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

Percentage Accurate: 99.8% → 99.8%

Time: 6.4s

Alternatives: 6

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. distribute-rgt-in 99.5%

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

   2. +-commutative 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-*l* 99.8%

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

   5. *-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 75.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{z} \cdot y\\ \mathbf{if}\;t_0 \leq -3.8 \cdot 10^{+34} \lor \neg \left(t_0 \leq 1.1 \cdot 10^{-49} \lor \neg \left(t_0 \leq 11200\right) \land t_0 \leq 6.2 \cdot 10^{+70}\right):\\ \;\;\;\;0.5 \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sqrt z) y)))
   (if (or (<= t_0 -3.8e+34)
           (not
            (or (<= t_0 1.1e-49)
                (and (not (<= t_0 11200.0)) (<= t_0 6.2e+70)))))
     (* 0.5 t_0)
     (* 0.5 x))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(z) * y;
	double tmp;
	if ((t_0 <= -3.8e+34) || !((t_0 <= 1.1e-49) || (!(t_0 <= 11200.0) && (t_0 <= 6.2e+70)))) {
		tmp = 0.5 * t_0;
	} else {
		tmp = 0.5 * 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) :: t_0
    real(8) :: tmp
    t_0 = sqrt(z) * y
    if ((t_0 <= (-3.8d+34)) .or. (.not. (t_0 <= 1.1d-49) .or. (.not. (t_0 <= 11200.0d0)) .and. (t_0 <= 6.2d+70))) then
        tmp = 0.5d0 * t_0
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sqrt(z) * y;
	double tmp;
	if ((t_0 <= -3.8e+34) || !((t_0 <= 1.1e-49) || (!(t_0 <= 11200.0) && (t_0 <= 6.2e+70)))) {
		tmp = 0.5 * t_0;
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sqrt(z) * y
	tmp = 0
	if (t_0 <= -3.8e+34) or not ((t_0 <= 1.1e-49) or (not (t_0 <= 11200.0) and (t_0 <= 6.2e+70))):
		tmp = 0.5 * t_0
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sqrt(z) * y)
	tmp = 0.0
	if ((t_0 <= -3.8e+34) || !((t_0 <= 1.1e-49) || (!(t_0 <= 11200.0) && (t_0 <= 6.2e+70))))
		tmp = Float64(0.5 * t_0);
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sqrt(z) * y;
	tmp = 0.0;
	if ((t_0 <= -3.8e+34) || ~(((t_0 <= 1.1e-49) || (~((t_0 <= 11200.0)) && (t_0 <= 6.2e+70)))))
		tmp = 0.5 * t_0;
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sqrt[z], $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -3.8e+34], N[Not[Or[LessEqual[t$95$0, 1.1e-49], And[N[Not[LessEqual[t$95$0, 11200.0]], $MachinePrecision], LessEqual[t$95$0, 6.2e+70]]]], $MachinePrecision]], N[(0.5 * t$95$0), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (sqrt.f64 z)) < -3.8000000000000001e34 or 1.09999999999999995e-49 < (*.f64 y (sqrt.f64 z)) < 11200 or 6.2000000000000006e70 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.0%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around 0 85.9%

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

   if -3.8000000000000001e34 < (*.f64 y (sqrt.f64 z)) < 1.09999999999999995e-49 or 11200 < (*.f64 y (sqrt.f64 z)) < 6.2000000000000006e70

