Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.8s

Alternatives: 12

Speedup: 1.0×

• 34.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 35.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134} \lor \neg \left(z \leq 5.2 \cdot 10^{-18}\right) \land z \leq 3.8 \cdot 10^{+138}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -8.2e-12)
     t_1
     (if (<= z -1.65e-250)
       x
       (if (or (<= z 1.55e-134) (and (not (<= z 5.2e-18)) (<= z 3.8e+138)))
         (* y t)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -8.2e-12) {
		tmp = t_1;
	} else if (z <= -1.65e-250) {
		tmp = x;
	} else if ((z <= 1.55e-134) || (!(z <= 5.2e-18) && (z <= 3.8e+138))) {
		tmp = 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 = t * -z
    if (z <= (-8.2d-12)) then
        tmp = t_1
    else if (z <= (-1.65d-250)) then
        tmp = x
    else if ((z <= 1.55d-134) .or. (.not. (z <= 5.2d-18)) .and. (z <= 3.8d+138)) then
        tmp = 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 = t * -z;
	double tmp;
	if (z <= -8.2e-12) {
		tmp = t_1;
	} else if (z <= -1.65e-250) {
		tmp = x;
	} else if ((z <= 1.55e-134) || (!(z <= 5.2e-18) && (z <= 3.8e+138))) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -8.2e-12:
		tmp = t_1
	elif z <= -1.65e-250:
		tmp = x
	elif (z <= 1.55e-134) or (not (z <= 5.2e-18) and (z <= 3.8e+138)):
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -8.2e-12)
		tmp = t_1;
	elseif (z <= -1.65e-250)
		tmp = x;
	elseif ((z <= 1.55e-134) || (!(z <= 5.2e-18) && (z <= 3.8e+138)))
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -8.2e-12)
		tmp = t_1;
	elseif (z <= -1.65e-250)
		tmp = x;
	elseif ((z <= 1.55e-134) || (~((z <= 5.2e-18)) && (z <= 3.8e+138)))
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -8.2e-12], t$95$1, If[LessEqual[z, -1.65e-250], x, If[Or[LessEqual[z, 1.55e-134], And[N[Not[LessEqual[z, 5.2e-18]], $MachinePrecision], LessEqual[z, 3.8e+138]]], N[(y * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999979e-12 or 1.55000000000000003e-134 < z < 5.2000000000000001e-18 or 3.80000000000000012e138 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 60.3%

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

   4. Taylor expanded in y around 0 58.7%

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

      1. associate-+r+ 58.7%

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

      2. mul-1-neg 58.7%

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

      3. sub-neg 58.7%

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

      4. associate-+l- 58.7%

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

   6. Applied egg-rr 58.7%

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

   7. Taylor expanded in z around inf 45.5%

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

      1. associate-*r* 45.5%

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

      2. neg-mul-1 45.5%

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

   9. Simplified 45.5%

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

   if -8.19999999999999979e-12 < z < -1.65e-250

   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 76.1%

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

   4. Taylor expanded in x around inf 47.0%

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

   if -1.65e-250 < z < 1.55000000000000003e-134 or 5.2000000000000001e-18 < z < 3.80000000000000012e138

