Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.6s

Alternatives: 11

Speedup: 1.0×

• 33.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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 2: 54.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+273}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2300000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 470000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+146} \lor \neg \left(z \leq 6.6 \cdot 10^{+180}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -2.8e+273)
     (* x z)
     (if (<= z -2300000.0)
       t_1
       (if (<= z 470000.0)
         (+ x (* y t))
         (if (or (<= z 2.3e+146) (not (<= z 6.6e+180))) t_1 (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -2.8e+273) {
		tmp = x * z;
	} else if (z <= -2300000.0) {
		tmp = t_1;
	} else if (z <= 470000.0) {
		tmp = x + (y * t);
	} else if ((z <= 2.3e+146) || !(z <= 6.6e+180)) {
		tmp = t_1;
	} else {
		tmp = x * 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) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (z <= (-2.8d+273)) then
        tmp = x * z
    else if (z <= (-2300000.0d0)) then
        tmp = t_1
    else if (z <= 470000.0d0) then
        tmp = x + (y * t)
    else if ((z <= 2.3d+146) .or. (.not. (z <= 6.6d+180))) then
        tmp = t_1
    else
        tmp = x * z
    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 <= -2.8e+273) {
		tmp = x * z;
	} else if (z <= -2300000.0) {
		tmp = t_1;
	} else if (z <= 470000.0) {
		tmp = x + (y * t);
	} else if ((z <= 2.3e+146) || !(z <= 6.6e+180)) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -2.8e+273:
		tmp = x * z
	elif z <= -2300000.0:
		tmp = t_1
	elif z <= 470000.0:
		tmp = x + (y * t)
	elif (z <= 2.3e+146) or not (z <= 6.6e+180):
		tmp = t_1
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -2.8e+273)
		tmp = Float64(x * z);
	elseif (z <= -2300000.0)
		tmp = t_1;
	elseif (z <= 470000.0)
		tmp = Float64(x + Float64(y * t));
	elseif ((z <= 2.3e+146) || !(z <= 6.6e+180))
		tmp = t_1;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -2.8e+273)
		tmp = x * z;
	elseif (z <= -2300000.0)
		tmp = t_1;
	elseif (z <= 470000.0)
		tmp = x + (y * t);
	elseif ((z <= 2.3e+146) || ~((z <= 6.6e+180)))
		tmp = t_1;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.8e+273], N[(x * z), $MachinePrecision], If[LessEqual[z, -2300000.0], t$95$1, If[LessEqual[z, 470000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.3e+146], N[Not[LessEqual[z, 6.6e+180]], $MachinePrecision]], t$95$1, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000018e273 or 2.3e146 < z < 6.59999999999999978e180

   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 89.5%

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

      1. mul-1-neg 89.5%

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

      2. distribute-rgt-neg-in 89.5%

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

      3. sub-neg 89.5%

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

      4. +-commutative 89.5%

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

      5. distribute-neg-in 89.5%

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

      6. remove-double-neg 89.5%

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

      7. sub-neg 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in z around inf 88.6%

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

       1. *-commutative 88.6%

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

   11. Simplified 88.6%

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

   if -2.80000000000000018e273 < z < -2.3e6 or 4.7e5 < z < 2.3e146 or 6.59999999999999978e180 < 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 63.7%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. *-commutative 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in x around 0 51.7%

