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

Percentage Accurate: 99.8% → 99.8%

Time: 8.5s

Alternatives: 8

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 79.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* z (+ 1.0 (* x (/ (sin y) z))))))
   (if (<= z -9e+74)
     t_0
     (if (<= z -3.8e-285)
       t_1
       (if (<= z 4.2e-204) (* x (sin y)) (if (<= z 3e+148) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = z * (1.0 + (x * (sin(y) / z)));
	double tmp;
	if (z <= -9e+74) {
		tmp = t_0;
	} else if (z <= -3.8e-285) {
		tmp = t_1;
	} else if (z <= 4.2e-204) {
		tmp = x * sin(y);
	} else if (z <= 3e+148) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * cos(y)
    t_1 = z * (1.0d0 + (x * (sin(y) / z)))
    if (z <= (-9d+74)) then
        tmp = t_0
    else if (z <= (-3.8d-285)) then
        tmp = t_1
    else if (z <= 4.2d-204) then
        tmp = x * sin(y)
    else if (z <= 3d+148) then
        tmp = t_1
    else
        tmp = t_0
    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 = z * (1.0 + (x * (Math.sin(y) / z)));
	double tmp;
	if (z <= -9e+74) {
		tmp = t_0;
	} else if (z <= -3.8e-285) {
		tmp = t_1;
	} else if (z <= 4.2e-204) {
		tmp = x * Math.sin(y);
	} else if (z <= 3e+148) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = z * (1.0 + (x * (math.sin(y) / z)))
	tmp = 0
	if z <= -9e+74:
		tmp = t_0
	elif z <= -3.8e-285:
		tmp = t_1
	elif z <= 4.2e-204:
		tmp = x * math.sin(y)
	elif z <= 3e+148:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(z * Float64(1.0 + Float64(x * Float64(sin(y) / z))))
	tmp = 0.0
	if (z <= -9e+74)
		tmp = t_0;
	elseif (z <= -3.8e-285)
		tmp = t_1;
	elseif (z <= 4.2e-204)
		tmp = Float64(x * sin(y));
	elseif (z <= 3e+148)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = z * (1.0 + (x * (sin(y) / z)));
	tmp = 0.0;
	if (z <= -9e+74)
		tmp = t_0;
	elseif (z <= -3.8e-285)
		tmp = t_1;
	elseif (z <= 4.2e-204)
		tmp = x * sin(y);
	elseif (z <= 3e+148)
		tmp = t_1;
	else
		tmp = t_0;
	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[(z * N[(1.0 + N[(x * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+74], t$95$0, If[LessEqual[z, -3.8e-285], t$95$1, If[LessEqual[z, 4.2e-204], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+148], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e74 or 3.00000000000000015e148 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.1%

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

   if -8.9999999999999999e74 < z < -3.8000000000000002e-285 or 4.20000000000000018e-204 < z < 3.00000000000000015e148

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.7%

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

      2. pow3 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in y around 0 87.3%

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

   6. Taylor expanded in z around inf 80.6%

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

      1. associate-*r/ 80.5%

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

   8. Simplified 80.5%

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

   if -3.8000000000000002e-285 < z < 4.20000000000000018e-204

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 84.1%

      \[\leadsto \color{blue}{x \cdot \sin y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+81} \lor \neg \left(x \leq 3.3 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+81) (not (<= x 3.3e+59))) (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+81) || !(x <= 3.3e+59)) {
		tmp = x * sin(y);
	} 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 <= (-5.2d+81)) .or. (.not. (x <= 3.3d+59))) then
        tmp = x * sin(y)
    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 <= -5.2e+81) || !(x <= 3.3e+59)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+81) or not (x <= 3.3e+59):
		tmp = x * math.sin(y)
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+81) || !(x <= 3.3e+59))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.2e+81) || ~((x <= 3.3e+59)))
		tmp = x * sin(y);
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+81], N[Not[LessEqual[x, 3.3e+59]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999984e81 or 3.2999999999999999e59 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.8%

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

   if -5.19999999999999984e81 < x < 3.2999999999999999e59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+81} \lor \neg \left(x \leq 3.3 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.053 \lor \neg \left(y \leq 0.038\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.053) (not (<= y 0.038)))
   (* x (sin y))
   (+ z (* y (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.053) || !(y <= 0.038)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * 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 <= (-0.053d0)) .or. (.not. (y <= 0.038d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.053) || !(y <= 0.038)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.053) or not (y <= 0.038):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.053) || !(y <= 0.038))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.053) || ~((y <= 0.038)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.053], N[Not[LessEqual[y, 0.038]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0529999999999999985 or 0.0379999999999999991 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -0.0529999999999999985 < y < 0.0379999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.053 \lor \neg \left(y \leq 0.038\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.6% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 1.5e+140) z (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+140) {
		tmp = z;
	} else {
		tmp = x * 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 <= 1.5d+140) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+140) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.5e+140:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.5e+140)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.5e+140)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.5e+140], z, N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.49999999999999998e140

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 53.8%

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

      1. +-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in x around 0 44.3%

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

   if 1.49999999999999998e140 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 48.1%

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

   7. Taylor expanded in x around inf 40.9%

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

Alternative 7: 51.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 53.0%

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

   1. +-commutative 53.0%

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

5. Simplified 53.0%

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

6. Final simplification 53.0%

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

Alternative 8: 38.2% 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. Add Preprocessing

3. Taylor expanded in y around 0 53.0%

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

   1. +-commutative 53.0%

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

5. Simplified 53.0%

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

6. Taylor expanded in x around 0 39.2%

   \[\leadsto \color{blue}{z} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(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))))