Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 12.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{y}{{z}^{-0.5}} + x\right) \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ (/ y (pow z -0.5)) x) 0.5))

C

double code(double x, double y, double z) {
	return ((y / pow(z, -0.5)) + x) * 0.5;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((y / (z ** (-0.5d0))) + x) * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return ((y / Math.pow(z, -0.5)) + x) * 0.5;
}

Python

def code(x, y, z):
	return ((y / math.pow(z, -0.5)) + x) * 0.5

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y / (z ^ -0.5)) + x) * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y / (z ^ -0.5)) + x) * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y / N[Power[z, -0.5], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]

10. Applied egg-rr 0

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 2: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ t_1 := \frac{y \cdot 0.5}{{z}^{-0.5}}\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))) (t_1 (/ (* y 0.5) (pow z -0.5))))
   (if (<= t_0 -100.0) t_1 (if (<= t_0 2e+32) (* x 0.5) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double t_1 = (y * 0.5) / pow(z, -0.5);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} 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 = y * sqrt(z)
    t_1 = (y * 0.5d0) / (z ** (-0.5d0))
    if (t_0 <= (-100.0d0)) then
        tmp = t_1
    else if (t_0 <= 2d+32) then
        tmp = x * 0.5d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.sqrt(z);
	double t_1 = (y * 0.5) / Math.pow(z, -0.5);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	t_1 = (y * 0.5) / math.pow(z, -0.5)
	tmp = 0
	if t_0 <= -100.0:
		tmp = t_1
	elif t_0 <= 2e+32:
		tmp = x * 0.5
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	t_1 = Float64(Float64(y * 0.5) / (z ^ -0.5))
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 2e+32)
		tmp = Float64(x * 0.5);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	t_1 = (y * 0.5) / (z ^ -0.5);
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 2e+32)
		tmp = x * 0.5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y * 0.5), $MachinePrecision] / N[Power[z, -0.5], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], t$95$1, If[LessEqual[t$95$0, 2e+32], N[(x * 0.5), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (sqrt.f64 z)) < -100 or 2.00000000000000011e32 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -100 < (*.f64 y (sqrt.f64 z)) < 2.00000000000000011e32

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;t\_0 \cdot 0.5\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{{z}^{-0.5}}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))))
   (if (<= t_0 -100.0)
     (* t_0 0.5)
     (if (<= t_0 2e+32) (* x 0.5) (/ 0.5 (/ (pow z -0.5) y))))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_0 * 0.5;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} else {
		tmp = 0.5 / (pow(z, -0.5) / 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) :: t_0
    real(8) :: tmp
    t_0 = y * sqrt(z)
    if (t_0 <= (-100.0d0)) then
        tmp = t_0 * 0.5d0
    else if (t_0 <= 2d+32) then
        tmp = x * 0.5d0
    else
        tmp = 0.5d0 / ((z ** (-0.5d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.sqrt(z);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_0 * 0.5;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} else {
		tmp = 0.5 / (Math.pow(z, -0.5) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	tmp = 0
	if t_0 <= -100.0:
		tmp = t_0 * 0.5
	elif t_0 <= 2e+32:
		tmp = x * 0.5
	else:
		tmp = 0.5 / (math.pow(z, -0.5) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = Float64(t_0 * 0.5);
	elseif (t_0 <= 2e+32)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(0.5 / Float64((z ^ -0.5) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = t_0 * 0.5;
	elseif (t_0 <= 2e+32)
		tmp = x * 0.5;
	else
		tmp = 0.5 / ((z ^ -0.5) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], N[(t$95$0 * 0.5), $MachinePrecision], If[LessEqual[t$95$0, 2e+32], N[(x * 0.5), $MachinePrecision], N[(0.5 / N[(N[Power[z, -0.5], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (sqrt.f64 z)) < -100

   1. Initial program 99.6%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -100 < (*.f64 y (sqrt.f64 z)) < 2.00000000000000011e32

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 2.00000000000000011e32 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ t_1 := t\_0 \cdot 0.5\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))) (t_1 (* t_0 0.5)))
   (if (<= t_0 -100.0) t_1 (if (<= t_0 2e+32) (* x 0.5) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double t_1 = t_0 * 0.5;
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} 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 = y * sqrt(z)
    t_1 = t_0 * 0.5d0
    if (t_0 <= (-100.0d0)) then
        tmp = t_1
    else if (t_0 <= 2d+32) then
        tmp = x * 0.5d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.sqrt(z);
	double t_1 = t_0 * 0.5;
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+32) {
		tmp = x * 0.5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	t_1 = t_0 * 0.5
	tmp = 0
	if t_0 <= -100.0:
		tmp = t_1
	elif t_0 <= 2e+32:
		tmp = x * 0.5
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	t_1 = Float64(t_0 * 0.5)
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 2e+32)
		tmp = Float64(x * 0.5);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	t_1 = t_0 * 0.5;
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 2e+32)
		tmp = x * 0.5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * 0.5), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], t$95$1, If[LessEqual[t$95$0, 2e+32], N[(x * 0.5), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (sqrt.f64 z)) < -100 or 2.00000000000000011e32 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -100 < (*.f64 y (sqrt.f64 z)) < 2.00000000000000011e32