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

      1. associate-*r* 51.7%

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

      2. neg-mul-1 51.7%

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

      3. *-commutative 51.7%

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

   9. Simplified 51.7%

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

   if -2.3e6 < z < 4.7e5

   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 71.5%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   6. Simplified 66.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+273}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2300000:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 470000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+146} \lor \neg \left(z \leq 6.6 \cdot 10^{+180}\right):\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+273}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 92:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+150} \lor \neg \left(z \leq 1.05 \cdot 10^{+179}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -4.8e+273)
     (* x z)
     (if (<= z -6.5e-15)
       t_1
       (if (<= z 92.0)
         x
         (if (or (<= z 3.6e+150) (not (<= z 1.05e+179))) t_1 (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -4.8e+273) {
		tmp = x * z;
	} else if (z <= -6.5e-15) {
		tmp = t_1;
	} else if (z <= 92.0) {
		tmp = x;
	} else if ((z <= 3.6e+150) || !(z <= 1.05e+179)) {
		tmp = t_1;
	} else {
		tmp = x * 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) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (z <= (-4.8d+273)) then
        tmp = x * z
    else if (z <= (-6.5d-15)) then
        tmp = t_1
    else if (z <= 92.0d0) then
        tmp = x
    else if ((z <= 3.6d+150) .or. (.not. (z <= 1.05d+179))) then
        tmp = t_1
    else
        tmp = x * z
    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 <= -4.8e+273) {
		tmp = x * z;
	} else if (z <= -6.5e-15) {
		tmp = t_1;
	} else if (z <= 92.0) {
		tmp = x;
	} else if ((z <= 3.6e+150) || !(z <= 1.05e+179)) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -4.8e+273:
		tmp = x * z
	elif z <= -6.5e-15:
		tmp = t_1
	elif z <= 92.0:
		tmp = x
	elif (z <= 3.6e+150) or not (z <= 1.05e+179):
		tmp = t_1
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -4.8e+273)
		tmp = Float64(x * z);
	elseif (z <= -6.5e-15)
		tmp = t_1;
	elseif (z <= 92.0)
		tmp = x;
	elseif ((z <= 3.6e+150) || !(z <= 1.05e+179))
		tmp = t_1;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -4.8e+273)
		tmp = x * z;
	elseif (z <= -6.5e-15)
		tmp = t_1;
	elseif (z <= 92.0)
		tmp = x;
	elseif ((z <= 3.6e+150) || ~((z <= 1.05e+179)))
		tmp = t_1;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -4.8e+273], N[(x * z), $MachinePrecision], If[LessEqual[z, -6.5e-15], t$95$1, If[LessEqual[z, 92.0], x, If[Or[LessEqual[z, 3.6e+150], N[Not[LessEqual[z, 1.05e+179]], $MachinePrecision]], t$95$1, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e273 or 3.59999999999999986e150 < z < 1.0499999999999999e179

   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 89.5%

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

      1. mul-1-neg 89.5%

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

      2. distribute-rgt-neg-in 89.5%

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

      3. sub-neg 89.5%

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

      4. +-commutative 89.5%

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

      5. distribute-neg-in 89.5%

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

      6. remove-double-neg 89.5%

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

      7. sub-neg 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in z around inf 88.6%

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

       1. *-commutative 88.6%

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

   11. Simplified 88.6%

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

   if -4.8000000000000003e273 < z < -6.49999999999999991e-15 or 92 < z < 3.59999999999999986e150 or 1.0499999999999999e179 < 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 63.0%

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

   4. Taylor expanded in y around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

      3. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in x around 0 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. *-commutative 50.2%

