Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 12.4s

Alternatives: 16

Speedup: 1.0×

• 34.5% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]
6. Add Preprocessing

Alternative 2: 37.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-299}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+195} \lor \neg \left(z \leq 1.25 \cdot 10^{+245}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.5e+126)
     t_1
     (if (<= z -9.5e+17)
       (* z x)
       (if (<= z -2.1e-33)
         t_1
         (if (<= z -3.9e-161)
           (* y (- x))
           (if (<= z -1.36e-299)
             (* y t)
             (if (<= z 3e-170)
               x
               (if (<= z 5.2e+23)
                 (* y t)
                 (if (or (<= z 5.7e+195) (not (<= z 1.25e+245)))
                   t_1
                   (* z x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.5e+126) {
		tmp = t_1;
	} else if (z <= -9.5e+17) {
		tmp = z * x;
	} else if (z <= -2.1e-33) {
		tmp = t_1;
	} else if (z <= -3.9e-161) {
		tmp = y * -x;
	} else if (z <= -1.36e-299) {
		tmp = y * t;
	} else if (z <= 3e-170) {
		tmp = x;
	} else if (z <= 5.2e+23) {
		tmp = y * t;
	} else if ((z <= 5.7e+195) || !(z <= 1.25e+245)) {
		tmp = t_1;
	} else {
		tmp = z * 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1.5d+126)) then
        tmp = t_1
    else if (z <= (-9.5d+17)) then
        tmp = z * x
    else if (z <= (-2.1d-33)) then
        tmp = t_1
    else if (z <= (-3.9d-161)) then
        tmp = y * -x
    else if (z <= (-1.36d-299)) then
        tmp = y * t
    else if (z <= 3d-170) then
        tmp = x
    else if (z <= 5.2d+23) then
        tmp = y * t
    else if ((z <= 5.7d+195) .or. (.not. (z <= 1.25d+245))) then
        tmp = t_1
    else
        tmp = z * x
    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 <= -1.5e+126) {
		tmp = t_1;
	} else if (z <= -9.5e+17) {
		tmp = z * x;
	} else if (z <= -2.1e-33) {
		tmp = t_1;
	} else if (z <= -3.9e-161) {
		tmp = y * -x;
	} else if (z <= -1.36e-299) {
		tmp = y * t;
	} else if (z <= 3e-170) {
		tmp = x;
	} else if (z <= 5.2e+23) {
		tmp = y * t;
	} else if ((z <= 5.7e+195) || !(z <= 1.25e+245)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.5e+126:
		tmp = t_1
	elif z <= -9.5e+17:
		tmp = z * x
	elif z <= -2.1e-33:
		tmp = t_1
	elif z <= -3.9e-161:
		tmp = y * -x
	elif z <= -1.36e-299:
		tmp = y * t
	elif z <= 3e-170:
		tmp = x
	elif z <= 5.2e+23:
		tmp = y * t
	elif (z <= 5.7e+195) or not (z <= 1.25e+245):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1.5e+126)
		tmp = t_1;
	elseif (z <= -9.5e+17)
		tmp = Float64(z * x);
	elseif (z <= -2.1e-33)
		tmp = t_1;
	elseif (z <= -3.9e-161)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -1.36e-299)
		tmp = Float64(y * t);
	elseif (z <= 3e-170)
		tmp = x;
	elseif (z <= 5.2e+23)
		tmp = Float64(y * t);
	elseif ((z <= 5.7e+195) || !(z <= 1.25e+245))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1.5e+126)
		tmp = t_1;
	elseif (z <= -9.5e+17)
		tmp = z * x;
	elseif (z <= -2.1e-33)
		tmp = t_1;
	elseif (z <= -3.9e-161)
		tmp = y * -x;
	elseif (z <= -1.36e-299)
		tmp = y * t;
	elseif (z <= 3e-170)
		tmp = x;
	elseif (z <= 5.2e+23)
		tmp = y * t;
	elseif ((z <= 5.7e+195) || ~((z <= 1.25e+245)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.5e+126], t$95$1, If[LessEqual[z, -9.5e+17], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.1e-33], t$95$1, If[LessEqual[z, -3.9e-161], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -1.36e-299], N[(y * t), $MachinePrecision], If[LessEqual[z, 3e-170], x, If[LessEqual[z, 5.2e+23], N[(y * t), $MachinePrecision], If[Or[LessEqual[z, 5.7e+195], N[Not[LessEqual[z, 1.25e+245]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5000000000000001e126 or -9.5e17 < z < -2.1e-33 or 5.19999999999999983e23 < z < 5.7000000000000002e195 or 1.25000000000000009e245 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 90.1%

