Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 15

Speedup: 1.0×

• 34.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1460:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1460.0)
     t_1
     (if (<= z -8.5e-301)
       (+ x (* y t))
       (if (<= z 1.4e-22)
         (* x (- 1.0 y))
         (if (<= z 2.3e+57) (* y (- t x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1460.0) {
		tmp = t_1;
	} else if (z <= -8.5e-301) {
		tmp = x + (y * t);
	} else if (z <= 1.4e-22) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.3e+57) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1460.0d0)) then
        tmp = t_1
    else if (z <= (-8.5d-301)) then
        tmp = x + (y * t)
    else if (z <= 1.4d-22) then
        tmp = x * (1.0d0 - y)
    else if (z <= 2.3d+57) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1460.0) {
		tmp = t_1;
	} else if (z <= -8.5e-301) {
		tmp = x + (y * t);
	} else if (z <= 1.4e-22) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.3e+57) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1460.0:
		tmp = t_1
	elif z <= -8.5e-301:
		tmp = x + (y * t)
	elif z <= 1.4e-22:
		tmp = x * (1.0 - y)
	elif z <= 2.3e+57:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1460.0)
		tmp = t_1;
	elseif (z <= -8.5e-301)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.4e-22)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 2.3e+57)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1460.0)
		tmp = t_1;
	elseif (z <= -8.5e-301)
		tmp = x + (y * t);
	elseif (z <= 1.4e-22)
		tmp = x * (1.0 - y);
	elseif (z <= 2.3e+57)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1460.0], t$95$1, If[LessEqual[z, -8.5e-301], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-22], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+57], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1460 or 2.2999999999999999e57 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 98.2%

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

      1. associate-*r* 98.2%

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

      2. neg-mul-1 98.2%

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

      3. associate--l+ 98.2%

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

      4. mul-1-neg 98.2%

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

      5. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around inf 82.6%

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

      1. sub-neg 82.6%

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

      2. distribute-rgt-out 77.3%

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

      3. distribute-lft-neg-out 77.3%

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

      4. mul-1-neg 77.3%

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

      5. +-commutative 77.3%

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

      6. distribute-lft-in 77.3%

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

      7. neg-mul-1 77.3%

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

      8. mul-1-neg 77.3%

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

      9. remove-double-neg 77.3%

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

      10. associate-*r* 77.3%

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

      11. distribute-rgt-in 82.6%

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

      12. mul-1-neg 82.6%

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

      13. sub-neg 82.6%

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

   8. Simplified 82.6%

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

   if -1460 < z < -8.50000000000000046e-301

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.7%

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

      1. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in t around inf 74.0%

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

      1. *-commutative 74.0%

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

   8. Simplified 74.0%

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

   if -8.50000000000000046e-301 < z < 1.39999999999999997e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. unsub-neg 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in z around 0 69.4%

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

   if 1.39999999999999997e-22 < z < 2.2999999999999999e57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. neg-mul-1 99.9%

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

      3. associate--l+ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around -inf 88.5%

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

Alternative 3: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+196} \lor \neg \left(z \leq 3.7 \cdot 10^{+287}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.3e+126)
     t_1
     (if (<= z 6.6e+62)
       (* x (- 1.0 y))
       (if (or (<= z 7.1e+196) (not (<= z 3.7e+287))) t_1 (* z x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.3e+126) {
		tmp = t_1;
	} else if (z <= 6.6e+62) {
		tmp = x * (1.0 - y);
	} else if ((z <= 7.1e+196) || !(z <= 3.7e+287)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-2.3d+126)) then
        tmp = t_1
    else if (z <= 6.6d+62) then
        tmp = x * (1.0d0 - y)
    else if ((z <= 7.1d+196) .or. (.not. (z <= 3.7d+287))) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.3e+126) {
		tmp = t_1;
	} else if (z <= 6.6e+62) {
		tmp = x * (1.0 - y);
	} else if ((z <= 7.1e+196) || !(z <= 3.7e+287)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.3e+126:
		tmp = t_1
	elif z <= 6.6e+62:
		tmp = x * (1.0 - y)
	elif (z <= 7.1e+196) or not (z <= 3.7e+287):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.3e+126)
		tmp = t_1;
	elseif (z <= 6.6e+62)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((z <= 7.1e+196) || !(z <= 3.7e+287))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2.3e+126)
		tmp = t_1;
	elseif (z <= 6.6e+62)
		tmp = x * (1.0 - y);
	elseif ((z <= 7.1e+196) || ~((z <= 3.7e+287)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.3e+126], t$95$1, If[LessEqual[z, 6.6e+62], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.1e+196], N[Not[LessEqual[z, 3.7e+287]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3000000000000001e126 or 6.6e62 < z < 7.10000000000000032e196 or 3.69999999999999997e287 < 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 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around inf 89.8%

