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

Percentage Accurate: 99.8% → 99.8%

Time: 13.1s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e-26)
   (fma x (sin y) z)
   (if (<= x 1.15e-126) (* z (cos y)) (+ (* x (sin y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-26) {
		tmp = fma(x, sin(y), z);
	} else if (x <= 1.15e-126) {
		tmp = z * cos(y);
	} else {
		tmp = (x * sin(y)) + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e-26)
		tmp = fma(x, sin(y), z);
	elseif (x <= 1.15e-126)
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x * sin(y)) + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e-26], N[(x * N[Sin[y], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 1.15e-126], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2000000000000001e-26

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 88.5%

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

   if -3.2000000000000001e-26 < x < 1.15000000000000005e-126

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 90.3%

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

   if 1.15000000000000005e-126 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 90.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]

Alternative 3: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := x \cdot \sin y\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.19:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;x \cdot y + \left(z + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* x (sin y))))
   (if (<= y -3.9e+119)
     t_0
     (if (<= y -0.19)
       t_1
       (if (<= y 0.0004)
         (+ (* x y) (+ z (* -0.5 (* z (* y y)))))
         (if (<= y 2.6e+63) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = x * sin(y);
	double tmp;
	if (y <= -3.9e+119) {
		tmp = t_0;
	} else if (y <= -0.19) {
		tmp = t_1;
	} else if (y <= 0.0004) {
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	} else if (y <= 2.6e+63) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = z * cos(y)
    t_1 = x * sin(y)
    if (y <= (-3.9d+119)) then
        tmp = t_0
    else if (y <= (-0.19d0)) then
        tmp = t_1
    else if (y <= 0.0004d0) then
        tmp = (x * y) + (z + ((-0.5d0) * (z * (y * y))))
    else if (y <= 2.6d+63) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double t_1 = x * Math.sin(y);
	double tmp;
	if (y <= -3.9e+119) {
		tmp = t_0;
	} else if (y <= -0.19) {
		tmp = t_1;
	} else if (y <= 0.0004) {
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	} else if (y <= 2.6e+63) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = x * math.sin(y)
	tmp = 0
	if y <= -3.9e+119:
		tmp = t_0
	elif y <= -0.19:
		tmp = t_1
	elif y <= 0.0004:
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))))
	elif y <= 2.6e+63:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -3.9e+119)
		tmp = t_0;
	elseif (y <= -0.19)
		tmp = t_1;
	elseif (y <= 0.0004)
		tmp = Float64(Float64(x * y) + Float64(z + Float64(-0.5 * Float64(z * Float64(y * y)))));
	elseif (y <= 2.6e+63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = x * sin(y);
	tmp = 0.0;
	if (y <= -3.9e+119)
		tmp = t_0;
	elseif (y <= -0.19)
		tmp = t_1;
	elseif (y <= 0.0004)
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	elseif (y <= 2.6e+63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+119], t$95$0, If[LessEqual[y, -0.19], t$95$1, If[LessEqual[y, 0.0004], N[(N[(x * y), $MachinePrecision] + N[(z + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+63], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8999999999999998e119 or 4.00000000000000019e-4 < y < 2.6000000000000001e63

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 66.9%

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

   if -3.8999999999999998e119 < y < -0.19 or 2.6000000000000001e63 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 61.9%

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

   if -0.19 < y < 4.00000000000000019e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \sin y + \color{blue}{\left(z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto x \cdot \sin y + \left(z + -0.5 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right) \]

      2. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -0.19:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;x \cdot y + \left(z + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.3 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-26) (not (<= x 1.3e-126)))
   (+ (* x (sin y)) z)
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-26) || !(x <= 1.3e-126)) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = z * 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 ((x <= (-5.8d-26)) .or. (.not. (x <= 1.3d-126))) then
        tmp = (x * sin(y)) + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-26) || !(x <= 1.3e-126)) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-26) or not (x <= 1.3e-126):
		tmp = (x * math.sin(y)) + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-26) || !(x <= 1.3e-126))
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e-26) || ~((x <= 1.3e-126)))
		tmp = (x * sin(y)) + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-26], N[Not[LessEqual[x, 1.3e-126]], $MachinePrecision]], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999996e-26 or 1.3e-126 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.3%

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

   if -5.7999999999999996e-26 < x < 1.3e-126

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 90.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.3 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 75.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0057 \lor \neg \left(y \leq 0.0046\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0057) (not (<= y 0.0046)))
   (* x (sin y))
   (+ (* x y) (+ z (* -0.5 (* z (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0057) || !(y <= 0.0046)) {
		tmp = x * sin(y);
	} else {
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.0057d0)) .or. (.not. (y <= 0.0046d0))) then
        tmp = x * sin(y)
    else
        tmp = (x * y) + (z + ((-0.5d0) * (z * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0057) || !(y <= 0.0046)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0057) or not (y <= 0.0046):
		tmp = x * math.sin(y)
	else:
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0057) || !(y <= 0.0046))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(Float64(x * y) + Float64(z + Float64(-0.5 * Float64(z * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0057) || ~((y <= 0.0046)))
		tmp = x * sin(y);
	else
		tmp = (x * y) + (z + (-0.5 * (z * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0057], N[Not[LessEqual[y, 0.0046]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0057000000000000002 or 0.0045999999999999999 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.2%

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

   if -0.0057000000000000002 < y < 0.0045999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \sin y + \color{blue}{\left(z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto x \cdot \sin y + \left(z + -0.5 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right) \]

      2. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0057 \lor \neg \left(y \leq 0.0046\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 6: 53.1% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.2%

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

   1. *-commutative 53.2%

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

4. Simplified 53.2%

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

5. Final simplification 53.2%

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

Alternative 7: 39.6% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.2%

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

   1. *-commutative 53.2%

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

4. Simplified 53.2%

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

5. Taylor expanded in z around inf 33.9%

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

6. Final simplification 33.9%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))