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

   4. Applied egg-rr 90.1%

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

   5. Taylor expanded in x around 0 58.9%

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

      1. associate-+r+ 58.9%

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

      2. mul-1-neg 58.9%

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

      3. *-commutative 58.9%

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

      4. sub-neg 58.9%

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

      5. associate-+l- 58.9%

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

      6. *-commutative 58.9%

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

   7. Applied egg-rr 58.9%

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

   8. Taylor expanded in z around inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

   10. Simplified 55.7%

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

   if -1.5000000000000001e126 < z < -9.5e17 or 5.7000000000000002e195 < z < 1.25000000000000009e245

   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 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-lft-neg-out 89.0%

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

      3. *-commutative 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around 0 66.6%

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

   7. Taylor expanded in z around inf 66.6%

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

      1. *-commutative 66.6%

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

   9. Simplified 66.6%

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

   if -2.1e-33 < z < -3.89999999999999973e-161

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. neg-sub0 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in y around inf 47.3%

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

      1. associate-*r* 47.3%

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

      2. neg-mul-1 47.3%

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

      3. *-commutative 47.3%

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

   8. Simplified 47.3%

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

   if -3.89999999999999973e-161 < z < -1.36000000000000007e-299 or 3.00000000000000013e-170 < z < 5.19999999999999983e23

   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 80.4%

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

   4. Taylor expanded in y around inf 46.1%

      \[\leadsto \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 46.1%

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

   6. Simplified 46.1%

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

   if -1.36000000000000007e-299 < z < 3.00000000000000013e-170

   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 93.4%

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

   4. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-299}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+195} \lor \neg \left(z \leq 1.25 \cdot 10^{+245}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -21000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -21000.0)
   (* z x)
   (if (<= z -4.9e-161)
     (* y (- x))
     (if (<= z -9.5e-301)
       (* y t)
       (if (<= z 5.2e-170) x (if (<= z 2.5e+20) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -21000.0) {
		tmp = z * x;
	} else if (z <= -4.9e-161) {
		tmp = y * -x;
	} else if (z <= -9.5e-301) {
		tmp = y * t;
	} else if (z <= 5.2e-170) {
		tmp = x;
	} else if (z <= 2.5e+20) {
		tmp = y * t;
	} else {
		tmp = z * 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 (z <= (-21000.0d0)) then
        tmp = z * x
    else if (z <= (-4.9d-161)) then
        tmp = y * -x
    else if (z <= (-9.5d-301)) then
        tmp = y * t
    else if (z <= 5.2d-170) then
        tmp = x
    else if (z <= 2.5d+20) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -21000.0) {
		tmp = z * x;
	} else if (z <= -4.9e-161) {
		tmp = y * -x;
	} else if (z <= -9.5e-301) {
		tmp = y * t;
	} else if (z <= 5.2e-170) {
		tmp = x;
	} else if (z <= 2.5e+20) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -21000.0:
		tmp = z * x
	elif z <= -4.9e-161:
		tmp = y * -x
	elif z <= -9.5e-301:
		tmp = y * t
	elif z <= 5.2e-170:
		tmp = x
	elif z <= 2.5e+20:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -21000.0)
		tmp = Float64(z * x);
	elseif (z <= -4.9e-161)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -9.5e-301)
		tmp = Float64(y * t);
	elseif (z <= 5.2e-170)
		tmp = x;
	elseif (z <= 2.5e+20)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -21000.0)
		tmp = z * x;
	elseif (z <= -4.9e-161)
		tmp = y * -x;
	elseif (z <= -9.5e-301)
		tmp = y * t;
	elseif (z <= 5.2e-170)
		tmp = x;
	elseif (z <= 2.5e+20)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -21000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -4.9e-161], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -9.5e-301], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.2e-170], x, If[LessEqual[z, 2.5e+20], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -21000 or 2.5e20 < z

   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 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-lft-neg-out 83.0%