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

   9. Simplified 50.2%

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

   if -6.49999999999999991e-15 < z < 92

   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 72.7%

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

   4. Taylor expanded in x around inf 30.8%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+273}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 92:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+150} \lor \neg \left(z \leq 1.05 \cdot 10^{+179}\right):\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := x + y \cdot t\\ \mathbf{if}\;t \leq -1 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+42}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 4.25 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (+ x (* y t))))
   (if (<= t -1e+209)
     t_1
     (if (<= t -1.7e+113)
       t_2
       (if (<= t 8.5e+42) (+ x (* x (- z y))) (if (<= t 4.25e+99) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x + (y * t);
	double tmp;
	if (t <= -1e+209) {
		tmp = t_1;
	} else if (t <= -1.7e+113) {
		tmp = t_2;
	} else if (t <= 8.5e+42) {
		tmp = x + (x * (z - y));
	} else if (t <= 4.25e+99) {
		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 = x - (z * t)
    t_2 = x + (y * t)
    if (t <= (-1d+209)) then
        tmp = t_1
    else if (t <= (-1.7d+113)) then
        tmp = t_2
    else if (t <= 8.5d+42) then
        tmp = x + (x * (z - y))
    else if (t <= 4.25d+99) 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 = x - (z * t);
	double t_2 = x + (y * t);
	double tmp;
	if (t <= -1e+209) {
		tmp = t_1;
	} else if (t <= -1.7e+113) {
		tmp = t_2;
	} else if (t <= 8.5e+42) {
		tmp = x + (x * (z - y));
	} else if (t <= 4.25e+99) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = x + (y * t)
	tmp = 0
	if t <= -1e+209:
		tmp = t_1
	elif t <= -1.7e+113:
		tmp = t_2
	elif t <= 8.5e+42:
		tmp = x + (x * (z - y))
	elif t <= 4.25e+99:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (t <= -1e+209)
		tmp = t_1;
	elseif (t <= -1.7e+113)
		tmp = t_2;
	elseif (t <= 8.5e+42)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	elseif (t <= 4.25e+99)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (t <= -1e+209)
		tmp = t_1;
	elseif (t <= -1.7e+113)
		tmp = t_2;
	elseif (t <= 8.5e+42)
		tmp = x + (x * (z - y));
	elseif (t <= 4.25e+99)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+209], t$95$1, If[LessEqual[t, -1.7e+113], t$95$2, If[LessEqual[t, 8.5e+42], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.25e+99], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0000000000000001e209 or 4.24999999999999992e99 < 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 98.4%

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

   4. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

      3. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -1.0000000000000001e209 < t < -1.70000000000000009e113 or 8.5000000000000003e42 < t < 4.24999999999999992e99

   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 88.4%

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

   4. Taylor expanded in y around inf 64.6%

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

      1. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if -1.70000000000000009e113 < t < 8.5000000000000003e42

   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 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-rgt-neg-in 76.0%

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

      3. sub-neg 76.0%

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

      4. +-commutative 76.0%

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

      5. distribute-neg-in 76.0%

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

      6. remove-double-neg 76.0%

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

      7. sub-neg 76.0%

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

   5. Simplified 76.0%

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

Alternative 5: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+272}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-124}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -1e+272)
     (* x z)
     (if (<= z -5.5e+92)
       t_1
       (if (<= z -6e-124)
         (- x (* x y))
         (if (<= z 18000.0) (+ x (* y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -1e+272) {
		tmp = x * z;
	} else if (z <= -5.5e+92) {
		tmp = t_1;
	} else if (z <= -6e-124) {
		tmp = x - (x * y);
	} else if (z <= 18000.0) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (z <= (-1d+272)) then
        tmp = x * z
    else if (z <= (-5.5d+92)) then
        tmp = t_1
    else if (z <= (-6d-124)) then
        tmp = x - (x * y)
    else if (z <= 18000.0d0) then
        tmp = x + (y * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -1e+272) {
		tmp = x * z;
	} else if (z <= -5.5e+92) {
		tmp = t_1;
	} else if (z <= -6e-124) {
		tmp = x - (x * y);
	} else if (z <= 18000.0) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -1e+272:
		tmp = x * z
	elif z <= -5.5e+92:
		tmp = t_1
	elif z <= -6e-124:
		tmp = x - (x * y)
	elif z <= 18000.0:
		tmp = x + (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 <= -1e+272)
		tmp = Float64(x * z);
	elseif (z <= -5.5e+92)
		tmp = t_1;
	elseif (z <= -6e-124)
		tmp = Float64(x - Float64(x * y));
	elseif (z <= 18000.0)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -1e+272)
		tmp = x * z;
	elseif (z <= -5.5e+92)
		tmp = t_1;
	elseif (z <= -6e-124)
		tmp = x - (x * y);
	elseif (z <= 18000.0)
		tmp = x + (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, -1e+272], N[(x * z), $MachinePrecision], If[LessEqual[z, -5.5e+92], t$95$1, If[LessEqual[z, -6e-124], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 18000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0000000000000001e272

