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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

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, 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 2: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot \cos y\right) \cdot {1}^{0.3333333333333333}\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x (cos y)) (pow 1.0 0.3333333333333333))))
   (if (<= x -5.8e+223) t_0 (if (<= x 6.5e+112) (fma (sin y) (- z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * cos(y)) * pow(1.0, 0.3333333333333333);
	double tmp;
	if (x <= -5.8e+223) {
		tmp = t_0;
	} else if (x <= 6.5e+112) {
		tmp = fma(sin(y), -z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * cos(y)) * (1.0 ^ 0.3333333333333333))
	tmp = 0.0
	if (x <= -5.8e+223)
		tmp = t_0;
	elseif (x <= 6.5e+112)
		tmp = fma(sin(y), Float64(-z), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Power[1.0, 0.3333333333333333], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+223], t$95$0, If[LessEqual[x, 6.5e+112], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000004e223 or 6.4999999999999998e112 < x

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.1%

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

      2. pow3 98.1%

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

   3. Applied egg-rr 98.1%

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

   4. Taylor expanded in y around 0 80.6%

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

   5. Taylor expanded in z around 0 94.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\cos y \cdot x\right)} \]

   if -5.8000000000000004e223 < x < 6.4999999999999998e112

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 86.1%

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

   3. Taylor expanded in x around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. *-commutative 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. fma-udef 86.1%

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

   5. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+223}:\\ \;\;\;\;\left(x \cdot \cos y\right) \cdot {1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \cos y\right) \cdot {1}^{0.3333333333333333}\\ \end{array} \]

Alternative 3: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.8e+160) (fma (sin y) (- z) x) (- (* x (cos y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.8e+160) {
		tmp = fma(sin(y), -z, x);
	} else {
		tmp = (x * cos(y)) - (y * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.8e+160)
		tmp = fma(sin(y), Float64(-z), x);
	else
		tmp = Float64(Float64(x * cos(y)) - Float64(y * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.8e+160], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.8e160

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 84.2%

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

   3. Taylor expanded in x around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. *-commutative 84.2%

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

      3. distribute-rgt-neg-in 84.2%

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

      4. fma-udef 84.2%

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

   5. Simplified 84.2%

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

   if 2.8e160 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.2%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \end{array} \]

Alternative 4: 80.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5.5e+156) (- x (* z (sin y))) (- (* x (cos y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.5e+156) {
		tmp = x - (z * sin(y));
	} else {
		tmp = (x * cos(y)) - (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 (x <= 5.5d+156) then
        tmp = x - (z * sin(y))
    else
        tmp = (x * cos(y)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.5e+156) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = (x * Math.cos(y)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5.5e+156:
		tmp = x - (z * math.sin(y))
	else:
		tmp = (x * math.cos(y)) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5.5e+156)
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(x * cos(y)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5.5e+156)
		tmp = x - (z * sin(y));
	else
		tmp = (x * cos(y)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5.5e+156], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.5000000000000003e156

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 84.2%

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

   if 5.5000000000000003e156 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.2%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \end{array} \]

Alternative 5: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 0.00062\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot y\right) \cdot \left(x \cdot -0.5\right)\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-6) (not (<= y 0.00062)))
   (* (sin y) (- z))
   (- (+ x (* (* y y) (* x -0.5))) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-6) || !(y <= 0.00062)) {
		tmp = sin(y) * -z;
	} else {
		tmp = (x + ((y * y) * (x * -0.5))) - (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 <= (-6.2d-6)) .or. (.not. (y <= 0.00062d0))) then
        tmp = sin(y) * -z
    else
        tmp = (x + ((y * y) * (x * (-0.5d0)))) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-6) || !(y <= 0.00062)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = (x + ((y * y) * (x * -0.5))) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-6) or not (y <= 0.00062):
		tmp = math.sin(y) * -z
	else:
		tmp = (x + ((y * y) * (x * -0.5))) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-6) || !(y <= 0.00062))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * y) * Float64(x * -0.5))) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e-6) || ~((y <= 0.00062)))
		tmp = sin(y) * -z;
	else
		tmp = (x + ((y * y) * (x * -0.5))) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-6], N[Not[LessEqual[y, 0.00062]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(N[(x + N[(N[(y * y), $MachinePrecision] * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999999e-6 or 6.2e-4 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 62.1%