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

      3. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in t around 0 42.5%

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

   7. Taylor expanded in z around inf 42.5%

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

      1. *-commutative 42.5%

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

   9. Simplified 42.5%

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

   if -21000 < z < -4.90000000000000035e-161

   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 73.2%

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

      1. mul-1-neg 73.2%

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

      2. distribute-rgt-neg-in 73.2%

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

      3. neg-sub0 73.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 73.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 73.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 73.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 73.2%

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

      8. remove-double-neg 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around inf 42.2%

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

      1. associate-*r* 42.2%

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

      2. neg-mul-1 42.2%

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

      3. *-commutative 42.2%

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

   8. Simplified 42.2%

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

   if -4.90000000000000035e-161 < z < -9.50000000000000032e-301 or 5.2000000000000003e-170 < z < 2.5e20

   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 81.4%

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

   4. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   if -9.50000000000000032e-301 < z < 5.2000000000000003e-170

   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 93.4%

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

   4. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -21000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-161}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -6.6e-34)
     t_1
     (if (<= z -5.9e-161)
       (- x (* y x))
       (if (<= z 3.2e+19) (+ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6.6e-34) {
		tmp = t_1;
	} else if (z <= -5.9e-161) {
		tmp = x - (y * x);
	} else if (z <= 3.2e+19) {
		tmp = x + ((y - z) * t);
	} 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 * (x - t)
    if (z <= (-6.6d-34)) then
        tmp = t_1
    else if (z <= (-5.9d-161)) then
        tmp = x - (y * x)
    else if (z <= 3.2d+19) then
        tmp = x + ((y - z) * t)
    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 * (x - t);
	double tmp;
	if (z <= -6.6e-34) {
		tmp = t_1;
	} else if (z <= -5.9e-161) {
		tmp = x - (y * x);
	} else if (z <= 3.2e+19) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -6.6e-34:
		tmp = t_1
	elif z <= -5.9e-161:
		tmp = x - (y * x)
	elif z <= 3.2e+19:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -6.6e-34)
		tmp = t_1;
	elseif (z <= -5.9e-161)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 3.2e+19)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -6.6e-34)
		tmp = t_1;
	elseif (z <= -5.9e-161)
		tmp = x - (y * x);
	elseif (z <= 3.2e+19)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-34], t$95$1, If[LessEqual[z, -5.9e-161], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+19], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999965e-34 or 3.2e19 < z

   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 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around 0 80.2%

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

   7. Taylor expanded in z around inf 80.8%

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

      1. neg-mul-1 80.8%

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

      2. unsub-neg 80.8%

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

   9. Simplified 80.8%

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

   if -6.59999999999999965e-34 < z < -5.9000000000000002e-161

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. neg-sub0 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around 0 76.9%

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

      1. *-rgt-identity 76.9%

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

      2. mul-1-neg 76.9%

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

      3. distribute-rgt-neg-out 76.9%

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

      4. distribute-lft-in 76.8%

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

      5. unsub-neg 76.8%

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

   8. Simplified 76.8%

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

   9. Taylor expanded in y around 0 76.9%

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

       1. mul-1-neg 76.9%

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

       2. *-commutative 76.9%

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

       3. sub-neg 76.9%

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

   11. Simplified 76.9%

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

   if -5.9000000000000002e-161 < z < 3.2e19

   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 84.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-161}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-210}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.36e-33)
     t_1
     (if (<= t 1.6e-210) (* z x) (if (<= t 1.5e-10) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.36e-33) {
		tmp = t_1;
	} else if (t <= 1.6e-210) {
		tmp = z * x;
	} else if (t <= 1.5e-10) {
		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 = (y - z) * t
    if (t <= (-1.36d-33)) then
        tmp = t_1
    else if (t <= 1.6d-210) then
        tmp = z * x
    else if (t <= 1.5d-10) 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 = (y - z) * t;
	double tmp;
	if (t <= -1.36e-33) {
		tmp = t_1;
	} else if (t <= 1.6e-210) {
		tmp = z * x;
	} else if (t <= 1.5e-10) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.36e-33:
		tmp = t_1
	elif t <= 1.6e-210:
		tmp = z * x
	elif t <= 1.5e-10:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.36e-33)
		tmp = t_1;
	elseif (t <= 1.6e-210)
		tmp = Float64(z * x);
	elseif (t <= 1.5e-10)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.36e-33)
		tmp = t_1;
	elseif (t <= 1.6e-210)
		tmp = z * x;
	elseif (t <= 1.5e-10)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.36e-33], t$95$1, If[LessEqual[t, 1.6e-210], N[(z * x), $MachinePrecision], If[LessEqual[t, 1.5e-10], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.36e-33 or 1.5e-10 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in x around 0 79.4%