   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 90.4%

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

      1. mul-1-neg 90.4%

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

      2. distribute-rgt-neg-in 90.4%

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

      3. sub-neg 90.4%

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

      4. +-commutative 90.4%

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

      5. distribute-neg-in 90.4%

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

      6. remove-double-neg 90.4%

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

      7. sub-neg 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in z around inf 88.7%

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

      1. *-commutative 88.7%

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

   8. Simplified 88.7%

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

   9. Taylor expanded in z around inf 88.7%

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

       1. *-commutative 88.7%

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

   11. Simplified 88.7%

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

   if -1.0000000000000001e272 < z < -5.50000000000000053e92 or 18000 < 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 60.6%

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

   4. Taylor expanded in y around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

      3. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in x around 0 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

      3. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if -5.50000000000000053e92 < z < -6e-124

   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 68.2%

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

      1. mul-1-neg 68.2%

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

      2. distribute-rgt-neg-in 68.2%

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

      3. sub-neg 68.2%

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

      4. +-commutative 68.2%

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

      5. distribute-neg-in 68.2%

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

      6. remove-double-neg 68.2%

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

      7. sub-neg 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in z around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

      3. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   if -6e-124 < z < 18000

   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 74.0%

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

   4. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   6. Simplified 69.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+272}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-124}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+30}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))))
   (if (<= y -1.95e+16)
     t_1
     (if (<= y 7.8e+30)
       (- x (* z t))
       (if (<= y 9.5e+209) t_1 (+ x (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double tmp;
	if (y <= -1.95e+16) {
		tmp = t_1;
	} else if (y <= 7.8e+30) {
		tmp = x - (z * t);
	} else if (y <= 9.5e+209) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * y)
    if (y <= (-1.95d+16)) then
        tmp = t_1
    else if (y <= 7.8d+30) then
        tmp = x - (z * t)
    else if (y <= 9.5d+209) then
        tmp = t_1
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double tmp;
	if (y <= -1.95e+16) {
		tmp = t_1;
	} else if (y <= 7.8e+30) {
		tmp = x - (z * t);
	} else if (y <= 9.5e+209) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	tmp = 0
	if y <= -1.95e+16:
		tmp = t_1
	elif y <= 7.8e+30:
		tmp = x - (z * t)
	elif y <= 9.5e+209:
		tmp = t_1
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	tmp = 0.0
	if (y <= -1.95e+16)
		tmp = t_1;
	elseif (y <= 7.8e+30)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 9.5e+209)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	tmp = 0.0;
	if (y <= -1.95e+16)
		tmp = t_1;
	elseif (y <= 7.8e+30)
		tmp = x - (z * t);
	elseif (y <= 9.5e+209)
		tmp = t_1;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+16], t$95$1, If[LessEqual[y, 7.8e+30], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+209], t$95$1, N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95e16 or 7.80000000000000021e30 < y < 9.50000000000000069e209

   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 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-rgt-neg-in 60.6%

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

      3. sub-neg 60.6%

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

      4. +-commutative 60.6%

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

      5. distribute-neg-in 60.6%

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

      6. remove-double-neg 60.6%

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

      7. sub-neg 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in z around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

      3. *-commutative 47.6%

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

   8. Simplified 47.6%

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

   if -1.95e16 < y < 7.80000000000000021e30

   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 79.3%

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

   4. Taylor expanded in y around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. unsub-neg 67.0%

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

      3. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   if 9.50000000000000069e209 < y

