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

Percentage Accurate: 99.8% → 99.8%

Time: 10.2s

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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \left(x \cdot \cos y + \mathsf{fma}\left(-z, \sin y, t_0\right)\right) - t_0 \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (- (+ (* x (cos y)) (fma (- z) (sin y) t_0)) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	return ((x * cos(y)) + fma(-z, sin(y), t_0)) - t_0;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	return Float64(Float64(Float64(x * cos(y)) + fma(Float64(-z), sin(y), t_0)) - t_0)
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[((-z) * N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. prod-diff 99.8%

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

   3. fma-def 99.8%

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

   4. +-commutative 99.8%

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

   5. associate-+l+ 99.8%

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

   6. distribute-rgt-neg-in 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

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. Final simplification 99.8%

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

Alternative 3: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -1 \cdot 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.001:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 0.0125:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= y -1e+172)
     t_0
     (if (<= y -0.001)
       (* z (- (sin y)))
       (if (<= y 0.0125) (- x (* z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (y <= -1e+172) {
		tmp = t_0;
	} else if (y <= -0.001) {
		tmp = z * -sin(y);
	} else if (y <= 0.0125) {
		tmp = x - (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * cos(y)
    if (y <= (-1d+172)) then
        tmp = t_0
    else if (y <= (-0.001d0)) then
        tmp = z * -sin(y)
    else if (y <= 0.0125d0) then
        tmp = x - (z * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double tmp;
	if (y <= -1e+172) {
		tmp = t_0;
	} else if (y <= -0.001) {
		tmp = z * -Math.sin(y);
	} else if (y <= 0.0125) {
		tmp = x - (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if y <= -1e+172:
		tmp = t_0
	elif y <= -0.001:
		tmp = z * -math.sin(y)
	elif y <= 0.0125:
		tmp = x - (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -1e+172)
		tmp = t_0;
	elseif (y <= -0.001)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (y <= 0.0125)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (y <= -1e+172)
		tmp = t_0;
	elseif (y <= -0.001)
		tmp = z * -sin(y);
	elseif (y <= 0.0125)
		tmp = x - (z * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+172], t$95$0, If[LessEqual[y, -0.001], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 0.0125], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e172 or 0.012500000000000001 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 55.0%

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

   if -1.0000000000000001e172 < y < -1e-3

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 59.9%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

      3. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   if -1e-3 < y < 0.012500000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. sub-neg 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.001:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 0.0125:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 85.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-141} \lor \neg \left(z \leq 7.2 \cdot 10^{-134}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-141) (not (<= z 7.2e-134)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-141) || !(z <= 7.2e-134)) {
		tmp = x - (z * sin(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 ((z <= (-3.4d-141)) .or. (.not. (z <= 7.2d-134))) then
        tmp = x - (z * sin(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 ((z <= -3.4e-141) || !(z <= 7.2e-134)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-141) or not (z <= 7.2e-134):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-141) || !(z <= 7.2e-134))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e-141) || ~((z <= 7.2e-134)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-141], N[Not[LessEqual[z, 7.2e-134]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999998e-141 or 7.1999999999999998e-134 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 88.4%

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

   if -3.3999999999999998e-141 < z < 7.1999999999999998e-134

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-141} \lor \neg \left(z \leq 7.2 \cdot 10^{-134}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 5: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-5} \lor \neg \left(y \leq 0.096\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.75e-5) (not (<= y 0.096))) (* x (cos y)) (- x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.75e-5) || !(y <= 0.096)) {
		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 <= (-1.75d-5)) .or. (.not. (y <= 0.096d0))) 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 <= -1.75e-5) || !(y <= 0.096)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.75e-5) or not (y <= 0.096):
		tmp = x * math.cos(y)
	else:
		tmp = x - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.75e-5) || !(y <= 0.096))
		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 <= -1.75e-5) || ~((y <= 0.096)))
		tmp = x * cos(y);
	else
		tmp = x - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.75e-5], N[Not[LessEqual[y, 0.096]], $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 < -1.7499999999999998e-5 or 0.096000000000000002 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 50.6%

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

   if -1.7499999999999998e-5 < y < 0.096000000000000002

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. sub-neg 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-5} \lor \neg \left(y \leq 0.096\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \]

Alternative 6: 40.1% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+244}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 3.4e+244) x (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.4e+244) {
		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 <= 3.4d+244) 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 <= 3.4e+244) {
		tmp = x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.4e+244:
		tmp = x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.4e+244)
		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 <= 3.4e+244)
		tmp = x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.4e+244], x, N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.4000000000000001e244

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in x around inf 48.3%

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

   if 3.4000000000000001e244 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 59.3%

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

      1. mul-1-neg 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in x around 0 59.3%

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

      1. *-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. sub-neg 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in x around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

   10. Simplified 52.2%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+244}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 7: 52.6% 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 57.0%

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

   1. mul-1-neg 57.0%

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

4. Simplified 57.0%

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

5. Taylor expanded in x around 0 57.0%

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

   1. *-commutative 57.0%

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

   2. mul-1-neg 57.0%

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

   3. sub-neg 57.0%

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

7. Simplified 57.0%

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

8. Final simplification 57.0%

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

Alternative 8: 38.8% 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 57.0%

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

   1. mul-1-neg 57.0%

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

4. Simplified 57.0%

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

5. Taylor expanded in x around inf 46.2%

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

6. Final simplification 46.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023326 
(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))))