Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 13

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-def 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: 37.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-300}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+200} \lor \neg \left(z \leq 3.2 \cdot 10^{+245}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.9e+125)
     t_1
     (if (<= z -1.35e+18)
       (* z x)
       (if (<= z -1.3e-33)
         t_1
         (if (<= z -4.8e-163)
           (* y (- x))
           (if (<= z -3.5e-300)
             (* y t)
             (if (<= z 6.1e-170)
               x
               (if (<= z 6.5e+24)
                 (* y t)
                 (if (or (<= z 3.3e+200) (not (<= z 3.2e+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 <= -2.9e+125) {
		tmp = t_1;
	} else if (z <= -1.35e+18) {
		tmp = z * x;
	} else if (z <= -1.3e-33) {
		tmp = t_1;
	} else if (z <= -4.8e-163) {
		tmp = y * -x;
	} else if (z <= -3.5e-300) {
		tmp = y * t;
	} else if (z <= 6.1e-170) {
		tmp = x;
	} else if (z <= 6.5e+24) {
		tmp = y * t;
	} else if ((z <= 3.3e+200) || !(z <= 3.2e+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 <= (-2.9d+125)) then
        tmp = t_1
    else if (z <= (-1.35d+18)) then
        tmp = z * x
    else if (z <= (-1.3d-33)) then
        tmp = t_1
    else if (z <= (-4.8d-163)) then
        tmp = y * -x
    else if (z <= (-3.5d-300)) then
        tmp = y * t
    else if (z <= 6.1d-170) then
        tmp = x
    else if (z <= 6.5d+24) then
        tmp = y * t
    else if ((z <= 3.3d+200) .or. (.not. (z <= 3.2d+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 <= -2.9e+125) {
		tmp = t_1;
	} else if (z <= -1.35e+18) {
		tmp = z * x;
	} else if (z <= -1.3e-33) {
		tmp = t_1;
	} else if (z <= -4.8e-163) {
		tmp = y * -x;
	} else if (z <= -3.5e-300) {
		tmp = y * t;
	} else if (z <= 6.1e-170) {
		tmp = x;
	} else if (z <= 6.5e+24) {
		tmp = y * t;
	} else if ((z <= 3.3e+200) || !(z <= 3.2e+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 <= -2.9e+125:
		tmp = t_1
	elif z <= -1.35e+18:
		tmp = z * x
	elif z <= -1.3e-33:
		tmp = t_1
	elif z <= -4.8e-163:
		tmp = y * -x
	elif z <= -3.5e-300:
		tmp = y * t
	elif z <= 6.1e-170:
		tmp = x
	elif z <= 6.5e+24:
		tmp = y * t
	elif (z <= 3.3e+200) or not (z <= 3.2e+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 <= -2.9e+125)
		tmp = t_1;
	elseif (z <= -1.35e+18)
		tmp = Float64(z * x);
	elseif (z <= -1.3e-33)
		tmp = t_1;
	elseif (z <= -4.8e-163)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -3.5e-300)
		tmp = Float64(y * t);
	elseif (z <= 6.1e-170)
		tmp = x;
	elseif (z <= 6.5e+24)
		tmp = Float64(y * t);
	elseif ((z <= 3.3e+200) || !(z <= 3.2e+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 <= -2.9e+125)
		tmp = t_1;
	elseif (z <= -1.35e+18)
		tmp = z * x;
	elseif (z <= -1.3e-33)
		tmp = t_1;
	elseif (z <= -4.8e-163)
		tmp = y * -x;
	elseif (z <= -3.5e-300)
		tmp = y * t;
	elseif (z <= 6.1e-170)
		tmp = x;
	elseif (z <= 6.5e+24)
		tmp = y * t;
	elseif ((z <= 3.3e+200) || ~((z <= 3.2e+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, -2.9e+125], t$95$1, If[LessEqual[z, -1.35e+18], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.3e-33], t$95$1, If[LessEqual[z, -4.8e-163], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -3.5e-300], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.1e-170], x, If[LessEqual[z, 6.5e+24], N[(y * t), $MachinePrecision], If[Or[LessEqual[z, 3.3e+200], N[Not[LessEqual[z, 3.2e+245]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.89999999999999993e125 or -1.35e18 < z < -1.29999999999999997e-33 or 6.4999999999999996e24 < z < 3.3e200 or 3.20000000000000024e245 < 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 -2.89999999999999993e125 < z < -1.35e18 or 3.3e200 < z < 3.20000000000000024e245

   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 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-in 69.3%

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

      3. neg-sub0 69.3%

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

      4. sub-neg 69.3%

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

      5. +-commutative 69.3%

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

      6. associate--r+ 69.3%

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

      7. neg-sub0 69.3%

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

      8. remove-double-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0 66.6%

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

   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 -1.29999999999999997e-33 < z < -4.8000000000000001e-163

   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 -4.8000000000000001e-163 < z < -3.5000000000000002e-300 or 6.09999999999999999e-170 < z < 6.4999999999999996e24

