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

Percentage Accurate: 99.8% → 99.8%

Time: 7.0s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 3: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.011:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117} \lor \neg \left(y \leq 2.8 \cdot 10^{+199}\right) \land y \leq 2.1 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)) (t_1 (* x (cos y))))
   (if (<= y -6e+146)
     t_0
     (if (<= y -8.5e+73)
       t_1
       (if (<= y -0.011)
         t_0
         (if (<= y 7.8e-16)
           (+ x (* y z))
           (if (or (<= y 8e+117) (and (not (<= y 2.8e+199)) (<= y 2.1e+277)))
             t_1
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = x * cos(y);
	double tmp;
	if (y <= -6e+146) {
		tmp = t_0;
	} else if (y <= -8.5e+73) {
		tmp = t_1;
	} else if (y <= -0.011) {
		tmp = t_0;
	} else if (y <= 7.8e-16) {
		tmp = x + (y * z);
	} else if ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 2.1e+277))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = sin(y) * z
    t_1 = x * cos(y)
    if (y <= (-6d+146)) then
        tmp = t_0
    else if (y <= (-8.5d+73)) then
        tmp = t_1
    else if (y <= (-0.011d0)) then
        tmp = t_0
    else if (y <= 7.8d-16) then
        tmp = x + (y * z)
    else if ((y <= 8d+117) .or. (.not. (y <= 2.8d+199)) .and. (y <= 2.1d+277)) then
        tmp = t_1
    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) * z;
	double t_1 = x * Math.cos(y);
	double tmp;
	if (y <= -6e+146) {
		tmp = t_0;
	} else if (y <= -8.5e+73) {
		tmp = t_1;
	} else if (y <= -0.011) {
		tmp = t_0;
	} else if (y <= 7.8e-16) {
		tmp = x + (y * z);
	} else if ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 2.1e+277))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	t_1 = x * math.cos(y)
	tmp = 0
	if y <= -6e+146:
		tmp = t_0
	elif y <= -8.5e+73:
		tmp = t_1
	elif y <= -0.011:
		tmp = t_0
	elif y <= 7.8e-16:
		tmp = x + (y * z)
	elif (y <= 8e+117) or (not (y <= 2.8e+199) and (y <= 2.1e+277)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -6e+146)
		tmp = t_0;
	elseif (y <= -8.5e+73)
		tmp = t_1;
	elseif (y <= -0.011)
		tmp = t_0;
	elseif (y <= 7.8e-16)
		tmp = Float64(x + Float64(y * z));
	elseif ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 2.1e+277)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	t_1 = x * cos(y);
	tmp = 0.0;
	if (y <= -6e+146)
		tmp = t_0;
	elseif (y <= -8.5e+73)
		tmp = t_1;
	elseif (y <= -0.011)
		tmp = t_0;
	elseif (y <= 7.8e-16)
		tmp = x + (y * z);
	elseif ((y <= 8e+117) || (~((y <= 2.8e+199)) && (y <= 2.1e+277)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+146], t$95$0, If[LessEqual[y, -8.5e+73], t$95$1, If[LessEqual[y, -0.011], t$95$0, If[LessEqual[y, 7.8e-16], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8e+117], And[N[Not[LessEqual[y, 2.8e+199]], $MachinePrecision], LessEqual[y, 2.1e+277]]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000005e146 or -8.4999999999999998e73 < y < -0.010999999999999999 or 8.0000000000000004e117 < y < 2.8000000000000001e199 or 2.09999999999999999e277 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 69.8%

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

   if -6.00000000000000005e146 < y < -8.4999999999999998e73 or 7.79999999999999954e-16 < y < 8.0000000000000004e117 or 2.8000000000000001e199 < y < 2.09999999999999999e277

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 75.2%

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

   if -0.010999999999999999 < y < 7.79999999999999954e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+146}:\\ \;\;\;\;\sin y \cdot z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.011:\\ \;\;\;\;\sin y \cdot z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117} \lor \neg \left(y \leq 2.8 \cdot 10^{+199}\right) \land y \leq 2.1 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot z\\ \end{array} \]

