Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 10

Speedup: 1.0×

• 34.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]
4. Add Preprocessing

Alternative 2: 53.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -7 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+101} \lor \neg \left(z \leq 4.3 \cdot 10^{+291}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (+ x (* y t))))
   (if (<= z -7e-10)
     t_1
     (if (<= z 3.6e-27)
       t_2
       (if (<= z 6e+35)
         t_1
         (if (<= z 4.2e+79)
           t_2
           (if (or (<= z 1.1e+101) (not (<= z 4.3e+291)))
             (+ x (* x z))
             t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -7e-10) {
		tmp = t_1;
	} else if (z <= 3.6e-27) {
		tmp = t_2;
	} else if (z <= 6e+35) {
		tmp = t_1;
	} else if (z <= 4.2e+79) {
		tmp = t_2;
	} else if ((z <= 1.1e+101) || !(z <= 4.3e+291)) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x + (y * t)
    if (z <= (-7d-10)) then
        tmp = t_1
    else if (z <= 3.6d-27) then
        tmp = t_2
    else if (z <= 6d+35) then
        tmp = t_1
    else if (z <= 4.2d+79) then
        tmp = t_2
    else if ((z <= 1.1d+101) .or. (.not. (z <= 4.3d+291))) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -7e-10) {
		tmp = t_1;
	} else if (z <= 3.6e-27) {
		tmp = t_2;
	} else if (z <= 6e+35) {
		tmp = t_1;
	} else if (z <= 4.2e+79) {
		tmp = t_2;
	} else if ((z <= 1.1e+101) || !(z <= 4.3e+291)) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x + (y * t)
	tmp = 0
	if z <= -7e-10:
		tmp = t_1
	elif z <= 3.6e-27:
		tmp = t_2
	elif z <= 6e+35:
		tmp = t_1
	elif z <= 4.2e+79:
		tmp = t_2
	elif (z <= 1.1e+101) or not (z <= 4.3e+291):
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -7e-10)
		tmp = t_1;
	elseif (z <= 3.6e-27)
		tmp = t_2;
	elseif (z <= 6e+35)
		tmp = t_1;
	elseif (z <= 4.2e+79)
		tmp = t_2;
	elseif ((z <= 1.1e+101) || !(z <= 4.3e+291))
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -7e-10)
		tmp = t_1;
	elseif (z <= 3.6e-27)
		tmp = t_2;
	elseif (z <= 6e+35)
		tmp = t_1;
	elseif (z <= 4.2e+79)
		tmp = t_2;
	elseif ((z <= 1.1e+101) || ~((z <= 4.3e+291)))
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-10], t$95$1, If[LessEqual[z, 3.6e-27], t$95$2, If[LessEqual[z, 6e+35], t$95$1, If[LessEqual[z, 4.2e+79], t$95$2, If[Or[LessEqual[z, 1.1e+101], N[Not[LessEqual[z, 4.3e+291]], $MachinePrecision]], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999961e-10 or 3.5999999999999999e-27 < z < 5.99999999999999981e35 or 1.1e101 < z < 4.2999999999999999e291

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.7%

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

   4. Taylor expanded in z around inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. *-commutative 54.0%

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

      3. neg-mul-1 54.0%

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

   6. Simplified 54.0%

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

   if -6.99999999999999961e-10 < z < 3.5999999999999999e-27 or 5.99999999999999981e35 < z < 4.20000000000000016e79

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 78.5%

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

   4. Taylor expanded in z around 0 70.9%

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

   if 4.20000000000000016e79 < z < 1.1e101 or 4.2999999999999999e291 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 90.9%