   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 63.7%

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

   4. Taylor expanded in y around 0 60.9%

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

      1. associate-+r+ 60.9%

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

      2. mul-1-neg 60.9%

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

      3. sub-neg 60.9%

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

      4. associate-+l- 60.9%

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

   6. Applied egg-rr 60.9%

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

   7. Taylor expanded in y around inf 40.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134} \lor \neg \left(z \leq 5.2 \cdot 10^{-18}\right) \land z \leq 3.8 \cdot 10^{+138}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-20} \lor \neg \left(z \leq 1.45 \cdot 10^{+112}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -3.5e-10)
     t_1
     (if (<= z -2.85e-248)
       x
       (if (<= z 1.55e-134)
         (* y t)
         (if (or (<= z 3.9e-20) (not (<= z 1.45e+112))) t_1 (* x (- y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -3.5e-10) {
		tmp = t_1;
	} else if (z <= -2.85e-248) {
		tmp = x;
	} else if (z <= 1.55e-134) {
		tmp = y * t;
	} else if ((z <= 3.9e-20) || !(z <= 1.45e+112)) {
		tmp = t_1;
	} else {
		tmp = x * -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) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (z <= (-3.5d-10)) then
        tmp = t_1
    else if (z <= (-2.85d-248)) then
        tmp = x
    else if (z <= 1.55d-134) then
        tmp = y * t
    else if ((z <= 3.9d-20) .or. (.not. (z <= 1.45d+112))) then
        tmp = t_1
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -3.5e-10) {
		tmp = t_1;
	} else if (z <= -2.85e-248) {
		tmp = x;
	} else if (z <= 1.55e-134) {
		tmp = y * t;
	} else if ((z <= 3.9e-20) || !(z <= 1.45e+112)) {
		tmp = t_1;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -3.5e-10:
		tmp = t_1
	elif z <= -2.85e-248:
		tmp = x
	elif z <= 1.55e-134:
		tmp = y * t
	elif (z <= 3.9e-20) or not (z <= 1.45e+112):
		tmp = t_1
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -3.5e-10)
		tmp = t_1;
	elseif (z <= -2.85e-248)
		tmp = x;
	elseif (z <= 1.55e-134)
		tmp = Float64(y * t);
	elseif ((z <= 3.9e-20) || !(z <= 1.45e+112))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -3.5e-10)
		tmp = t_1;
	elseif (z <= -2.85e-248)
		tmp = x;
	elseif (z <= 1.55e-134)
		tmp = y * t;
	elseif ((z <= 3.9e-20) || ~((z <= 1.45e+112)))
		tmp = t_1;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.5e-10], t$95$1, If[LessEqual[z, -2.85e-248], x, If[LessEqual[z, 1.55e-134], N[(y * t), $MachinePrecision], If[Or[LessEqual[z, 3.9e-20], N[Not[LessEqual[z, 1.45e+112]], $MachinePrecision]], t$95$1, N[(x * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e-10 or 1.55000000000000003e-134 < z < 3.90000000000000007e-20 or 1.4500000000000001e112 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.0%

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

   4. Taylor expanded in y around 0 58.0%

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

      1. associate-+r+ 58.0%

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

      2. mul-1-neg 58.0%

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

      3. sub-neg 58.0%

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

      4. associate-+l- 58.0%

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

   6. Applied egg-rr 58.0%

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

   7. Taylor expanded in z around inf 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

   9. Simplified 45.4%

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

   if -3.4999999999999998e-10 < z < -2.8499999999999999e-248

   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 76.1%

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

   4. Taylor expanded in x around inf 47.0%

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

   if -2.8499999999999999e-248 < z < 1.55000000000000003e-134

   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 79.7%

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

   4. Taylor expanded in y around 0 79.7%

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

      1. associate-+r+ 79.7%

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

      2. mul-1-neg 79.7%

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

      3. sub-neg 79.7%

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

      4. associate-+l- 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in y around inf 49.5%

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

   if 3.90000000000000007e-20 < z < 1.4500000000000001e112

   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 71.6%

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

      1. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in x around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

   8. Simplified 56.9%

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

   9. Taylor expanded in y around inf 49.8%

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

       1. associate-*r* 49.8%

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

       2. mul-1-neg 49.8%

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

   11. Simplified 49.8%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-20} \lor \neg \left(z \leq 1.45 \cdot 10^{+112}\right):\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + x \cdot z\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-192}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 14000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* x z))))
   (if (<= y -1.75e-19)
     t_1
     (if (<= y -5.8e-149)
       t_2
       (if (<= y -2.9e-192)
         (* (- y z) t)
         (if (<= y 14000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + (x * z);
	double tmp;
	if (y <= -1.75e-19) {
		tmp = t_1;
	} else if (y <= -5.8e-149) {
		tmp = t_2;
	} else if (y <= -2.9e-192) {
		tmp = (y - z) * t;
	} else if (y <= 14000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x + (x * z)
    if (y <= (-1.75d-19)) then
        tmp = t_1
    else if (y <= (-5.8d-149)) then
        tmp = t_2
    else if (y <= (-2.9d-192)) then
        tmp = (y - z) * t
    else if (y <= 14000000000.0d0) then
        tmp = t_2
    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 * (t - x);
	double t_2 = x + (x * z);
	double tmp;
	if (y <= -1.75e-19) {
		tmp = t_1;
	} else if (y <= -5.8e-149) {
		tmp = t_2;
	} else if (y <= -2.9e-192) {
		tmp = (y - z) * t;
	} else if (y <= 14000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + (x * z)
	tmp = 0
	if y <= -1.75e-19:
		tmp = t_1
	elif y <= -5.8e-149:
		tmp = t_2
	elif y <= -2.9e-192:
		tmp = (y - z) * t
	elif y <= 14000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (y <= -1.75e-19)
		tmp = t_1;
	elseif (y <= -5.8e-149)
		tmp = t_2;
	elseif (y <= -2.9e-192)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 14000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x + (x * z);
	tmp = 0.0;
	if (y <= -1.75e-19)
		tmp = t_1;
	elseif (y <= -5.8e-149)
		tmp = t_2;
	elseif (y <= -2.9e-192)
		tmp = (y - z) * t;
	elseif (y <= 14000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-19], t$95$1, If[LessEqual[y, -5.8e-149], t$95$2, If[LessEqual[y, -2.9e-192], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 14000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000008e-19 or 1.4e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.3%