Alternative 4: 86.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-72} \lor \neg \left(z \leq 5.2 \cdot 10^{-86}\right):\\ \;\;\;\;x + \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.9e-72) (not (<= z 5.2e-86)))
   (+ x (* (sin y) z))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e-72) || !(z <= 5.2e-86)) {
		tmp = x + (sin(y) * z);
	} 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 <= (-2.9d-72)) .or. (.not. (z <= 5.2d-86))) then
        tmp = x + (sin(y) * z)
    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 <= -2.9e-72) || !(z <= 5.2e-86)) {
		tmp = x + (Math.sin(y) * z);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.9e-72) or not (z <= 5.2e-86):
		tmp = x + (math.sin(y) * z)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.9e-72) || !(z <= 5.2e-86))
		tmp = Float64(x + Float64(sin(y) * z));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.9e-72) || ~((z <= 5.2e-86)))
		tmp = x + (sin(y) * z);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.9e-72], N[Not[LessEqual[z, 5.2e-86]], $MachinePrecision]], N[(x + N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999998e-72 or 5.2000000000000002e-86 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 88.4%

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

   if -2.89999999999999998e-72 < z < 5.2000000000000002e-86

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around 0 90.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-72} \lor \neg \left(z \leq 5.2 \cdot 10^{-86}\right):\\ \;\;\;\;x + \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 5: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0125 \lor \neg \left(y \leq 1600\right):\\ \;\;\;\;\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0125) (not (<= y 1600.0)))
   (* (sin y) z)
   (+ (* y z) (* x (+ 1.0 (* -0.5 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0125) || !(y <= 1600.0)) {
		tmp = sin(y) * z;
	} else {
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.0125d0)) .or. (.not. (y <= 1600.0d0))) then
        tmp = sin(y) * z
    else
        tmp = (y * z) + (x * (1.0d0 + ((-0.5d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0125) || !(y <= 1600.0)) {
		tmp = Math.sin(y) * z;
	} else {
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0125) or not (y <= 1600.0):
		tmp = math.sin(y) * z
	else:
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0125) || !(y <= 1600.0))
		tmp = Float64(sin(y) * z);
	else
		tmp = Float64(Float64(y * z) + Float64(x * Float64(1.0 + Float64(-0.5 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0125) || ~((y <= 1600.0)))
		tmp = sin(y) * z;
	else
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0125], N[Not[LessEqual[y, 1600.0]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.012500000000000001 or 1600 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 53.6%

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

   if -0.012500000000000001 < y < 1600

   1. Initial program 100.0%

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

      1. add-cbrt-cube 100.0%

         \[\leadsto x \cdot \color{blue}{\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \cos y}} + z \cdot \sin y \]

      2. pow3 100.0%

         \[\leadsto x \cdot \sqrt[3]{\color{blue}{{\cos y}^{3}}} + z \cdot \sin y \]

   3. Applied egg-rr 100.0%

      \[\leadsto x \cdot \color{blue}{\sqrt[3]{{\cos y}^{3}}} + z \cdot \sin y \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto x \cdot \sqrt[3]{{\cos y}^{3}} + \color{blue}{y \cdot z} \]

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)} + y \cdot z \]
   6. Step-by-step derivation

      1. unpow2 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0125 \lor \neg \left(y \leq 1600\right):\\ \;\;\;\;\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \]

Alternative 6: 40.7% accurate, 40.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.5e+223) x (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.5e+223) {
		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 <= 2.5d+223) 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 <= 2.5e+223) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.5e+223:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.5e+223)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.5e+223)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.5e+223], x, N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.49999999999999992e223

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 39.6%

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

   if 2.49999999999999992e223 < z

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 70.9%

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

   5. Taylor expanded in x around 0 57.3%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 53.0% 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 51.5%

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

3. Final simplification 51.5%

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

Alternative 8: 39.5% 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. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 37.1%

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

5. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))