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

      1. associate-+r+ 79.4%

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

      2. mul-1-neg 79.4%

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

      3. *-commutative 79.4%

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

      4. sub-neg 79.4%

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

      5. associate-+l- 79.4%

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

      6. *-commutative 79.4%

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

   7. Applied egg-rr 79.4%

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

   8. Taylor expanded in x around 0 71.3%

      \[\leadsto \color{blue}{t \cdot y - t \cdot z} \]
   9. Step-by-step derivation

      1. distribute-lft-out-- 76.5%

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

   10. Simplified 76.5%

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

   if -1.36e-33 < t < 1.60000000000000014e-210

   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 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-lft-neg-out 76.6%

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

      3. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in t around 0 71.4%

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

   7. Taylor expanded in z around inf 41.8%

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

      1. *-commutative 41.8%

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

   9. Simplified 41.8%

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

   if 1.60000000000000014e-210 < t < 1.5e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in x around inf 44.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-33}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-210}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.25e-19)
     t_1
     (if (<= t -7.2e-119)
       (* z (- x t))
       (if (<= t 3.6e+24) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.25e-19) {
		tmp = t_1;
	} else if (t <= -7.2e-119) {
		tmp = z * (x - t);
	} else if (t <= 3.6e+24) {
		tmp = x * (1.0 - y);
	} 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 = (y - z) * t
    if (t <= (-1.25d-19)) then
        tmp = t_1
    else if (t <= (-7.2d-119)) then
        tmp = z * (x - t)
    else if (t <= 3.6d+24) then
        tmp = x * (1.0d0 - y)
    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 = (y - z) * t;
	double tmp;
	if (t <= -1.25e-19) {
		tmp = t_1;
	} else if (t <= -7.2e-119) {
		tmp = z * (x - t);
	} else if (t <= 3.6e+24) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.25e-19:
		tmp = t_1
	elif t <= -7.2e-119:
		tmp = z * (x - t)
	elif t <= 3.6e+24:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.25e-19)
		tmp = t_1;
	elseif (t <= -7.2e-119)
		tmp = Float64(z * Float64(x - t));
	elseif (t <= 3.6e+24)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.25e-19)
		tmp = t_1;
	elseif (t <= -7.2e-119)
		tmp = z * (x - t);
	elseif (t <= 3.6e+24)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.25e-19], t$95$1, If[LessEqual[t, -7.2e-119], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+24], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2500000000000001e-19 or 3.59999999999999983e24 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. associate-+r+ 80.2%

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

      2. mul-1-neg 80.2%

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

      3. *-commutative 80.2%

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

      4. sub-neg 80.2%

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

      5. associate-+l- 80.2%

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

      6. *-commutative 80.2%

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

   7. Applied egg-rr 80.2%

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

   8. Taylor expanded in x around 0 73.5%

      \[\leadsto \color{blue}{t \cdot y - t \cdot z} \]
   9. Step-by-step derivation

      1. distribute-lft-out-- 79.1%

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

   10. Simplified 79.1%

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

   if -1.2500000000000001e-19 < t < -7.2e-119

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-lft-neg-out 84.5%

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

      3. *-commutative 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in x around 0 84.5%

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

   7. Taylor expanded in z around inf 64.0%

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

      1. neg-mul-1 64.0%

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

      2. unsub-neg 64.0%

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

   9. Simplified 64.0%

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

   if -7.2e-119 < t < 3.59999999999999983e24

   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 88.0%

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

      1. mul-1-neg 88.0%

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

      2. distribute-rgt-neg-in 88.0%

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

      3. neg-sub0 88.0%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 88.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 88.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 88.0%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 88.0%

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

      8. remove-double-neg 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around 0 60.3%