   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 -3.5000000000000002e-300 < z < 6.09999999999999999e-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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-300}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+200} \lor \neg \left(z \leq 3.2 \cdot 10^{+245}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2950:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2950.0)
   (* z x)
   (if (<= z -1.1e-162)
     (* y (- x))
     (if (<= z -4.5e-299)
       (* y t)
       (if (<= z 1.45e-169) x (if (<= z 1.4e+21) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2950.0) {
		tmp = z * x;
	} else if (z <= -1.1e-162) {
		tmp = y * -x;
	} else if (z <= -4.5e-299) {
		tmp = y * t;
	} else if (z <= 1.45e-169) {
		tmp = x;
	} else if (z <= 1.4e+21) {
		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 <= (-2950.0d0)) then
        tmp = z * x
    else if (z <= (-1.1d-162)) then
        tmp = y * -x
    else if (z <= (-4.5d-299)) then
        tmp = y * t
    else if (z <= 1.45d-169) then
        tmp = x
    else if (z <= 1.4d+21) 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 <= -2950.0) {
		tmp = z * x;
	} else if (z <= -1.1e-162) {
		tmp = y * -x;
	} else if (z <= -4.5e-299) {
		tmp = y * t;
	} else if (z <= 1.45e-169) {
		tmp = x;
	} else if (z <= 1.4e+21) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2950.0:
		tmp = z * x
	elif z <= -1.1e-162:
		tmp = y * -x
	elif z <= -4.5e-299:
		tmp = y * t
	elif z <= 1.45e-169:
		tmp = x
	elif z <= 1.4e+21:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2950.0)
		tmp = Float64(z * x);
	elseif (z <= -1.1e-162)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -4.5e-299)
		tmp = Float64(y * t);
	elseif (z <= 1.45e-169)
		tmp = x;
	elseif (z <= 1.4e+21)
		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 <= -2950.0)
		tmp = z * x;
	elseif (z <= -1.1e-162)
		tmp = y * -x;
	elseif (z <= -4.5e-299)
		tmp = y * t;
	elseif (z <= 1.45e-169)
		tmp = x;
	elseif (z <= 1.4e+21)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2950.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.1e-162], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -4.5e-299], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.45e-169], x, If[LessEqual[z, 1.4e+21], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2950 or 1.4e21 < 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 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-rgt-neg-in 50.7%

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

      3. neg-sub0 50.7%

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

      4. sub-neg 50.7%

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

      5. +-commutative 50.7%

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

      6. associate--r+ 50.7%

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

      7. neg-sub0 50.7%

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

      8. remove-double-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around 0 42.5%

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

   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 -2950 < z < -1.1e-162

   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 -1.1e-162 < z < -4.50000000000000003e-299 or 1.4500000000000001e-169 < z < 1.4e21

   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 -4.50000000000000003e-299 < z < 1.4500000000000001e-169

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2950:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.05e-33)
     t_1
     (if (<= t 1.9e-213) (* 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 <= -1.05e-33) {
		tmp = t_1;
	} else if (t <= 1.9e-213) {
		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 <= (-1.05d-33)) then
        tmp = t_1
    else if (t <= 1.9d-213) 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 <= -1.05e-33) {
		tmp = t_1;
	} else if (t <= 1.9e-213) {
		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 <= -1.05e-33:
		tmp = t_1
	elif t <= 1.9e-213:
		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 <= -1.05e-33)
		tmp = t_1;
	elseif (t <= 1.9e-213)
		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 <= -1.05e-33)
		tmp = t_1;
	elseif (t <= 1.9e-213)
		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, -1.05e-33], t$95$1, If[LessEqual[t, 1.9e-213], N[(z * x), $MachinePrecision], If[LessEqual[t, 1.5e-10], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-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 -1.05e-33 < t < 1.9e-213

   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 93.4%

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

      1. mul-1-neg 93.4%

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

      2. distribute-rgt-neg-in 93.4%

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

      3. neg-sub0 93.4%

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

      4. sub-neg 93.4%

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

      5. +-commutative 93.4%

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

      6. associate--r+ 93.4%

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

      7. neg-sub0 93.4%

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

      8. remove-double-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 71.4%

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

   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 1.9e-213 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-114}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-20)
   (* y t)
   (if (<= y -5.6e-114) (* z x) (if (<= y 2.9e-8) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-20) {
		tmp = y * t;
	} else if (y <= -5.6e-114) {
		tmp = z * x;
	} else if (y <= 2.9e-8) {
		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 <= (-3.5d-20)) then
        tmp = y * t
    else if (y <= (-5.6d-114)) then
        tmp = z * x
    else if (y <= 2.9d-8) 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 <= -3.5e-20) {
		tmp = y * t;
	} else if (y <= -5.6e-114) {
		tmp = z * x;
	} else if (y <= 2.9e-8) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-20:
		tmp = y * t
	elif y <= -5.6e-114:
		tmp = z * x
	elif y <= 2.9e-8:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-20)
		tmp = Float64(y * t);
	elseif (y <= -5.6e-114)
		tmp = Float64(z * x);
	elseif (y <= 2.9e-8)
		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 <= -3.5e-20)
		tmp = y * t;
	elseif (y <= -5.6e-114)
		tmp = z * x;
	elseif (y <= 2.9e-8)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-20], N[(y * t), $MachinePrecision], If[LessEqual[y, -5.6e-114], N[(z * x), $MachinePrecision], If[LessEqual[y, 2.9e-8], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000003e-20 or 2.9000000000000002e-8 < 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 -3.50000000000000003e-20 < y < -5.6000000000000003e-114

