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

Percentage Accurate: 99.8% → 99.8%

Time: 10.0s

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

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

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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 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. Add Preprocessing
3. Add Preprocessing

Alternative 3: 75.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(\cos y + 1\right) + -1\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+29)
   (* z (- (sin y)))
   (if (<= y 5.2e+34)
     (- (* x (+ (+ (cos y) 1.0) -1.0)) (* z y))
     (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+29) {
		tmp = z * -sin(y);
	} else if (y <= 5.2e+34) {
		tmp = (x * ((cos(y) + 1.0) + -1.0)) - (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 <= (-4.5d+29)) then
        tmp = z * -sin(y)
    else if (y <= 5.2d+34) then
        tmp = (x * ((cos(y) + 1.0d0) + (-1.0d0))) - (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 <= -4.5e+29) {
		tmp = z * -Math.sin(y);
	} else if (y <= 5.2e+34) {
		tmp = (x * ((Math.cos(y) + 1.0) + -1.0)) - (z * y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+29:
		tmp = z * -math.sin(y)
	elif y <= 5.2e+34:
		tmp = (x * ((math.cos(y) + 1.0) + -1.0)) - (z * y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+29)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (y <= 5.2e+34)
		tmp = Float64(Float64(x * Float64(Float64(cos(y) + 1.0) + -1.0)) - 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 <= -4.5e+29)
		tmp = z * -sin(y);
	elseif (y <= 5.2e+34)
		tmp = (x * ((cos(y) + 1.0) + -1.0)) - (z * y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+29], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 5.2e+34], N[(N[(x * N[(N[(N[Cos[y], $MachinePrecision] + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000002e29

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 57.6%

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

      1. neg-mul-1 57.6%

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

      2. *-commutative 57.6%

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

      3. distribute-rgt-neg-in 57.6%

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

   5. Simplified 57.6%

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

   if -4.5000000000000002e29 < y < 5.19999999999999995e34

   1. Initial program 99.9%

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

      1. expm1-log1p-u 99.9%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} - z \cdot \sin y \]

      2. expm1-undefine 99.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y\right)} - 1\right)} - z \cdot \sin y \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y\right)} - 1\right)} - z \cdot \sin y \]
   5. Step-by-step derivation

      1. expm1-define 99.9%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} - z \cdot \sin y \]

   6. Simplified 99.9%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} - z \cdot \sin y \]
   7. Step-by-step derivation

      1. expm1-undefine 99.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y\right)} - 1\right)} - z \cdot \sin y \]

      2. log1p-undefine 99.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log \left(1 + \cos y\right)}} - 1\right) - z \cdot \sin y \]

      3. rem-exp-log 99.9%

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

      4. +-commutative 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in y around 0 94.4%

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

       1. *-commutative 94.4%

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

   11. Simplified 94.4%

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

   if 5.19999999999999995e34 < y

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(\cos y + 1\right) + -1\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-55} \lor \neg \left(x \leq 6.1 \cdot 10^{-158}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e-55) (not (<= x 6.1e-158)))
   (* x (cos y))
   (* z (- (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e-55) || !(x <= 6.1e-158)) {
		tmp = x * cos(y);
	} else {
		tmp = z * -sin(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 ((x <= (-1.6d-55)) .or. (.not. (x <= 6.1d-158))) then
        tmp = x * cos(y)
    else
        tmp = z * -sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e-55) || !(x <= 6.1e-158)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = z * -Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e-55) or not (x <= 6.1e-158):
		tmp = x * math.cos(y)
	else:
		tmp = z * -math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e-55) || !(x <= 6.1e-158))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(z * Float64(-sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.6e-55) || ~((x <= 6.1e-158)))
		tmp = x * cos(y);
	else
		tmp = z * -sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e-55], N[Not[LessEqual[x, 6.1e-158]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e-55 or 6.0999999999999998e-158 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.5%

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

   if -1.6000000000000001e-55 < x < 6.0999999999999998e-158

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.9%

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

      1. neg-mul-1 75.9%

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

      2. *-commutative 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-55} \lor \neg \left(x \leq 6.1 \cdot 10^{-158}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0112 \lor \neg \left(y \leq 1350\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + \left(z \cdot y\right) \cdot 0.16666666666666666\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0112) (not (<= y 1350.0)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* (* z y) 0.16666666666666666))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0112) || !(y <= 1350.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + ((z * y) * 0.16666666666666666))) - 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 <= (-0.0112d0)) .or. (.not. (y <= 1350.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + ((z * y) * 0.16666666666666666d0))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0112) || !(y <= 1350.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + ((z * y) * 0.16666666666666666))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0112) or not (y <= 1350.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + ((z * y) * 0.16666666666666666))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0112) || !(y <= 1350.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(Float64(z * y) * 0.16666666666666666))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0112) || ~((y <= 1350.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + ((z * y) * 0.16666666666666666))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0112], N[Not[LessEqual[y, 1350.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0111999999999999999 or 1350 < y

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.9%

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

   if -0.0111999999999999999 < y < 1350

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.7%

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(-0.5 \cdot x + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0112 \lor \neg \left(y \leq 1350\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + \left(z \cdot y\right) \cdot 0.16666666666666666\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.5% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e-58) x (if (<= x 7.5e-201) (* z (- y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-58) {
		tmp = x;
	} else if (x <= 7.5e-201) {
		tmp = z * -y;
	} 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 (x <= (-4.8d-58)) then
        tmp = x
    else if (x <= 7.5d-201) then
        tmp = z * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-58) {
		tmp = x;
	} else if (x <= 7.5e-201) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e-58:
		tmp = x
	elif x <= 7.5e-201:
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e-58)
		tmp = x;
	elseif (x <= 7.5e-201)
		tmp = Float64(z * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e-58)
		tmp = x;
	elseif (x <= 7.5e-201)
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e-58], x, If[LessEqual[x, 7.5e-201], N[(z * (-y)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000001e-58 or 7.49999999999999987e-201 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.8%

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

   if -4.8000000000000001e-58 < x < 7.49999999999999987e-201

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in x around 0 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

      3. *-commutative 41.7%

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

   8. Simplified 41.7%

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

Alternative 7: 52.7% 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. Add Preprocessing

3. Taylor expanded in y around 0 54.2%

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

   1. mul-1-neg 54.2%

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

   2. unsub-neg 54.2%

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

   3. *-commutative 54.2%

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

5. Simplified 54.2%

   \[\leadsto \color{blue}{x - z \cdot y} \]
6. Add Preprocessing

Alternative 8: 39.0% 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. Add Preprocessing

3. Taylor expanded in y around 0 38.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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))))