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

      1. *-rgt-identity 60.3%

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

      2. mul-1-neg 60.3%

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

      3. distribute-rgt-neg-out 60.3%

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

      4. distribute-lft-in 60.3%

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

      5. unsub-neg 60.3%

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

   8. Simplified 60.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -3.5e-33)
     t_1
     (if (<= z -5.5e-162)
       (* x (- 1.0 y))
       (if (<= z 1.65e+19) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -3.5e-33) {
		tmp = t_1;
	} else if (z <= -5.5e-162) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.65e+19) {
		tmp = x + (y * t);
	} 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 * (x - t)
    if (z <= (-3.5d-33)) then
        tmp = t_1
    else if (z <= (-5.5d-162)) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.65d+19) then
        tmp = x + (y * t)
    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 * (x - t);
	double tmp;
	if (z <= -3.5e-33) {
		tmp = t_1;
	} else if (z <= -5.5e-162) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.65e+19) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -3.5e-33:
		tmp = t_1
	elif z <= -5.5e-162:
		tmp = x * (1.0 - y)
	elif z <= 1.65e+19:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -3.5e-33)
		tmp = t_1;
	elseif (z <= -5.5e-162)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.65e+19)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -3.5e-33)
		tmp = t_1;
	elseif (z <= -5.5e-162)
		tmp = x * (1.0 - y);
	elseif (z <= 1.65e+19)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-33], t$95$1, If[LessEqual[z, -5.5e-162], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+19], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e-33 or 1.65e19 < z

   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 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around 0 80.2%

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

   7. Taylor expanded in z around inf 80.8%

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

      1. neg-mul-1 80.8%

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

      2. unsub-neg 80.8%

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

   9. Simplified 80.8%

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

   if -3.4999999999999999e-33 < z < -5.50000000000000006e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. neg-sub0 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around 0 76.9%

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

      1. *-rgt-identity 76.9%

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

      2. mul-1-neg 76.9%

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

      3. distribute-rgt-neg-out 76.9%

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

      4. distribute-lft-in 76.8%

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

      5. unsub-neg 76.8%

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

   8. Simplified 76.8%

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

   if -5.50000000000000006e-162 < z < 1.65e19

   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 84.3%

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

   4. Taylor expanded in z around 0 76.6%

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

      1. *-commutative 76.6%

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

   6. Simplified 76.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-162}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.25e-34)
     t_1
     (if (<= z -1.95e-162)
       (- x (* y x))
       (if (<= z 1.7e+19) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.25e-34) {
		tmp = t_1;
	} else if (z <= -1.95e-162) {
		tmp = x - (y * x);
	} else if (z <= 1.7e+19) {
		tmp = x + (y * t);
	} 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 * (x - t)
    if (z <= (-1.25d-34)) then
        tmp = t_1
    else if (z <= (-1.95d-162)) then
        tmp = x - (y * x)
    else if (z <= 1.7d+19) then
        tmp = x + (y * t)
    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 * (x - t);
	double tmp;
	if (z <= -1.25e-34) {
		tmp = t_1;
	} else if (z <= -1.95e-162) {
		tmp = x - (y * x);
	} else if (z <= 1.7e+19) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.25e-34:
		tmp = t_1
	elif z <= -1.95e-162:
		tmp = x - (y * x)
	elif z <= 1.7e+19:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.25e-34)
		tmp = t_1;
	elseif (z <= -1.95e-162)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 1.7e+19)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.25e-34)
		tmp = t_1;
	elseif (z <= -1.95e-162)
		tmp = x - (y * x);
	elseif (z <= 1.7e+19)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-34], t$95$1, If[LessEqual[z, -1.95e-162], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+19], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2500000000000001e-34 or 1.7e19 < z

   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 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around 0 80.2%

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

   7. Taylor expanded in z around inf 80.8%

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

      1. neg-mul-1 80.8%

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

      2. unsub-neg 80.8%

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

   9. Simplified 80.8%

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

   if -1.2500000000000001e-34 < z < -1.95e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. neg-sub0 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 76.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 76.9%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around 0 76.9%

