq 1.55 \cdot 10^{-25}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq 0.0095\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(\left(y \cdot y\right) \cdot -0.5 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-6) (not (<= y 0.0095)))
   (* z (sin y))
   (+ (* y z) (* x (+ (* (* y y) -0.5) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 0.0095)) {
		tmp = z * sin(y);
	} else {
		tmp = (y * z) + (x * (((y * y) * -0.5) + 1.0));
	}
	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) :: tmp
    if ((y <= (-6.5d-6)) .or. (.not. (y <= 0.0095d0))) then
        tmp = z * sin(y)
    else
        tmp = (y * z) + (x * (((y * y) * (-0.5d0)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 0.0095)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = (y * z) + (x * (((y * y) * -0.5) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-6) or not (y <= 0.0095):
		tmp = z * math.sin(y)
	else:
		tmp = (y * z) + (x * (((y * y) * -0.5) + 1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-6) || !(y <= 0.0095))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(Float64(y * z) + Float64(x * Float64(Float64(Float64(y * y) * -0.5) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-6) || ~((y <= 0.0095)))
		tmp = z * sin(y);
	else
		tmp = (y * z) + (x * (((y * y) * -0.5) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-6], N[Not[LessEqual[y, 0.0095]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x * N[(N[(N[(y * y), $MachinePrecision] * -0.5), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999996e-6 or 0.00949999999999999976 < y

   1. Initial program 99.6%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in x around 0 60.0%

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

   if -6.4999999999999996e-6 < y < 0.00949999999999999976

   1. Initial program 100.0%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{y \cdot z + \left(-0.5 \cdot \left({y}^{2} \cdot x\right) + x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.5%

         \[\leadsto y \cdot z + \left(\color{blue}{\left(-0.5 \cdot {y}^{2}\right) \cdot x} + x\right) \]

      2. distribute-lft1-in 99.5%

         \[\leadsto y \cdot z + \color{blue}{\left(-0.5 \cdot {y}^{2} + 1\right) \cdot x} \]

      3. *-commutative 99.5%

         \[\leadsto y \cdot z + \left(\color{blue}{{y}^{2} \cdot -0.5} + 1\right) \cdot x \]

      4. unpow2 99.5%

         \[\leadsto y \cdot z + \left(\color{blue}{\left(y \cdot y\right)} \cdot -0.5 + 1\right) \cdot x \]

   4. Applied egg-rr 99.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq 0.0095\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(\left(y \cdot y\right) \cdot -0.5 + 1\right)\\ \end{array} \]

Alternative 5: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+137} \lor \neg \left(z \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+137) (not (<= z 4.8e-5))) (* z (sin y)) (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+137) || !(z <= 4.8e-5)) {
		tmp = z * sin(y);
	} else {
		tmp = x * 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 ((z <= (-2.2d+137)) .or. (.not. (z <= 4.8d-5))) then
        tmp = z * sin(y)
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+137) || !(z <= 4.8e-5)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e+137) or not (z <= 4.8e-5):
		tmp = z * math.sin(y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+137) || !(z <= 4.8e-5))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.2e+137) || ~((z <= 4.8e-5)))
		tmp = z * sin(y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+137], N[Not[LessEqual[z, 4.8e-5]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000015e137 or 4.8000000000000001e-5 < z

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in x around 0 79.7%

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

   if -2.20000000000000015e137 < z < 4.8000000000000001e-5

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 54.7%

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

      3. associate-*r* 54.7%

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

      4. fma-def 54.7%

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

   3. Applied egg-rr 54.7%

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

   4. Taylor expanded in z around 0 82.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+137} \lor \neg \left(z \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 6: 41.8% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+189}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e+189) (* y z) (if (<= z 3.5e+142) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+189) {
		tmp = y * z;
	} else if (z <= 3.5e+142) {
		tmp = x;
	} else {
		tmp = y * 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 <= (-1.15d+189)) then
        tmp = y * z
    else if (z <= 3.5d+142) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+189) {
		tmp = y * z;
	} else if (z <= 3.5e+142) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e+189:
		tmp = y * z
	elif z <= 3.5e+142:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e+189)
		tmp = Float64(y * z);
	elseif (z <= 3.5e+142)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e+189)
		tmp = y * z;
	elseif (z <= 3.5e+142)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e+189], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.5e+142], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e189 or 3.49999999999999997e142 < z

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 57.1%

      \[\leadsto \color{blue}{y \cdot z + \left(-0.5 \cdot \left({y}^{2} \cdot x\right) + x\right)} \]

   3. Taylor expanded in z around inf 45.4%

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

   if -1.15e189 < z < 3.49999999999999997e142

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 54.2%

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

      3. associate-*r* 54.2%

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

      4. fma-def 54.2%

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

   3. Applied egg-rr 54.2%

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

   4. Taylor expanded in z around 0 72.6%

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

   5. Taylor expanded in y around 0 47.5%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+189}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 52.5% 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. Taylor expanded in y around 0 53.2%

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

3. Final simplification 53.2%

   \[\leadsto x + y \cdot z \]

Alternative 8: 38.6% 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. Step-by-step derivation

   1. +-commutative 99.8%

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

   2. add-sqr-sqrt 55.6%

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

   3. associate-*r* 55.6%

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

   4. fma-def 55.6%

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

3. Applied egg-rr 55.6%

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

4. Taylor expanded in z around 0 56.4%

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

5. Taylor expanded in y around 0 38.4%

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

6. Final simplification 38.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))