   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 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-rgt-neg-in 68.1%

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

      3. neg-sub0 68.1%

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

      4. sub-neg 68.1%

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

      5. +-commutative 68.1%

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

      6. associate--r+ 68.1%

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

      7. neg-sub0 68.1%

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

      8. remove-double-neg 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in y around 0 68.1%

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

   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 -5.6000000000000003e-114 < y < 2.9000000000000002e-8

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-114}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-33} \lor \neg \left(t \leq 8 \cdot 10^{-94}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e-33) (not (<= t 8e-94)))
   (+ x (* t (- y z)))
   (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e-33) || !(t <= 8e-94)) {
		tmp = x + (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 <= (-1.05d-33)) .or. (.not. (t <= 8d-94))) then
        tmp = x + (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 <= -1.05e-33) || !(t <= 8e-94)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e-33) or not (t <= 8e-94):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e-33) || !(t <= 8e-94))
		tmp = Float64(x + 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 <= -1.05e-33) || ~((t <= 8e-94)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e-33], N[Not[LessEqual[t, 8e-94]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e-33 or 7.9999999999999996e-94 < t

   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 84.0%

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

   if -1.05e-33 < t < 7.9999999999999996e-94

   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 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-rgt-neg-in 91.5%

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

      3. neg-sub0 91.5%

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

      4. sub-neg 91.5%

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

      5. +-commutative 91.5%

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

      6. associate--r+ 91.5%

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

      7. neg-sub0 91.5%

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

      8. remove-double-neg 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around 0 68.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-33} \lor \neg \left(t \leq 8 \cdot 10^{-94}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 83.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e-34) (not (<= z 6.5e+19)))
   (+ x (* z (- x t)))
   (+ 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 * (x - t));
	} 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 * (x - t))
    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 * (x - t));
	} 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 * (x - t))
	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(x - t)));
	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 * (x - t));
	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[(x - t), $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%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

   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%

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

Alternative 9: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-6} \lor \neg \left(t \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e-6) (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 <= -3e-6) || !(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 <= (-3d-6)) .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 <= -3e-6) || !(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 <= -3e-6) 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 <= -3e-6) || !(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 <= -3e-6) || ~((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, -3e-6], 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 < -3.0000000000000001e-6 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 -3.0000000000000001e-6 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-6} \lor \neg \left(t \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-8} \lor \neg \left(t \leq 9 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.4e-8) (not (<= t 9e-10))) (* t (- y z)) (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e-8) || !(t <= 9e-10)) {
		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 <= (-1.4d-8)) .or. (.not. (t <= 9d-10))) 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 <= -1.4e-8) || !(t <= 9e-10)) {
		tmp = t * (y - z);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.4e-8) or not (t <= 9e-10):
		tmp = t * (y - z)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.4e-8) || !(t <= 9e-10))
		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 <= -1.4e-8) || ~((t <= 9e-10)))
		tmp = t * (y - z);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.4e-8], N[Not[LessEqual[t, 9e-10]], $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 < -1.4e-8 or 8.9999999999999999e-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 93.2%

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

   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 -1.4e-8 < t < 8.9999999999999999e-10

   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 87.8%

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

      1. mul-1-neg 87.8%

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

      2. distribute-rgt-neg-in 87.8%

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

      3. neg-sub0 87.8%

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

      4. sub-neg 87.8%

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

      5. +-commutative 87.8%

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

      6. associate--r+ 87.8%

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

      7. neg-sub0 87.8%

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

      8. remove-double-neg 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in y around 0 67.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-8} \lor \neg \left(t \leq 9 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-11} \lor \neg \left(y \leq 1.8 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e-11) (not (<= y 1.8e-13))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-11) || !(y <= 1.8e-13)) {
		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 <= (-1.85d-11)) .or. (.not. (y <= 1.8d-13))) 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 <= -1.85e-11) || !(y <= 1.8e-13)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e-11) or not (y <= 1.8e-13):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e-11) || !(y <= 1.8e-13))
		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 <= -1.85e-11) || ~((y <= 1.8e-13)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e-11], N[Not[LessEqual[y, 1.8e-13]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e-11 or 1.7999999999999999e-13 < 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 -1.8500000000000001e-11 < y < 1.7999999999999999e-13

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-11} \lor \neg \left(y \leq 1.8 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 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))))