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.7%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{z} \cdot y \leq -3.8 \cdot 10^{+34} \lor \neg \left(\sqrt{z} \cdot y \leq 1.1 \cdot 10^{-49} \lor \neg \left(\sqrt{z} \cdot y \leq 11200\right) \land \sqrt{z} \cdot y \leq 6.2 \cdot 10^{+70}\right):\\ \;\;\;\;0.5 \cdot \left(\sqrt{z} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{z} \cdot y\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{-57} \lor \neg \left(t_0 \leq 5000\right) \land t_0 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sqrt z) y)))
   (if (<= t_0 -2e+41)
     (* (sqrt z) (* y 0.5))
     (if (or (<= t_0 4e-57) (and (not (<= t_0 5000.0)) (<= t_0 5e+70)))
       (* 0.5 x)
       (* 0.5 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(z) * y;
	double tmp;
	if (t_0 <= -2e+41) {
		tmp = sqrt(z) * (y * 0.5);
	} else if ((t_0 <= 4e-57) || (!(t_0 <= 5000.0) && (t_0 <= 5e+70))) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * 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 = sqrt(z) * y
    if (t_0 <= (-2d+41)) then
        tmp = sqrt(z) * (y * 0.5d0)
    else if ((t_0 <= 4d-57) .or. (.not. (t_0 <= 5000.0d0)) .and. (t_0 <= 5d+70)) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sqrt(z) * y;
	double tmp;
	if (t_0 <= -2e+41) {
		tmp = Math.sqrt(z) * (y * 0.5);
	} else if ((t_0 <= 4e-57) || (!(t_0 <= 5000.0) && (t_0 <= 5e+70))) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sqrt(z) * y
	tmp = 0
	if t_0 <= -2e+41:
		tmp = math.sqrt(z) * (y * 0.5)
	elif (t_0 <= 4e-57) or (not (t_0 <= 5000.0) and (t_0 <= 5e+70)):
		tmp = 0.5 * x
	else:
		tmp = 0.5 * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sqrt(z) * y)
	tmp = 0.0
	if (t_0 <= -2e+41)
		tmp = Float64(sqrt(z) * Float64(y * 0.5));
	elseif ((t_0 <= 4e-57) || (!(t_0 <= 5000.0) && (t_0 <= 5e+70)))
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sqrt(z) * y;
	tmp = 0.0;
	if (t_0 <= -2e+41)
		tmp = sqrt(z) * (y * 0.5);
	elseif ((t_0 <= 4e-57) || (~((t_0 <= 5000.0)) && (t_0 <= 5e+70)))
		tmp = 0.5 * x;
	else
		tmp = 0.5 * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sqrt[z], $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+41], N[(N[Sqrt[z], $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, 4e-57], And[N[Not[LessEqual[t$95$0, 5000.0]], $MachinePrecision], LessEqual[t$95$0, 5e+70]]], N[(0.5 * x), $MachinePrecision], N[(0.5 * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (sqrt.f64 z)) < -2.00000000000000001e41

   1. Initial program 97.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around 0 85.5%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 1.0%

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

      3. *-commutative 1.0%

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

      4. *-commutative 1.0%

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

      5. swap-sqr 0.9%

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

      6. add-sqr-sqrt 0.9%

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

   6. Applied egg-rr 0.9%

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

      1. *-commutative 0.9%

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

      2. associate-*l* 1.0%

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

   8. Simplified 1.0%

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

   9. Taylor expanded in y around 0 85.5%

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

       1. associate-*r* 87.3%

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

       2. *-commutative 87.3%

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

       3. *-commutative 87.3%

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

   11. Simplified 87.3%

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

   if -2.00000000000000001e41 < (*.f64 y (sqrt.f64 z)) < 3.99999999999999982e-57 or 5e3 < (*.f64 y (sqrt.f64 z)) < 5.0000000000000002e70

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.7%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 3.99999999999999982e-57 < (*.f64 y (sqrt.f64 z)) < 5e3 or 5.0000000000000002e70 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 86.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{z} \cdot y \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;\sqrt{z} \cdot y \leq 4 \cdot 10^{-57} \lor \neg \left(\sqrt{z} \cdot y \leq 5000\right) \land \sqrt{z} \cdot y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\sqrt{z} \cdot y\right)\\ \end{array} \]