   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 68.8%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   6. Simplified 66.9%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+16}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+30}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+209}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6300000 \lor \neg \left(z \leq 0.024\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6300000.0) (not (<= z 0.024)))
   (+ x (* z (- x t)))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6300000.0) || !(z <= 0.024)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (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 ((z <= (-6300000.0d0)) .or. (.not. (z <= 0.024d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6300000.0) || !(z <= 0.024)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6300000.0) or not (z <= 0.024):
		tmp = x + (z * (x - t))
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6300000.0) || !(z <= 0.024))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6300000.0) || ~((z <= 0.024)))
		tmp = x + (z * (x - t));
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6300000.0], N[Not[LessEqual[z, 0.024]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.3e6 or 0.024 < 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 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

   5. Simplified 80.0%

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

   if -6.3e6 < z < 0.024

   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 95.1%

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

      1. *-commutative 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6300000 \lor \neg \left(z \leq 0.024\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-32} \lor \neg \left(t \leq 3.1 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e-32) (not (<= t 3.1e+40)))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e-32) || !(t <= 3.1e+40)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - 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 <= (-9d-32)) .or. (.not. (t <= 3.1d+40))) then
        tmp = x - (t * (z - y))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e-32) || !(t <= 3.1e+40)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e-32) or not (t <= 3.1e+40):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e-32) || !(t <= 3.1e+40))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9e-32) || ~((t <= 3.1e+40)))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e-32], N[Not[LessEqual[t, 3.1e+40]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000009e-32 or 3.0999999999999998e40 < 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 88.9%

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

   if -9.00000000000000009e-32 < t < 3.0999999999999998e40

   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 81.6%

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

      1. mul-1-neg 81.6%

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

      2. distribute-rgt-neg-in 81.6%

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

      3. sub-neg 81.6%

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

      4. +-commutative 81.6%

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

      5. distribute-neg-in 81.6%

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

      6. remove-double-neg 81.6%

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

      7. sub-neg 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-32} \lor \neg \left(t \leq 3.1 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -860000000000 \lor \neg \left(y \leq 0.0026\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -860000000000.0) (not (<= y 0.0026)))
   (- x (* y (- x t)))
   (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -860000000000.0) || !(y <= 0.0026)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x - (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 ((y <= (-860000000000.0d0)) .or. (.not. (y <= 0.0026d0))) then
        tmp = x - (y * (x - t))
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -860000000000.0) || !(y <= 0.0026)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -860000000000.0) or not (y <= 0.0026):
		tmp = x - (y * (x - t))
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -860000000000.0) || !(y <= 0.0026))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -860000000000.0) || ~((y <= 0.0026)))
		tmp = x - (y * (x - t));
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -860000000000.0], N[Not[LessEqual[y, 0.0026]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6e11 or 0.0025999999999999999 < 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 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   if -8.6e11 < y < 0.0025999999999999999

   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 78.3%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

      3. *-commutative 68.5%

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

   6. Simplified 68.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -860000000000 \lor \neg \left(y \leq 0.0026\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+16) (not (<= z 1.0))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+16) || !(z <= 1.0)) {
		tmp = x * z;
	} 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 ((z <= (-1.15d+16)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * z
    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 ((z <= -1.15e+16) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+16) or not (z <= 1.0):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+16) || !(z <= 1.0))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+16) || ~((z <= 1.0)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+16], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e16 or 1 < 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 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-rgt-neg-in 51.9%

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

      3. sub-neg 51.9%

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

      4. +-commutative 51.9%

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

      5. distribute-neg-in 51.9%

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

      6. remove-double-neg 51.9%

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

      7. sub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in z around inf 39.7%

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

       1. *-commutative 39.7%

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

   11. Simplified 39.7%

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

   if -1.15e16 < z < 1

   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 71.9%

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

   4. Taylor expanded in x around inf 29.6%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 18.4% 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 64.8%

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

4. Taylor expanded in x around inf 16.0%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer target: 96.3% 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 2024110 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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