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

      1. *-rgt-identity 76.9%

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

      2. mul-1-neg 76.9%

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

      3. distribute-rgt-neg-out 76.9%

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

      4. distribute-lft-in 76.8%

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

      5. unsub-neg 76.8%

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

   8. Simplified 76.8%

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

   9. Taylor expanded in y around 0 76.9%

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

       1. mul-1-neg 76.9%

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

       2. *-commutative 76.9%

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

       3. sub-neg 76.9%

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

   11. Simplified 76.9%

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

   if -1.95e-162 < z < 1.7e19

   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 84.3%

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

   4. Taylor expanded in z around 0 76.6%

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

      1. *-commutative 76.6%

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

   6. Simplified 76.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-162}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.95e-24)
   (* y t)
   (if (<= y -1.92e-121) (* z x) (if (<= y 3.6e-15) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e-24) {
		tmp = y * t;
	} else if (y <= -1.92e-121) {
		tmp = z * x;
	} else if (y <= 3.6e-15) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-2.95d-24)) then
        tmp = y * t
    else if (y <= (-1.92d-121)) then
        tmp = z * x
    else if (y <= 3.6d-15) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e-24) {
		tmp = y * t;
	} else if (y <= -1.92e-121) {
		tmp = z * x;
	} else if (y <= 3.6e-15) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.95e-24:
		tmp = y * t
	elif y <= -1.92e-121:
		tmp = z * x
	elif y <= 3.6e-15:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.95e-24)
		tmp = Float64(y * t);
	elseif (y <= -1.92e-121)
		tmp = Float64(z * x);
	elseif (y <= 3.6e-15)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.95e-24)
		tmp = y * t;
	elseif (y <= -1.92e-121)
		tmp = z * x;
	elseif (y <= 3.6e-15)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.95e-24], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.92e-121], N[(z * x), $MachinePrecision], If[LessEqual[y, 3.6e-15], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9500000000000001e-24 or 3.6000000000000001e-15 < 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 58.5%

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

   4. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 45.4%

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

   6. Simplified 45.4%

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

   if -2.9500000000000001e-24 < y < -1.9199999999999999e-121

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. distribute-lft-neg-out 90.9%

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

      3. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in t around 0 68.1%

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

   7. Taylor expanded in z around inf 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

   if -1.9199999999999999e-121 < y < 3.6000000000000001e-15

   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 83.8%

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

   4. Taylor expanded in x around inf 37.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+39} \lor \neg \left(x \leq 4.4 \cdot 10^{+105}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e+39) (not (<= x 4.4e+105)))
   (+ x (* x (- z y)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+39) || !(x <= 4.4e+105)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	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 <= (-5.2d+39)) .or. (.not. (x <= 4.4d+105))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+39) || !(x <= 4.4e+105)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.2e+39) or not (x <= 4.4e+105):
		tmp = x + (x * (z - y))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.2e+39) || !(x <= 4.4e+105))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.2e+39) || ~((x <= 4.4e+105)))
		tmp = x + (x * (z - y));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.2e+39], N[Not[LessEqual[x, 4.4e+105]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e39 or 4.40000000000000014e105 < 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 93.3%

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

      1. mul-1-neg 93.3%

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

      2. distribute-rgt-neg-in 93.3%

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

      3. neg-sub0 93.3%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 93.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 93.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 93.3%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 93.3%

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

      8. remove-double-neg 93.3%

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

   5. Simplified 93.3%

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

   if -5.2e39 < x < 4.40000000000000014e105

   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 83.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+39} \lor \neg \left(x \leq 4.4 \cdot 10^{+105}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-34} \lor \neg \left(z \leq 6.5 \cdot 10^{+19}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e-34) (not (<= z 6.5e+19)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-34) || !(z <= 6.5e+19)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - 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 ((z <= (-6.6d-34)) .or. (.not. (z <= 6.5d+19))) then
        tmp = x - (z * (t - x))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-34) || !(z <= 6.5e+19)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e-34) or not (z <= 6.5e+19):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e-34) || !(z <= 6.5e+19))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e-34) || ~((z <= 6.5e+19)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e-34], N[Not[LessEqual[z, 6.5e+19]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.59999999999999965e-34 or 6.5e19 < z

   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 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. *-commutative 82.5%

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

   5. Simplified 82.5%

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

      1. distribute-rgt-neg-out 82.5%

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

      2. unsub-neg 82.5%

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

   7. Applied egg-rr 82.5%

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

   if -6.59999999999999965e-34 < z < 6.5e19

   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 91.9%

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

      1. *-commutative 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-34} \lor \neg \left(z \leq 6.5 \cdot 10^{+19}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-7} \lor \neg \left(t \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4e-7) (not (<= t 3.4e+24))) (* t (- y z)) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e-7) || !(t <= 3.4e+24)) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	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 ((t <= (-4d-7)) .or. (.not. (t <= 3.4d+24))) then
        tmp = t * (y - z)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e-7) || !(t <= 3.4e+24)) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4e-7) or not (t <= 3.4e+24):
		tmp = t * (y - z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4e-7) || !(t <= 3.4e+24))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4e-7) || ~((t <= 3.4e+24)))
		tmp = t * (y - z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4e-7], N[Not[LessEqual[t, 3.4e+24]], $MachinePrecision]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9999999999999998e-7 or 3.4000000000000001e24 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in x around 0 80.5%