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

      1. *-commutative 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in x around -inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. sub-neg 74.0%

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

      5. metadata-eval 74.0%

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

      6. +-commutative 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in y around inf 76.6%

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

   if -1.75000000000000008e-19 < y < -5.8e-149 or -2.90000000000000016e-192 < y < 1.4e10

   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 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-lft-neg-out 62.7%

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

      3. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around 0 61.8%

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

      1. *-commutative 61.8%

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

   8. Simplified 61.8%

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

   if -5.8e-149 < y < -2.90000000000000016e-192

   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 91.8%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. associate-+r+ 91.8%

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

      2. mul-1-neg 91.8%

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

      3. sub-neg 91.8%

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

      4. associate-+l- 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in x around 0 83.0%

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

      1. distribute-lft-out-- 83.0%

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

   9. Simplified 83.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-149}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-192}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 14000000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -0.36:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-127}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 35000000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -0.36)
     t_1
     (if (<= y 3.55e-127)
       (- x (* z t))
       (if (<= y 35000000000.0)
         (+ x (* x z))
         (if (<= y 5.4e+110) (* (- y z) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -0.36) {
		tmp = t_1;
	} else if (y <= 3.55e-127) {
		tmp = x - (z * t);
	} else if (y <= 35000000000.0) {
		tmp = x + (x * z);
	} else if (y <= 5.4e+110) {
		tmp = (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 = y * (t - x)
    if (y <= (-0.36d0)) then
        tmp = t_1
    else if (y <= 3.55d-127) then
        tmp = x - (z * t)
    else if (y <= 35000000000.0d0) then
        tmp = x + (x * z)
    else if (y <= 5.4d+110) then
        tmp = (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 = y * (t - x);
	double tmp;
	if (y <= -0.36) {
		tmp = t_1;
	} else if (y <= 3.55e-127) {
		tmp = x - (z * t);
	} else if (y <= 35000000000.0) {
		tmp = x + (x * z);
	} else if (y <= 5.4e+110) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -0.36:
		tmp = t_1
	elif y <= 3.55e-127:
		tmp = x - (z * t)
	elif y <= 35000000000.0:
		tmp = x + (x * z)
	elif y <= 5.4e+110:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -0.36)
		tmp = t_1;
	elseif (y <= 3.55e-127)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 35000000000.0)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 5.4e+110)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -0.36)
		tmp = t_1;
	elseif (y <= 3.55e-127)
		tmp = x - (z * t);
	elseif (y <= 35000000000.0)
		tmp = x + (x * z);
	elseif (y <= 5.4e+110)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.36], t$95$1, If[LessEqual[y, 3.55e-127], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 35000000000.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+110], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.35999999999999999 or 5.40000000000000019e110 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around -inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

      4. sub-neg 77.5%

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

      5. metadata-eval 77.5%

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

      6. +-commutative 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in y around inf 84.4%

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

   if -0.35999999999999999 < y < 3.5500000000000001e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.5%

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

   4. Taylor expanded in y around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

   6. Simplified 74.6%

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

   if 3.5500000000000001e-127 < y < 3.5e10

   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 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-lft-neg-out 68.1%