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

   3. Taylor expanded in x around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. *-commutative 58.8%

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

      3. distribute-rgt-neg-in 58.8%

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

   5. Simplified 58.8%

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

   if -6.1999999999999999e-6 < y < 6.2e-4

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.3%

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

      2. pow3 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in y around 0 97.9%

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

   5. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{\left({1}^{0.3333333333333333} \cdot x + \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \cdot {y}^{2}\right)} - y \cdot z \]
   6. Step-by-step derivation

      1. pow-base-1 99.6%

         \[\leadsto \left(\color{blue}{1} \cdot x + \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \cdot {y}^{2}\right) - y \cdot z \]

      2. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{x} + \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \cdot {y}^{2}\right) - y \cdot z \]

      3. *-commutative 99.6%

         \[\leadsto \left(x + \color{blue}{{y}^{2} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right)}\right) - y \cdot z \]

      4. unpow2 99.6%

         \[\leadsto \left(x + \color{blue}{\left(y \cdot y\right)} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right)\right) - y \cdot z \]

      5. distribute-rgt-out 99.6%

         \[\leadsto \left(x + \left(y \cdot y\right) \cdot \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot x\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)}\right) - y \cdot z \]

      6. pow-base-1 99.6%

         \[\leadsto \left(x + \left(y \cdot y\right) \cdot \left(\left(\color{blue}{1} \cdot x\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)\right) - y \cdot z \]

      7. *-lft-identity 99.6%

         \[\leadsto \left(x + \left(y \cdot y\right) \cdot \left(\color{blue}{x} \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)\right) - y \cdot z \]

      8. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 0.00062\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot y\right) \cdot \left(x \cdot -0.5\right)\right) - y \cdot z\\ \end{array} \]

Alternative 6: 77.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 81.8%

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

3. Final simplification 81.8%

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

Alternative 7: 41.9% accurate, 20.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+91} \lor \neg \left(z \leq 1.3 \cdot 10^{+118}\right) \land z \leq 3.6 \cdot 10^{+303}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e+91) (and (not (<= z 1.3e+118)) (<= z 3.6e+303)))
   (* y (- z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+91) || (!(z <= 1.3e+118) && (z <= 3.6e+303))) {
		tmp = y * -z;
	} else {
		tmp = 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 <= (-3.2d+91)) .or. (.not. (z <= 1.3d+118)) .and. (z <= 3.6d+303)) then
        tmp = y * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+91) || (!(z <= 1.3e+118) && (z <= 3.6e+303))) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e+91) or (not (z <= 1.3e+118) and (z <= 3.6e+303)):
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e+91) || (!(z <= 1.3e+118) && (z <= 3.6e+303)))
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.2e+91) || (~((z <= 1.3e+118)) && (z <= 3.6e+303)))
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e+91], And[N[Not[LessEqual[z, 1.3e+118]], $MachinePrecision], LessEqual[z, 3.6e+303]]], N[(y * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999989e91 or 1.30000000000000008e118 < z < 3.6000000000000001e303

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.3%

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

      2. pow3 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around 0 49.4%

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

   5. Taylor expanded in x around 0 34.9%

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

      1. associate-*r* 34.9%

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

      2. neg-mul-1 34.9%

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

      3. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   if -3.19999999999999989e91 < z < 1.30000000000000008e118 or 3.6000000000000001e303 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 78.5%

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

   3. Taylor expanded in x around inf 51.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+91} \lor \neg \left(z \leq 1.3 \cdot 10^{+118}\right) \land z \leq 3.6 \cdot 10^{+303}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 53.9% 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 81.8%

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

3. Taylor expanded in y around 0 55.0%

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

   1. +-commutative 55.0%

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

   2. mul-1-neg 55.0%

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

   3. unsub-neg 55.0%

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

   4. *-commutative 55.0%

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

5. Simplified 55.0%

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

6. Final simplification 55.0%

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

Alternative 9: 39.2% 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 81.8%

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

3. Taylor expanded in x around inf 41.4%

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

4. Final simplification 41.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023185 
(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))))