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

      1. *-commutative 90.9%

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

   8. Simplified 90.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+101} \lor \neg \left(z \leq 4.3 \cdot 10^{+291}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+270}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-16} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+270)
   (* y t)
   (if (<= y -3.6e+242)
     (* x (- y))
     (if (or (<= y -1.8e-16) (not (<= y 1.8e-26))) (* y t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+270) {
		tmp = y * t;
	} else if (y <= -3.6e+242) {
		tmp = x * -y;
	} else if ((y <= -1.8e-16) || !(y <= 1.8e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+270)) then
        tmp = y * t
    else if (y <= (-3.6d+242)) then
        tmp = x * -y
    else if ((y <= (-1.8d-16)) .or. (.not. (y <= 1.8d-26))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+270) {
		tmp = y * t;
	} else if (y <= -3.6e+242) {
		tmp = x * -y;
	} else if ((y <= -1.8e-16) || !(y <= 1.8e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+270:
		tmp = y * t
	elif y <= -3.6e+242:
		tmp = x * -y
	elif (y <= -1.8e-16) or not (y <= 1.8e-26):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+270)
		tmp = Float64(y * t);
	elseif (y <= -3.6e+242)
		tmp = Float64(x * Float64(-y));
	elseif ((y <= -1.8e-16) || !(y <= 1.8e-26))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e+270)
		tmp = y * t;
	elseif (y <= -3.6e+242)
		tmp = x * -y;
	elseif ((y <= -1.8e-16) || ~((y <= 1.8e-26)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+270], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.6e+242], N[(x * (-y)), $MachinePrecision], If[Or[LessEqual[y, -1.8e-16], N[Not[LessEqual[y, 1.8e-26]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8000000000000001e270 or -3.59999999999999995e242 < y < -1.79999999999999991e-16 or 1.8000000000000001e-26 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 60.1%

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

   4. Taylor expanded in y around inf 48.0%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -1.8000000000000001e270 < y < -3.59999999999999995e242

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 87.9%

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

      1. mul-1-neg 87.9%

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

      2. distribute-rgt-neg-in 87.9%

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

      3. sub-neg 87.9%

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

      4. +-commutative 87.9%

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

      5. distribute-neg-in 87.9%

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

      6. remove-double-neg 87.9%

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

      7. sub-neg 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in z around 0 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in y around inf 87.9%

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

       1. associate-*r* 87.9%

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

       2. neg-mul-1 87.9%

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

       3. *-commutative 87.9%

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

   11. Simplified 87.9%

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

   if -1.79999999999999991e-16 < y < 1.8000000000000001e-26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

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

   4. Taylor expanded in x around inf 34.8%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+270}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-16} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-275}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -8.5e-10)
     t_1
     (if (<= z -4.5e-275) (* y t) (if (<= z 7.5e-29) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8.5e-10) {
		tmp = t_1;
	} else if (z <= -4.5e-275) {
		tmp = y * t;
	} else if (z <= 7.5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-8.5d-10)) then
        tmp = t_1
    else if (z <= (-4.5d-275)) then
        tmp = y * t
    else if (z <= 7.5d-29) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8.5e-10) {
		tmp = t_1;
	} else if (z <= -4.5e-275) {
		tmp = y * t;
	} else if (z <= 7.5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -8.5e-10:
		tmp = t_1
	elif z <= -4.5e-275:
		tmp = y * t
	elif z <= 7.5e-29:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -8.5e-10)
		tmp = t_1;
	elseif (z <= -4.5e-275)
		tmp = Float64(y * t);
	elseif (z <= 7.5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -8.5e-10)
		tmp = t_1;
	elseif (z <= -4.5e-275)
		tmp = y * t;
	elseif (z <= 7.5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -8.5e-10], t$95$1, If[LessEqual[z, -4.5e-275], N[(y * t), $MachinePrecision], If[LessEqual[z, 7.5e-29], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999996e-10 or 7.50000000000000006e-29 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.2%

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

   4. Taylor expanded in z around inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. *-commutative 47.1%

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

      3. neg-mul-1 47.1%

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

   6. Simplified 47.1%

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

   if -8.4999999999999996e-10 < z < -4.49999999999999978e-275

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 78.1%

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

   4. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -4.49999999999999978e-275 < z < 7.50000000000000006e-29

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.7%

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

   4. Taylor expanded in x around inf 49.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-275}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+172} \lor \neg \left(x \leq 1.1 \cdot 10^{+105}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e+172) (not (<= x 1.1e+105)))
   (+ x (* x z))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+172) || !(x <= 1.1e+105)) {
		tmp = x + (x * z);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d+172)) .or. (.not. (x <= 1.1d+105))) then
        tmp = x + (x * z)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+172) || !(x <= 1.1e+105)) {
		tmp = x + (x * z);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e+172) or not (x <= 1.1e+105):
		tmp = x + (x * z)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e+172) || !(x <= 1.1e+105))
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e+172) || ~((x <= 1.1e+105)))
		tmp = x + (x * z);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e+172], N[Not[LessEqual[x, 1.1e+105]], $MachinePrecision]], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999995e172 or 1.10000000000000003e105 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 93.8%