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

      3. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

   8. Simplified 64.4%

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

   if 3.5e10 < y < 5.40000000000000019e110

   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 64.5%

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

   4. Taylor expanded in y around 0 64.5%

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

      1. associate-+r+ 64.5%

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

      2. mul-1-neg 64.5%

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

      3. sub-neg 64.5%

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

      4. associate-+l- 64.5%

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

   6. Applied egg-rr 64.5%

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

   7. Taylor expanded in x around 0 64.8%

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

      1. distribute-lft-out-- 64.8%

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

   9. Simplified 64.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.36:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-127}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 35000000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;y \leq 70000000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* y (- t x))))
   (if (<= y -6.2e+27)
     t_2
     (if (<= y 1.75e-25)
       (+ x t_1)
       (if (<= y 70000000000.0) (+ x (* x z)) (if (<= y 1.1e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -6.2e+27) {
		tmp = t_2;
	} else if (y <= 1.75e-25) {
		tmp = x + t_1;
	} else if (y <= 70000000000.0) {
		tmp = x + (x * z);
	} else if (y <= 1.1e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = y * (t - x)
    if (y <= (-6.2d+27)) then
        tmp = t_2
    else if (y <= 1.75d-25) then
        tmp = x + t_1
    else if (y <= 70000000000.0d0) then
        tmp = x + (x * z)
    else if (y <= 1.1d+111) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = y * (t - x);
	double tmp;
	if (y <= -6.2e+27) {
		tmp = t_2;
	} else if (y <= 1.75e-25) {
		tmp = x + t_1;
	} else if (y <= 70000000000.0) {
		tmp = x + (x * z);
	} else if (y <= 1.1e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = y * (t - x)
	tmp = 0
	if y <= -6.2e+27:
		tmp = t_2
	elif y <= 1.75e-25:
		tmp = x + t_1
	elif y <= 70000000000.0:
		tmp = x + (x * z)
	elif y <= 1.1e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -6.2e+27)
		tmp = t_2;
	elseif (y <= 1.75e-25)
		tmp = Float64(x + t_1);
	elseif (y <= 70000000000.0)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.1e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = y * (t - x);
	tmp = 0.0;
	if (y <= -6.2e+27)
		tmp = t_2;
	elseif (y <= 1.75e-25)
		tmp = x + t_1;
	elseif (y <= 70000000000.0)
		tmp = x + (x * z);
	elseif (y <= 1.1e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+27], t$95$2, If[LessEqual[y, 1.75e-25], N[(x + t$95$1), $MachinePrecision], If[LessEqual[y, 70000000000.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.19999999999999992e27 or 1.09999999999999999e111 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around -inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

      4. sub-neg 77.5%

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

      5. metadata-eval 77.5%

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

      6. +-commutative 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in y around inf 84.4%

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

   if -6.19999999999999992e27 < y < 1.7500000000000001e-25

   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%

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

   if 1.7500000000000001e-25 < y < 7e10

   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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-lft-neg-out 86.3%

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

      3. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 72.1%

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

      1. *-commutative 72.1%

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

   8. Simplified 72.1%

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

   if 7e10 < y < 1.09999999999999999e111

   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 64.5%

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

   4. Taylor expanded in y around 0 64.5%

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

      1. associate-+r+ 64.5%

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

      2. mul-1-neg 64.5%

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

      3. sub-neg 64.5%

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

      4. associate-+l- 64.5%

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

   6. Applied egg-rr 64.5%

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

   7. Taylor expanded in x around 0 64.8%

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

      1. distribute-lft-out-- 64.8%

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

   9. Simplified 64.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 70000000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+111}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -650000 \lor \neg \left(y \leq 5.1 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -650000.0) (not (<= y 5.1e+14)))
   (* y (- t x))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -650000.0) || !(y <= 5.1e+14)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-650000.0d0)) .or. (.not. (y <= 5.1d+14))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -650000.0) || !(y <= 5.1e+14)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -650000.0) or not (y <= 5.1e+14):
		tmp = y * (t - x)
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -650000.0) || !(y <= 5.1e+14))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -650000.0) || ~((y <= 5.1e+14)))
		tmp = y * (t - x);
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -650000.0], N[Not[LessEqual[y, 5.1e+14]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e5 or 5.1e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in x around -inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. sub-neg 74.2%

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

      5. metadata-eval 74.2%

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

      6. +-commutative 74.2%

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

   8. Simplified 74.2%

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

   9. Taylor expanded in y around inf 79.9%

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

   if -6.5e5 < y < 5.1e14

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in y around 0 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-*r* 87.3%

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

      3. distribute-rgt-in 89.6%

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

      4. mul-1-neg 89.6%

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

      5. sub-neg 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -650000 \lor \neg \left(y \leq 5.1 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-19}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+19}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.75e-19)
     (+ x t_1)
     (if (<= y 6.8e+19) (+ x (* z (- x t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.75e-19) {
		tmp = x + t_1;
	} else if (y <= 6.8e+19) {
		tmp = x + (z * (x - 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 = y * (t - x)
    if (y <= (-1.75d-19)) then
        tmp = x + t_1
    else if (y <= 6.8d+19) then
        tmp = x + (z * (x - 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 = y * (t - x);
	double tmp;
	if (y <= -1.75e-19) {
		tmp = x + t_1;
	} else if (y <= 6.8e+19) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1.75e-19:
		tmp = x + t_1
	elif y <= 6.8e+19:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.75e-19)
		tmp = Float64(x + t_1);
	elseif (y <= 6.8e+19)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.75e-19)
		tmp = x + t_1;
	elseif (y <= 6.8e+19)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-19], N[(x + t$95$1), $MachinePrecision], If[LessEqual[y, 6.8e+19], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000008e-19

