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

Percentage Accurate: 99.8% → 99.8%

Time: 11.6s

Alternatives: 9

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * (-N[Sin[y], $MachinePrecision]) + 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. cancel-sign-sub-inv 99.8%

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

   2. +-commutative 99.8%

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

   3. distribute-lft-neg-out 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sin-neg 99.8%

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

   6. fma-def 99.8%

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

   7. sin-neg 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-73} \lor \neg \left(z \leq 1.7 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-73) (not (<= z 1.7e-44)))
   (fma z (- (sin y)) x)
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-73) || !(z <= 1.7e-44)) {
		tmp = fma(z, -sin(y), x);
	} else {
		tmp = x * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e-73) || !(z <= 1.7e-44))
		tmp = fma(z, Float64(-sin(y)), x);
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e-73], N[Not[LessEqual[z, 1.7e-44]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999997e-74 or 1.70000000000000008e-44 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sin-neg 99.8%

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

      6. fma-def 99.8%

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

      7. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 90.0%

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

   if -9.99999999999999997e-74 < z < 1.70000000000000008e-44

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 87.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-73} \lor \neg \left(z \leq 1.7 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 3: 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. Final simplification 99.8%

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

Alternative 4: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.25e-8)
   (* z (- (sin y)))
   (if (<= y 8e-7) (fma (- y) z x) (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.25e-8) {
		tmp = z * -sin(y);
	} else if (y <= 8e-7) {
		tmp = fma(-y, z, x);
	} else {
		tmp = x * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.25e-8)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (y <= 8e-7)
		tmp = fma(Float64(-y), z, x);
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.25e-8], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 8e-7], N[((-y) * z + x), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.24999999999999996e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 63.5%

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

      1. neg-mul-1 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

   4. Simplified 63.5%

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

   if -2.24999999999999996e-8 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. fma-udef 100.0%

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

   7. Simplified 100.0%

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

   if 7.9999999999999996e-7 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 56.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 5: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00026 \lor \neg \left(y \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00026) (not (<= y 8e-7))) (* x (cos y)) (- x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00026) || !(y <= 8e-7)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (z * 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 <= (-0.00026d0)) .or. (.not. (y <= 8d-7))) then
        tmp = x * cos(y)
    else
        tmp = x - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00026) || !(y <= 8e-7)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00026) or not (y <= 8e-7):
		tmp = x * math.cos(y)
	else:
		tmp = x - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00026) || !(y <= 8e-7))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00026) || ~((y <= 8e-7)))
		tmp = x * cos(y);
	else
		tmp = x - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00026], N[Not[LessEqual[y, 8e-7]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999977e-4 or 7.9999999999999996e-7 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 49.4%

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

   if -2.59999999999999977e-4 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00026 \lor \neg \left(y \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \]

Alternative 6: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.25e-8)
   (* z (- (sin y)))
   (if (<= y 8e-7) (- x (* z y)) (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.25e-8) {
		tmp = z * -sin(y);
	} else if (y <= 8e-7) {
		tmp = x - (z * 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 (y <= (-2.25d-8)) then
        tmp = z * -sin(y)
    else if (y <= 8d-7) then
        tmp = x - (z * 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 (y <= -2.25e-8) {
		tmp = z * -Math.sin(y);
	} else if (y <= 8e-7) {
		tmp = x - (z * y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.25e-8:
		tmp = z * -math.sin(y)
	elif y <= 8e-7:
		tmp = x - (z * y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.25e-8)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (y <= 8e-7)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.25e-8)
		tmp = z * -sin(y);
	elseif (y <= 8e-7)
		tmp = x - (z * y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.25e-8], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 8e-7], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.24999999999999996e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 63.5%

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

      1. neg-mul-1 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

   4. Simplified 63.5%

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

   if -2.24999999999999996e-8 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   if 7.9999999999999996e-7 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 56.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 7: 39.9% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 9.2e+65) x (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 9.2e+65) {
		tmp = x;
	} else {
		tmp = z * -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 <= 9.2d+65) then
        tmp = x
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 9.2e+65) {
		tmp = x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 9.2e+65:
		tmp = x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 9.2e+65)
		tmp = x;
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 9.2e+65)
		tmp = x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 9.2e+65], x, N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.2e65

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   4. Simplified 54.0%

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

   5. Taylor expanded in x around inf 43.2%

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

   if 9.2e65 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in x around 0 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

   7. Simplified 44.4%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 8: 52.3% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	return x - (z * y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 56.0%

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

   1. mul-1-neg 56.0%

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

   2. unsub-neg 56.0%

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

4. Simplified 56.0%

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

5. Final simplification 56.0%

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

Alternative 9: 38.5% 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. Taylor expanded in y around 0 56.0%

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

   1. mul-1-neg 56.0%

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

   2. unsub-neg 56.0%

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

4. Simplified 56.0%

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

5. Taylor expanded in x around inf 38.6%

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

6. Final simplification 38.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023287 
(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))))