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

Percentage Accurate: 99.8% → 99.8%

Time: 9.1s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

2. Taylor expanded in x around 0 99.7%

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

   1. mul-1-neg 99.7%

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

   2. distribute-rgt-neg-out 99.7%

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

   3. +-commutative 99.7%

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

   4. fma-udef 99.8%

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

   5. distribute-rgt-neg-out 99.8%

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

   6. *-commutative 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

4. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

2. Final simplification 99.7%

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

Alternative 3: 74.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ t_1 := \cos y \cdot x\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.0018:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117} \lor \neg \left(y \leq 2.8 \cdot 10^{+199}\right) \land y \leq 1.8 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))) (t_1 (* (cos y) x)))
   (if (<= y -5.6e+146)
     t_0
     (if (<= y -8.5e+73)
       t_1
       (if (<= y -0.0018)
         t_0
         (if (<= y 7.8e-16)
           (- x (* y z))
           (if (or (<= y 8e+117) (and (not (<= y 2.8e+199)) (<= y 1.8e+277)))
             t_1
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double t_1 = cos(y) * x;
	double tmp;
	if (y <= -5.6e+146) {
		tmp = t_0;
	} else if (y <= -8.5e+73) {
		tmp = t_1;
	} else if (y <= -0.0018) {
		tmp = t_0;
	} else if (y <= 7.8e-16) {
		tmp = x - (y * z);
	} else if ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 1.8e+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 = cos(y) * x
    if (y <= (-5.6d+146)) then
        tmp = t_0
    else if (y <= (-8.5d+73)) then
        tmp = t_1
    else if (y <= (-0.0018d0)) 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 <= 1.8d+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 = Math.cos(y) * x;
	double tmp;
	if (y <= -5.6e+146) {
		tmp = t_0;
	} else if (y <= -8.5e+73) {
		tmp = t_1;
	} else if (y <= -0.0018) {
		tmp = t_0;
	} else if (y <= 7.8e-16) {
		tmp = x - (y * z);
	} else if ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 1.8e+277))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	t_1 = math.cos(y) * x
	tmp = 0
	if y <= -5.6e+146:
		tmp = t_0
	elif y <= -8.5e+73:
		tmp = t_1
	elif y <= -0.0018:
		tmp = t_0
	elif y <= 7.8e-16:
		tmp = x - (y * z)
	elif (y <= 8e+117) or (not (y <= 2.8e+199) and (y <= 1.8e+277)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	t_1 = Float64(cos(y) * x)
	tmp = 0.0
	if (y <= -5.6e+146)
		tmp = t_0;
	elseif (y <= -8.5e+73)
		tmp = t_1;
	elseif (y <= -0.0018)
		tmp = t_0;
	elseif (y <= 7.8e-16)
		tmp = Float64(x - Float64(y * z));
	elseif ((y <= 8e+117) || (!(y <= 2.8e+199) && (y <= 1.8e+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 = cos(y) * x;
	tmp = 0.0;
	if (y <= -5.6e+146)
		tmp = t_0;
	elseif (y <= -8.5e+73)
		tmp = t_1;
	elseif (y <= -0.0018)
		tmp = t_0;
	elseif (y <= 7.8e-16)
		tmp = x - (y * z);
	elseif ((y <= 8e+117) || (~((y <= 2.8e+199)) && (y <= 1.8e+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[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -5.6e+146], t$95$0, If[LessEqual[y, -8.5e+73], t$95$1, If[LessEqual[y, -0.0018], 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, 1.8e+277]]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000002e146 or -8.4999999999999998e73 < y < -0.0018 or 8.0000000000000004e117 < y < 2.8000000000000001e199 or 1.80000000000000004e277 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

   4. Simplified 70.3%

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

   if -5.6000000000000002e146 < y < -8.4999999999999998e73 or 7.79999999999999954e-16 < y < 8.0000000000000004e117 or 2.8000000000000001e199 < y < 1.80000000000000004e277

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-out 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-udef 99.6%

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

      5. distribute-rgt-neg-out 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -0.0018 < 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%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+146}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+73}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{elif}\;y \leq -0.0018:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117} \lor \neg \left(y \leq 2.8 \cdot 10^{+199}\right) \land y \leq 1.8 \cdot 10^{+277}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 86.7% accurate, 1.9× speedup

Math

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

FPCore

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

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 = cos(y) * 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 ((z <= (-2.9d-72)) .or. (.not. (z <= 5.2d-86))) then
        tmp = x - (sin(y) * z)
    else
        tmp = cos(y) * x
    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 = Math.cos(y) * x;
	}
	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 = math.cos(y) * x
	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(cos(y) * x);
	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 = cos(y) * x;
	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[(N[Cos[y], $MachinePrecision] * x), $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. Taylor expanded in x around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-out 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-udef 99.7%

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

      5. distribute-rgt-neg-out 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 90.7%

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

4. Final simplification 89.2%

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

Alternative 5: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+23) (not (<= y 7.8e-16))) (* (cos y) x) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+23) || !(y <= 7.8e-16)) {
		tmp = cos(y) * x;
	} else {
		tmp = x - (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 ((y <= (-4.5d+23)) .or. (.not. (y <= 7.8d-16))) then
        tmp = cos(y) * x
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+23) || !(y <= 7.8e-16)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+23) or not (y <= 7.8e-16):
		tmp = math.cos(y) * x
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+23) || !(y <= 7.8e-16))
		tmp = Float64(cos(y) * x);
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e+23) || ~((y <= 7.8e-16)))
		tmp = cos(y) * x;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+23], N[Not[LessEqual[y, 7.8e-16]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999979e23 or 7.79999999999999954e-16 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-rgt-neg-out 99.5%

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

      3. +-commutative 99.5%

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

      4. fma-udef 99.5%

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

      5. distribute-rgt-neg-out 99.5%

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

      6. *-commutative 99.5%

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

      7. distribute-rgt-neg-in 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x around inf 50.6%

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

   if -4.49999999999999979e23 < y < 7.79999999999999954e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. mul-1-neg 96.1%

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

      3. unsub-neg 96.1%

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

   4. Simplified 96.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 6: 40.7% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.35e+225) x (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.35e+225) {
		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 <= 1.35d+225) 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 <= 1.35e+225) {
		tmp = x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.35e+225:
		tmp = x
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.35e+225)
		tmp = x;
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.35e+225)
		tmp = x;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.35e+225], x, N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.3499999999999999e225

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-out 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-udef 99.7%

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

      5. distribute-rgt-neg-out 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around 0 39.6%

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

   if 1.3499999999999999e225 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. *-commutative 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-rgt-neg-in 55.4%

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

   7. Simplified 55.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

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 99.7%

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

2. Taylor expanded in y around 0 51.4%

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

   1. +-commutative 51.4%

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

   2. mul-1-neg 51.4%

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

   3. unsub-neg 51.4%

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

4. Simplified 51.4%

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

5. Final simplification 51.4%

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

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 99.7%

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

2. Taylor expanded in x around 0 99.7%

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

   1. mul-1-neg 99.7%

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

   2. distribute-rgt-neg-out 99.7%

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

   3. +-commutative 99.7%

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

   4. fma-udef 99.8%

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

   5. distribute-rgt-neg-out 99.8%

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

   6. *-commutative 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

4. Simplified 99.8%

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

5. Taylor expanded in y around 0 37.1%

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

6. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(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))))