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return 0.5 * (x + (y * sqrt(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 = 0.5d0 * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return 0.5 * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(0.5 * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(0.5 * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 6: 52.9% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.1 \cdot 10^{+183}:\\ \;\;\;\;\frac{-1}{0 - \frac{x}{z \cdot \left(y \cdot \left(y \cdot -0.5\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.1e+183) (/ -1.0 (- 0.0 (/ x (* z (* y (* y -0.5)))))) (* x 0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.1e+183) {
		tmp = -1.0 / (0.0 - (x / (z * (y * (y * -0.5)))));
	} else {
		tmp = x * 0.5;
	}
	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 <= (-8.1d+183)) then
        tmp = (-1.0d0) / (0.0d0 - (x / (z * (y * (y * (-0.5d0))))))
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.1e+183) {
		tmp = -1.0 / (0.0 - (x / (z * (y * (y * -0.5)))));
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.1e+183:
		tmp = -1.0 / (0.0 - (x / (z * (y * (y * -0.5)))))
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.1e+183)
		tmp = Float64(-1.0 / Float64(0.0 - Float64(x / Float64(z * Float64(y * Float64(y * -0.5))))));
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.1e+183)
		tmp = -1.0 / (0.0 - (x / (z * (y * (y * -0.5)))));
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.1e+183], N[(-1.0 / N[(0.0 - N[(x / N[(z * N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.09999999999999993e183

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   14. Applied egg-rr 0

       \[\leadsto expr\]

   if -8.09999999999999993e183 < y

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 52.8% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(z \cdot \left(\frac{x}{z} - \frac{y \cdot y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 6e+68) (* x 0.5) (* 0.5 (* z (- (/ x z) (/ (* y y) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 6e+68) {
		tmp = x * 0.5;
	} else {
		tmp = 0.5 * (z * ((x / z) - ((y * y) / 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 <= 6d+68) then
        tmp = x * 0.5d0
    else
        tmp = 0.5d0 * (z * ((x / z) - ((y * y) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 6e+68) {
		tmp = x * 0.5;
	} else {
		tmp = 0.5 * (z * ((x / z) - ((y * y) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 6e+68:
		tmp = x * 0.5
	else:
		tmp = 0.5 * (z * ((x / z) - ((y * y) / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 6e+68)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(0.5 * Float64(z * Float64(Float64(x / z) - Float64(Float64(y * y) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 6e+68)
		tmp = x * 0.5;
	else
		tmp = 0.5 * (z * ((x / z) - ((y * y) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 6e+68], N[(x * 0.5), $MachinePrecision], N[(0.5 * N[(z * N[(N[(x / z), $MachinePrecision] - N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.0000000000000004e68

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 6.0000000000000004e68 < z

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in z around inf 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 51.2% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+236}:\\ \;\;\;\;\frac{y \cdot -0.5}{x} \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+236) (* (/ (* y -0.5) x) (* y z)) (* x 0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+236) {
		tmp = ((y * -0.5) / x) * (y * z);
	} else {
		tmp = x * 0.5;
	}
	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 <= (-2.9d+236)) then
        tmp = ((y * (-0.5d0)) / x) * (y * z)
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+236) {
		tmp = ((y * -0.5) / x) * (y * z);
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e+236:
		tmp = ((y * -0.5) / x) * (y * z)
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+236)
		tmp = Float64(Float64(Float64(y * -0.5) / x) * Float64(y * z));
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.9e+236)
		tmp = ((y * -0.5) / x) * (y * z);
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+236], N[(N[(N[(y * -0.5), $MachinePrecision] / x), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000001e236

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   14. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.9000000000000001e236 < y

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 51.2% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+234}:\\ \;\;\;\;\left(z \cdot -0.5\right) \cdot \frac{y}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+234) (* (* z -0.5) (/ y (/ x y))) (* x 0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+234) {
		tmp = (z * -0.5) * (y / (x / y));
	} else {
		tmp = x * 0.5;
	}
	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 <= (-2.8d+234)) then
        tmp = (z * (-0.5d0)) * (y / (x / y))
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+234) {
		tmp = (z * -0.5) * (y / (x / y));
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+234:
		tmp = (z * -0.5) * (y / (x / y))
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+234)
		tmp = Float64(Float64(z * -0.5) * Float64(y / Float64(x / y)));
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+234)
		tmp = (z * -0.5) * (y / (x / y));
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+234], N[(N[(z * -0.5), $MachinePrecision] * N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999998e234

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   14. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.7999999999999998e234 < y

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 51.2% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+235}:\\ \;\;\;\;\left(y \cdot \left(y \cdot -0.5\right)\right) \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+235) (* (* y (* y -0.5)) (/ z x)) (* x 0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+235) {
		tmp = (y * (y * -0.5)) * (z / x);
	} else {
		tmp = x * 0.5;
	}
	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 <= (-3.8d+235)) then
        tmp = (y * (y * (-0.5d0))) * (z / x)
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+235) {
		tmp = (y * (y * -0.5)) * (z / x);
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+235:
		tmp = (y * (y * -0.5)) * (z / x)
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+235)
		tmp = Float64(Float64(y * Float64(y * -0.5)) * Float64(z / x));
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+235)
		tmp = (y * (y * -0.5)) * (z / x);
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+235], N[(N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999975e235

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   14. Applied egg-rr 0

       \[\leadsto expr\]

   if -3.79999999999999975e235 < y

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.7% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 0.5))

C

double code(double x, double y, double z) {
	return x * 0.5;
}

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 * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 0.5;
}

Python

def code(x, y, z):
	return x * 0.5

Julia

function code(x, y, z)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))