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

   7. Taylor expanded in x around 0 60.6%

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

      1. neg-mul-1 60.6%

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

   9. Simplified 60.6%

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

   if -2.3000000000000001e126 < z < 6.6e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 57.2%

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

   if 7.10000000000000032e196 < z < 3.69999999999999997e287

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 65.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+196} \lor \neg \left(z \leq 3.7 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -34000.0)
   (* x (- y))
   (if (<= y -3.4e-56)
     (* z x)
     (if (<= y -2.5e-256) x (if (<= y 7.6e+55) (* z (- t)) (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -34000.0) {
		tmp = x * -y;
	} else if (y <= -3.4e-56) {
		tmp = z * x;
	} else if (y <= -2.5e-256) {
		tmp = x;
	} else if (y <= 7.6e+55) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-34000.0d0)) then
        tmp = x * -y
    else if (y <= (-3.4d-56)) then
        tmp = z * x
    else if (y <= (-2.5d-256)) then
        tmp = x
    else if (y <= 7.6d+55) then
        tmp = z * -t
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -34000.0) {
		tmp = x * -y;
	} else if (y <= -3.4e-56) {
		tmp = z * x;
	} else if (y <= -2.5e-256) {
		tmp = x;
	} else if (y <= 7.6e+55) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -34000.0:
		tmp = x * -y
	elif y <= -3.4e-56:
		tmp = z * x
	elif y <= -2.5e-256:
		tmp = x
	elif y <= 7.6e+55:
		tmp = z * -t
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -34000.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= -3.4e-56)
		tmp = Float64(z * x);
	elseif (y <= -2.5e-256)
		tmp = x;
	elseif (y <= 7.6e+55)
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -34000.0)
		tmp = x * -y;
	elseif (y <= -3.4e-56)
		tmp = z * x;
	elseif (y <= -2.5e-256)
		tmp = x;
	elseif (y <= 7.6e+55)
		tmp = z * -t;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -34000.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, -3.4e-56], N[(z * x), $MachinePrecision], If[LessEqual[y, -2.5e-256], x, If[LessEqual[y, 7.6e+55], N[(z * (-t)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -34000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. neg-mul-1 49.1%

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

   8. Simplified 49.1%

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

   if -34000 < y < -3.39999999999999982e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in z around inf 51.2%

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

   if -3.39999999999999982e-56 < y < -2.5e-256

   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 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in y around 0 49.4%

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

   if -2.5e-256 < y < 7.5999999999999999e55

   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 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in z around inf 83.6%

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

   7. Taylor expanded in x around 0 43.8%

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

      1. neg-mul-1 43.8%

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

   9. Simplified 43.8%

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

   if 7.5999999999999999e55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 83.2%

