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

Percentage Accurate: 99.8% → 99.8%

Time: 9.2s

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. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(z, -\sin y, x \cdot \cos y\right) \]
6. 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. Final simplification 99.8%

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

Alternative 3: 74.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.155 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+227)
   (* x (cos y))
   (if (or (<= y -0.155) (not (<= y 0.035)))
     (* z (- (sin y)))
     (+ x (* y (- (* y (* x -0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+227) {
		tmp = x * cos(y);
	} else if ((y <= -0.155) || !(y <= 0.035)) {
		tmp = z * -sin(y);
	} else {
		tmp = x + (y * ((y * (x * -0.5)) - 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 <= (-7.5d+227)) then
        tmp = x * cos(y)
    else if ((y <= (-0.155d0)) .or. (.not. (y <= 0.035d0))) then
        tmp = z * -sin(y)
    else
        tmp = x + (y * ((y * (x * (-0.5d0))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+227) {
		tmp = x * Math.cos(y);
	} else if ((y <= -0.155) || !(y <= 0.035)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + (y * ((y * (x * -0.5)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+227:
		tmp = x * math.cos(y)
	elif (y <= -0.155) or not (y <= 0.035):
		tmp = z * -math.sin(y)
	else:
		tmp = x + (y * ((y * (x * -0.5)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+227)
		tmp = Float64(x * cos(y));
	elseif ((y <= -0.155) || !(y <= 0.035))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(x * -0.5)) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.5e+227)
		tmp = x * cos(y);
	elseif ((y <= -0.155) || ~((y <= 0.035)))
		tmp = z * -sin(y);
	else
		tmp = x + (y * ((y * (x * -0.5)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+227], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -0.155], N[Not[LessEqual[y, 0.035]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000003e227

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 88.7%

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

   if -7.5000000000000003e227 < y < -0.154999999999999999 or 0.035000000000000003 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 58.7%

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

      1. neg-mul-1 58.7%

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

      2. distribute-rgt-neg-in 58.7%

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

   5. Simplified 58.7%

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

   if -0.154999999999999999 < y < 0.035000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. neg-mul-1 99.7%

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

      4. neg-mul-1 99.7%

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

      5. +-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. associate-*r* 99.7%

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

      8. *-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.155 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+61} \lor \neg \left(x \leq 0.27\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e+61) (not (<= x 0.27)))
   (* x (cos y))
   (- x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e+61) || !(x <= 0.27)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (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 <= (-1.55d+61)) .or. (.not. (x <= 0.27d0))) then
        tmp = x * cos(y)
    else
        tmp = x - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e+61) || !(x <= 0.27)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e+61) or not (x <= 0.27):
		tmp = x * math.cos(y)
	else:
		tmp = x - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e+61) || !(x <= 0.27))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55e+61) || ~((x <= 0.27)))
		tmp = x * cos(y);
	else
		tmp = x - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e+61], N[Not[LessEqual[x, 0.27]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e61 or 0.27000000000000002 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 88.2%

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

   if -1.55e61 < x < 0.27000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+61} \lor \neg \left(x \leq 0.27\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0105 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0105) (not (<= y 3.1e+51)))
   (* x (cos y))
   (+ x (* y (- (* y (* x -0.5)) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0105) || !(y <= 3.1e+51)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * (x * -0.5)) - 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 <= (-0.0105d0)) .or. (.not. (y <= 3.1d+51))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * (x * (-0.5d0))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0105) || !(y <= 3.1e+51)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * (x * -0.5)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0105) or not (y <= 3.1e+51):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * (x * -0.5)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0105) || !(y <= 3.1e+51))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(x * -0.5)) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0105) || ~((y <= 3.1e+51)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * (x * -0.5)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0105], N[Not[LessEqual[y, 3.1e+51]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0105000000000000007 or 3.10000000000000011e51 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 52.1%

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

   if -0.0105000000000000007 < y < 3.10000000000000011e51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. sub-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. neg-mul-1 95.2%

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

      4. neg-mul-1 95.2%

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

      5. +-commutative 95.2%

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

      6. sub-neg 95.2%

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

      7. associate-*r* 95.2%

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

      8. *-commutative 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0105 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.5% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+75} \lor \neg \left(z \leq 3.8 \cdot 10^{+169}\right) \land z \leq 8.7 \cdot 10^{+276}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.75e+75) (and (not (<= z 3.8e+169)) (<= z 8.7e+276)))
   (* z (- y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276))) {
		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 ((z <= (-1.75d+75)) .or. (.not. (z <= 3.8d+169)) .and. (z <= 8.7d+276)) 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 ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276))) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.75e+75) or (not (z <= 3.8e+169) and (z <= 8.7e+276)):
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276)))
		tmp = Float64(z * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.75e+75) || (~((z <= 3.8e+169)) && (z <= 8.7e+276)))
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.75e+75], And[N[Not[LessEqual[z, 3.8e+169]], $MachinePrecision], LessEqual[z, 8.7e+276]]], N[(z * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7499999999999999e75 or 3.79999999999999992e169 < z < 8.7000000000000003e276

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. neg-mul-1 74.6%

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

      2. distribute-rgt-neg-in 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around 0 35.2%

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

      1. associate-*r* 35.2%

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

      2. mul-1-neg 35.2%

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

   8. Simplified 35.2%

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

   if -1.7499999999999999e75 < z < 3.79999999999999992e169 or 8.7000000000000003e276 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 83.5%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around 0 49.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+75} \lor \neg \left(z \leq 3.8 \cdot 10^{+169}\right) \land z \leq 8.7 \cdot 10^{+276}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% 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 53.0%

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

   1. mul-1-neg 53.0%

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

   2. unsub-neg 53.0%

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

5. Simplified 53.0%

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

6. Final simplification 53.0%

   \[\leadsto x - z \cdot y \]
7. Add Preprocessing

Alternative 8: 38.7% 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 z around inf 88.8%

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

   1. associate-/l* 88.3%

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

5. Simplified 88.3%

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

6. Taylor expanded in y around 0 39.3%

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

7. Final simplification 39.3%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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))))