Alternative 4: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{z} \cdot y\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{-57}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;t_0 \leq 5000:\\ \;\;\;\;0.5 \cdot \sqrt{y \cdot \left(z \cdot y\right)}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sqrt z) y)))
   (if (<= t_0 -2e+41)
     (* (sqrt z) (* y 0.5))
     (if (<= t_0 4e-57)
       (* 0.5 x)
       (if (<= t_0 5000.0)
         (* 0.5 (sqrt (* y (* z y))))
         (if (<= t_0 5e+70) (* 0.5 x) (* 0.5 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(z) * y;
	double tmp;
	if (t_0 <= -2e+41) {
		tmp = sqrt(z) * (y * 0.5);
	} else if (t_0 <= 4e-57) {
		tmp = 0.5 * x;
	} else if (t_0 <= 5000.0) {
		tmp = 0.5 * sqrt((y * (z * y)));
	} else if (t_0 <= 5e+70) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * 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 = sqrt(z) * y
    if (t_0 <= (-2d+41)) then
        tmp = sqrt(z) * (y * 0.5d0)
    else if (t_0 <= 4d-57) then
        tmp = 0.5d0 * x
    else if (t_0 <= 5000.0d0) then
        tmp = 0.5d0 * sqrt((y * (z * y)))
    else if (t_0 <= 5d+70) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sqrt(z) * y;
	double tmp;
	if (t_0 <= -2e+41) {
		tmp = Math.sqrt(z) * (y * 0.5);
	} else if (t_0 <= 4e-57) {
		tmp = 0.5 * x;
	} else if (t_0 <= 5000.0) {
		tmp = 0.5 * Math.sqrt((y * (z * y)));
	} else if (t_0 <= 5e+70) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sqrt(z) * y
	tmp = 0
	if t_0 <= -2e+41:
		tmp = math.sqrt(z) * (y * 0.5)
	elif t_0 <= 4e-57:
		tmp = 0.5 * x
	elif t_0 <= 5000.0:
		tmp = 0.5 * math.sqrt((y * (z * y)))
	elif t_0 <= 5e+70:
		tmp = 0.5 * x
	else:
		tmp = 0.5 * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sqrt(z) * y)
	tmp = 0.0
	if (t_0 <= -2e+41)
		tmp = Float64(sqrt(z) * Float64(y * 0.5));
	elseif (t_0 <= 4e-57)
		tmp = Float64(0.5 * x);
	elseif (t_0 <= 5000.0)
		tmp = Float64(0.5 * sqrt(Float64(y * Float64(z * y))));
	elseif (t_0 <= 5e+70)
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sqrt(z) * y;
	tmp = 0.0;
	if (t_0 <= -2e+41)
		tmp = sqrt(z) * (y * 0.5);
	elseif (t_0 <= 4e-57)
		tmp = 0.5 * x;
	elseif (t_0 <= 5000.0)
		tmp = 0.5 * sqrt((y * (z * y)));
	elseif (t_0 <= 5e+70)
		tmp = 0.5 * x;
	else
		tmp = 0.5 * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sqrt[z], $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+41], N[(N[Sqrt[z], $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e-57], N[(0.5 * x), $MachinePrecision], If[LessEqual[t$95$0, 5000.0], N[(0.5 * N[Sqrt[N[(y * N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+70], N[(0.5 * x), $MachinePrecision], N[(0.5 * t$95$0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y (sqrt.f64 z)) < -2.00000000000000001e41

   1. Initial program 97.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around 0 85.5%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 1.0%

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

      3. *-commutative 1.0%

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

      4. *-commutative 1.0%

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

      5. swap-sqr 0.9%

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

      6. add-sqr-sqrt 0.9%

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

   6. Applied egg-rr 0.9%

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

      1. *-commutative 0.9%

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

      2. associate-*l* 1.0%

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

   8. Simplified 1.0%

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

   9. Taylor expanded in y around 0 85.5%

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

       1. associate-*r* 87.3%

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

       2. *-commutative 87.3%

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

       3. *-commutative 87.3%

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

   11. Simplified 87.3%

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

   if -2.00000000000000001e41 < (*.f64 y (sqrt.f64 z)) < 3.99999999999999982e-57 or 5e3 < (*.f64 y (sqrt.f64 z)) < 5.0000000000000002e70

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.7%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 3.99999999999999982e-57 < (*.f64 y (sqrt.f64 z)) < 5e3

   1. Initial program 99.4%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 97.7%

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

      1. add-sqr-sqrt 97.1%

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

      2. sqrt-unprod 97.7%

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

      3. *-commutative 97.7%

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

      4. *-commutative 97.7%

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

      5. swap-sqr 98.2%

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

      6. add-sqr-sqrt 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 98.2%

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

   8. Simplified 98.2%

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

   if 5.0000000000000002e70 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 84.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(y \cdot \sqrt{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{z} \cdot y \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;\sqrt{z} \cdot y \leq 4 \cdot 10^{-57}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;\sqrt{z} \cdot y \leq 5000:\\ \;\;\;\;0.5 \cdot \sqrt{y \cdot \left(z \cdot y\right)}\\ \mathbf{elif}\;\sqrt{z} \cdot y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\sqrt{z} \cdot y\right)\\ \end{array} \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 6: 51.6% accurate, 36.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 53.2%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

5. Final simplification 53.2%

   \[\leadsto 0.5 \cdot x \]

Reproduce

herbie shell --seed 2023213 
(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)))))