   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 78.8%

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

      1. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   if -1.75000000000000008e-19 < y < 6.8e19

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r* 90.9%

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

      3. distribute-rgt-in 92.5%

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

      4. mul-1-neg 92.5%

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

      5. sub-neg 92.5%

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

   7. Simplified 92.5%

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

   if 6.8e19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in x around -inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. metadata-eval 72.5%

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

      6. +-commutative 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in y around inf 81.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+19}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -13000000000 \lor \neg \left(x \leq 5.1 \cdot 10^{+197}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -13000000000.0) (not (<= x 5.1e+197)))
   (* x (- y))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -13000000000.0) || !(x <= 5.1e+197)) {
		tmp = x * -y;
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-13000000000.0d0)) .or. (.not. (x <= 5.1d+197))) then
        tmp = x * -y
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -13000000000.0) || !(x <= 5.1e+197)) {
		tmp = x * -y;
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -13000000000.0) or not (x <= 5.1e+197):
		tmp = x * -y
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -13000000000.0) || !(x <= 5.1e+197))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -13000000000.0) || ~((x <= 5.1e+197)))
		tmp = x * -y;
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -13000000000.0], N[Not[LessEqual[x, 5.1e+197]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e10 or 5.09999999999999992e197 < x

   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 71.2%

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

      1. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in y around inf 45.3%

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

       1. associate-*r* 45.3%

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

       2. mul-1-neg 45.3%

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

   11. Simplified 45.3%

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

   if -1.3e10 < x < 5.09999999999999992e197

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.0%

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

   4. Taylor expanded in y around 0 75.2%

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

      1. associate-+r+ 75.2%

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

      2. mul-1-neg 75.2%

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

      3. sub-neg 75.2%

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

      4. associate-+l- 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in x around 0 60.3%

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

      1. distribute-lft-out-- 62.0%

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

   9. Simplified 62.0%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -13000000000 \lor \neg \left(x \leq 5.1 \cdot 10^{+197}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -505 \lor \neg \left(x \leq 5.8 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -505.0) (not (<= x 5.8e+48))) (* x (- 1.0 y)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -505.0) || !(x <= 5.8e+48)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-505.0d0)) .or. (.not. (x <= 5.8d+48))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -505.0) || !(x <= 5.8e+48)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -505.0) or not (x <= 5.8e+48):
		tmp = x * (1.0 - y)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -505.0) || !(x <= 5.8e+48))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -505.0) || ~((x <= 5.8e+48)))
		tmp = x * (1.0 - y);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -505.0], N[Not[LessEqual[x, 5.8e+48]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -505 or 5.7999999999999998e48 < x

   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 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

   8. Simplified 59.8%

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

   if -505 < x < 5.7999999999999998e48

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.1%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. associate-+r+ 80.6%

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

      2. mul-1-neg 80.6%

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

      3. sub-neg 80.6%

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

      4. associate-+l- 80.6%

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

   6. Applied egg-rr 80.6%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. distribute-lft-out-- 70.0%

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

   9. Simplified 70.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -505 \lor \neg \left(x \leq 5.8 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-20} \lor \neg \left(y \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.2e-20) (not (<= y 1.25e-34))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e-20) || !(y <= 1.25e-34)) {
		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 <= (-8.2d-20)) .or. (.not. (y <= 1.25d-34))) 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 <= -8.2e-20) || !(y <= 1.25e-34)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.2e-20) or not (y <= 1.25e-34):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.2e-20) || !(y <= 1.25e-34))
		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 <= -8.2e-20) || ~((y <= 1.25e-34)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.2e-20], N[Not[LessEqual[y, 1.25e-34]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000002e-20 or 1.2500000000000001e-34 < 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 51.2%

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

   4. Taylor expanded in y around 0 48.3%

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

      1. associate-+r+ 48.3%

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

      2. mul-1-neg 48.3%

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

      3. sub-neg 48.3%

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

      4. associate-+l- 48.3%

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

   6. Applied egg-rr 48.3%

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

   7. Taylor expanded in y around inf 36.9%

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

   if -8.2000000000000002e-20 < y < 1.2500000000000001e-34

   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 81.1%

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

   4. Taylor expanded in x around inf 38.5%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-20} \lor \neg \left(y \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 17.5% 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 64.6%

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

4. Taylor expanded in x around inf 19.7%

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

5. Final simplification 19.7%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.5% 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 2024039 
(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))))