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

      1. associate-+r+ 80.5%

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

      2. mul-1-neg 80.5%

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

      3. *-commutative 80.5%

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

      4. sub-neg 80.5%

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

      5. associate-+l- 80.5%

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

      6. *-commutative 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in x around 0 74.3%

      \[\leadsto \color{blue}{t \cdot y - t \cdot z} \]
   9. Step-by-step derivation

      1. distribute-lft-out-- 80.1%

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

   10. Simplified 80.1%

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

   if -3.9999999999999998e-7 < t < 3.4000000000000001e24

   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 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-rgt-neg-in 85.4%

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

      3. neg-sub0 85.4%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 85.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 85.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 85.4%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 85.4%

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

      8. remove-double-neg 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around 0 56.2%

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

      1. *-rgt-identity 56.2%

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

      2. mul-1-neg 56.2%

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

      3. distribute-rgt-neg-out 56.2%

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

      4. distribute-lft-in 56.2%

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

      5. unsub-neg 56.2%

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

   8. Simplified 56.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-7} \lor \neg \left(t \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-9} \lor \neg \left(t \leq 1.46 \cdot 10^{-7}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.5e-9) (not (<= t 1.46e-7))) (* t (- y z)) (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e-9) || !(t <= 1.46e-7)) {
		tmp = t * (y - z);
	} else {
		tmp = x + (z * 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 ((t <= (-6.5d-9)) .or. (.not. (t <= 1.46d-7))) then
        tmp = t * (y - z)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e-9) || !(t <= 1.46e-7)) {
		tmp = t * (y - z);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.5e-9) or not (t <= 1.46e-7):
		tmp = t * (y - z)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.5e-9) || !(t <= 1.46e-7))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.5e-9) || ~((t <= 1.46e-7)))
		tmp = t * (y - z);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.5e-9], N[Not[LessEqual[t, 1.46e-7]], $MachinePrecision]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000003e-9 or 1.4600000000000001e-7 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 93.2%

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

   4. Applied egg-rr 93.2%

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

   5. Taylor expanded in x around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. mul-1-neg 79.1%

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

      3. *-commutative 79.1%

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

      4. sub-neg 79.1%

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

      5. associate-+l- 79.1%

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

      6. *-commutative 79.1%

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

   7. Applied egg-rr 79.1%

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

   8. Taylor expanded in x around 0 72.6%

      \[\leadsto \color{blue}{t \cdot y - t \cdot z} \]
   9. Step-by-step derivation

      1. distribute-lft-out-- 78.0%

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

   10. Simplified 78.0%

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

   if -6.5000000000000003e-9 < t < 1.4600000000000001e-7

   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 73.8%

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

      1. mul-1-neg 73.8%

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

      2. distribute-lft-neg-out 73.8%

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

      3. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around 0 67.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-9} \lor \neg \left(t \leq 1.46 \cdot 10^{-7}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-12} \lor \neg \left(y \leq 2.8 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e-12) (not (<= y 2.8e-12))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-12) || !(y <= 2.8e-12)) {
		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 <= (-1.1d-12)) .or. (.not. (y <= 2.8d-12))) 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 <= -1.1e-12) || !(y <= 2.8e-12)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.1e-12) or not (y <= 2.8e-12):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e-12) || !(y <= 2.8e-12))
		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 <= -1.1e-12) || ~((y <= 2.8e-12)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e-12], N[Not[LessEqual[y, 2.8e-12]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.09999999999999996e-12 or 2.8000000000000002e-12 < 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 57.9%

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

   4. Taylor expanded in y around inf 46.1%

      \[\leadsto \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 46.1%

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

   6. Simplified 46.1%

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

   if -1.09999999999999996e-12 < y < 2.8000000000000002e-12

   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 78.2%

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

   4. Taylor expanded in x around inf 35.1%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-12} \lor \neg \left(y \leq 2.8 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 16: 18.0% 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 68.5%

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

4. Taylor expanded in x around inf 19.8%

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

5. Final simplification 19.8%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.4% 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 2024041 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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