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

      1. associate-*r* 83.2%

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

      2. neg-mul-1 83.2%

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

      3. associate--l+ 83.2%

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

      4. mul-1-neg 83.2%

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

      5. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around -inf 90.1%

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

   7. Taylor expanded in t around inf 54.9%

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

      1. *-commutative 54.9%

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

   9. Simplified 54.9%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -62:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -62.0)
     t_1
     (if (<= y -3.5e-52)
       (* z (- x t))
       (if (<= y 8.5e+49) (- x (* 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 <= -62.0) {
		tmp = t_1;
	} else if (y <= -3.5e-52) {
		tmp = z * (x - t);
	} else if (y <= 8.5e+49) {
		tmp = x - (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 <= (-62.0d0)) then
        tmp = t_1
    else if (y <= (-3.5d-52)) then
        tmp = z * (x - t)
    else if (y <= 8.5d+49) then
        tmp = x - (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 <= -62.0) {
		tmp = t_1;
	} else if (y <= -3.5e-52) {
		tmp = z * (x - t);
	} else if (y <= 8.5e+49) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -62.0:
		tmp = t_1
	elif y <= -3.5e-52:
		tmp = z * (x - t)
	elif y <= 8.5e+49:
		tmp = x - (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 <= -62.0)
		tmp = t_1;
	elseif (y <= -3.5e-52)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 8.5e+49)
		tmp = Float64(x - Float64(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 <= -62.0)
		tmp = t_1;
	elseif (y <= -3.5e-52)
		tmp = z * (x - t);
	elseif (y <= 8.5e+49)
		tmp = x - (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, -62.0], t$95$1, If[LessEqual[y, -3.5e-52], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+49], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -62 or 8.4999999999999996e49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 84.6%

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

      1. associate-*r* 84.6%

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

      2. neg-mul-1 84.6%

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

      3. associate--l+ 84.6%

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

      4. mul-1-neg 84.6%

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

      5. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in y around -inf 85.9%

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

   if -62 < y < -3.5e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. associate--l+ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 87.9%

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

      1. sub-neg 87.9%

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

      2. distribute-rgt-out 87.9%

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

      3. distribute-lft-neg-out 87.9%

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

      4. mul-1-neg 87.9%

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

      5. +-commutative 87.9%

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

      6. distribute-lft-in 87.9%

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

      7. neg-mul-1 87.9%

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

      8. mul-1-neg 87.9%

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

      9. remove-double-neg 87.9%

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

      10. associate-*r* 87.9%

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

      11. distribute-rgt-in 87.9%

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

      12. mul-1-neg 87.9%

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

      13. sub-neg 87.9%

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

   8. Simplified 87.9%

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

   if -3.5e-52 < y < 8.4999999999999996e49

   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 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in t around inf 73.8%

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

Alternative 6: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -0.72:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -0.72)
     t_1
     (if (<= y -5.9e-264)
       (* x (+ z 1.0))
       (if (<= y 9e+49) (* 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 <= -0.72) {
		tmp = t_1;
	} else if (y <= -5.9e-264) {
		tmp = x * (z + 1.0);
	} else if (y <= 9e+49) {
		tmp = 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 <= (-0.72d0)) then
        tmp = t_1
    else if (y <= (-5.9d-264)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 9d+49) then
        tmp = 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 <= -0.72) {
		tmp = t_1;
	} else if (y <= -5.9e-264) {
		tmp = x * (z + 1.0);
	} else if (y <= 9e+49) {
		tmp = 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 <= -0.72:
		tmp = t_1
	elif y <= -5.9e-264:
		tmp = x * (z + 1.0)
	elif y <= 9e+49:
		tmp = 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 <= -0.72)
		tmp = t_1;
	elseif (y <= -5.9e-264)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 9e+49)
		tmp = 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 <= -0.72)
		tmp = t_1;
	elseif (y <= -5.9e-264)
		tmp = x * (z + 1.0);
	elseif (y <= 9e+49)
		tmp = 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, -0.72], t$95$1, If[LessEqual[y, -5.9e-264], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+49], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.71999999999999997 or 8.99999999999999965e49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 84.6%

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

      1. associate-*r* 84.6%

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

      2. neg-mul-1 84.6%

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

      3. associate--l+ 84.6%

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

      4. mul-1-neg 84.6%

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

      5. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in y around -inf 85.9%

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

   if -0.71999999999999997 < y < -5.8999999999999999e-264

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in y around 0 64.5%

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

      1. +-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -5.8999999999999999e-264 < y < 8.99999999999999965e49