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

      1. mul-1-neg 93.8%

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

      2. distribute-rgt-neg-in 93.8%

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

      3. sub-neg 93.8%

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

      4. +-commutative 93.8%

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

      5. distribute-neg-in 93.8%

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

      6. remove-double-neg 93.8%

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

      7. sub-neg 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around 0 73.6%

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

      1. *-commutative 73.6%

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

   8. Simplified 73.6%

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

   if -7.1999999999999995e172 < x < 1.10000000000000003e105

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+172} \lor \neg \left(x \leq 1.1 \cdot 10^{+105}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+25} \lor \neg \left(x \leq 4.5 \cdot 10^{+95}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.7e+25) (not (<= x 4.5e+95)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.7e+25) || !(x <= 4.5e+95)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.7d+25)) .or. (.not. (x <= 4.5d+95))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.7e+25) || !(x <= 4.5e+95)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.7e+25) or not (x <= 4.5e+95):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.7e+25) || !(x <= 4.5e+95))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.7e+25) || ~((x <= 4.5e+95)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.7e+25], N[Not[LessEqual[x, 4.5e+95]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999998e25 or 4.50000000000000017e95 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-in 85.6%

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

      3. sub-neg 85.6%

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

      4. +-commutative 85.6%

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

      5. distribute-neg-in 85.6%

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

      6. remove-double-neg 85.6%

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

      7. sub-neg 85.6%

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

   5. Simplified 85.6%

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

   if -4.6999999999999998e25 < x < 4.50000000000000017e95

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+25} \lor \neg \left(x \leq 4.5 \cdot 10^{+95}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+16} \lor \neg \left(y \leq 8.5 \cdot 10^{-26}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e+16) (not (<= y 8.5e-26)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+16) || !(y <= 8.5e-26)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d+16)) .or. (.not. (y <= 8.5d-26))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+16) || !(y <= 8.5e-26)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e+16) or not (y <= 8.5e-26):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e+16) || !(y <= 8.5e-26))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e+16) || ~((y <= 8.5e-26)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e+16], N[Not[LessEqual[y, 8.5e-26]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e16 or 8.50000000000000004e-26 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.2%

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

      1. *-commutative 80.2%

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

   5. Simplified 80.2%

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

   if -6.5e16 < y < 8.50000000000000004e-26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. distribute-rgt-neg-in 96.4%

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

      3. sub-neg 96.4%

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

      4. +-commutative 96.4%

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

      5. distribute-neg-in 96.4%

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

      6. remove-double-neg 96.4%

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

      7. sub-neg 96.4%

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

   5. Simplified 96.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+16} \lor \neg \left(y \leq 8.5 \cdot 10^{-26}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-9} \lor \neg \left(z \leq 3.6 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.55e-9) (not (<= z 3.6e-27))) (* z (- t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.55e-9) || !(z <= 3.6e-27)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.55d-9)) .or. (.not. (z <= 3.6d-27))) then
        tmp = z * -t
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.55e-9) || !(z <= 3.6e-27)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.55e-9) or not (z <= 3.6e-27):
		tmp = z * -t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.55e-9) || !(z <= 3.6e-27))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.55e-9) || ~((z <= 3.6e-27)))
		tmp = z * -t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.55e-9], N[Not[LessEqual[z, 3.6e-27]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.54999999999999994e-9 or 3.5999999999999999e-27 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.9%

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

   4. Taylor expanded in z around inf 47.4%

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

      1. associate-*r* 47.4%

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

      2. *-commutative 47.4%

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

      3. neg-mul-1 47.4%

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

   6. Simplified 47.4%

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

   if -3.54999999999999994e-9 < z < 3.5999999999999999e-27

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.5%

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

   4. Taylor expanded in z around 0 73.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-9} \lor \neg \left(z \leq 3.6 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-16} \lor \neg \left(y \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-16) (not (<= y 2.3e-26))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-16) || !(y <= 2.3e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d-16)) .or. (.not. (y <= 2.3d-26))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-16) || !(y <= 2.3e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-16) or not (y <= 2.3e-26):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-16) || !(y <= 2.3e-26))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-16) || ~((y <= 2.3e-26)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-16], N[Not[LessEqual[y, 2.3e-26]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2e-16 or 2.30000000000000009e-26 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.1%

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

   4. Taylor expanded in y around inf 46.8%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -2e-16 < y < 2.30000000000000009e-26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

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

   4. Taylor expanded in x around inf 34.8%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-16} \lor \neg \left(y \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 17.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf 67.5%

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

4. Taylor expanded in x around inf 18.4%

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

5. Final simplification 18.4%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((t * (y - z)) + (-x * (y - z)));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))