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 89.1%

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

      1. associate-*r* 89.1%

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

      2. neg-mul-1 89.1%

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

      3. associate--l+ 89.1%

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

      4. mul-1-neg 89.1%

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

      5. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-out 58.6%

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

      3. distribute-lft-neg-out 58.6%

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

      4. mul-1-neg 58.6%

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

      5. +-commutative 58.6%

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

      6. distribute-lft-in 58.6%

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

      7. neg-mul-1 58.6%

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

      8. mul-1-neg 58.6%

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

      9. remove-double-neg 58.6%

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

      10. associate-*r* 58.6%

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

      11. distribute-rgt-in 64.4%

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

      12. mul-1-neg 64.4%

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

      13. sub-neg 64.4%

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

   8. Simplified 64.4%

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

Alternative 7: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -86000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-52}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -86000.0)
   (* y (- x))
   (if (<= y -1.35e-52) (* z x) (if (<= y 3.6e+15) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -86000.0) {
		tmp = y * -x;
	} else if (y <= -1.35e-52) {
		tmp = z * x;
	} else if (y <= 3.6e+15) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-86000.0d0)) then
        tmp = y * -x
    else if (y <= (-1.35d-52)) then
        tmp = z * x
    else if (y <= 3.6d+15) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -86000.0) {
		tmp = y * -x;
	} else if (y <= -1.35e-52) {
		tmp = z * x;
	} else if (y <= 3.6e+15) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -86000.0:
		tmp = y * -x
	elif y <= -1.35e-52:
		tmp = z * x
	elif y <= 3.6e+15:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -86000.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -1.35e-52)
		tmp = Float64(z * x);
	elseif (y <= 3.6e+15)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -86000.0)
		tmp = y * -x;
	elseif (y <= -1.35e-52)
		tmp = z * x;
	elseif (y <= 3.6e+15)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -86000.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -1.35e-52], N[(z * x), $MachinePrecision], If[LessEqual[y, 3.6e+15], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -86000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. neg-mul-1 49.1%

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

   8. Simplified 49.1%

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

   if -86000 < y < -1.35000000000000005e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in z around inf 51.2%

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

   if -1.35000000000000005e-52 < y < 3.6e15

   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 45.9%

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

      1. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in y around 0 40.3%

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

   if 3.6e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 85.1%

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

      1. associate-*r* 85.1%

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

      2. neg-mul-1 85.1%

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

      3. associate--l+ 85.1%

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

      4. mul-1-neg 85.1%

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

      5. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in y around -inf 82.3%

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

   7. Taylor expanded in t around inf 50.9%

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

      1. *-commutative 50.9%

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

   9. Simplified 50.9%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -86000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-52}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+36} \lor \neg \left(z \leq 2.2 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e+36) (not (<= z 2.2e+57)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+36) || !(z <= 2.2e+57)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.1d+36)) .or. (.not. (z <= 2.2d+57))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+36) || !(z <= 2.2e+57)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e+36) or not (z <= 2.2e+57):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e+36) || !(z <= 2.2e+57))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e+36) || ~((z <= 2.2e+57)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e+36], N[Not[LessEqual[z, 2.2e+57]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.09999999999999973e36 or 2.2000000000000001e57 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 98.1%

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

      1. associate-*r* 98.1%

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

      2. neg-mul-1 98.1%

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

      3. associate--l+ 98.1%

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

      4. mul-1-neg 98.1%

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

      5. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in z around inf 84.4%

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

      1. sub-neg 84.4%

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

      2. distribute-rgt-out 78.8%

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

      3. distribute-lft-neg-out 78.8%

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

      4. mul-1-neg 78.8%

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

      5. +-commutative 78.8%

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

      6. distribute-lft-in 78.8%

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

      7. neg-mul-1 78.8%

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

      8. mul-1-neg 78.8%

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

      9. remove-double-neg 78.8%

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

      10. associate-*r* 78.8%

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

      11. distribute-rgt-in 84.4%

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

      12. mul-1-neg 84.4%

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

      13. sub-neg 84.4%

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

   8. Simplified 84.4%

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

   if -5.09999999999999973e36 < z < 2.2000000000000001e57

   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 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+36} \lor \neg \left(z \leq 2.2 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.8:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.8) (+ x t_1) (if (<= y 6e+52) (+ 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 <= -1.8) {
		tmp = x + t_1;
	} else if (y <= 6e+52) {
		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 <= (-1.8d0)) then
        tmp = x + t_1
    else if (y <= 6d+52) 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 <= -1.8) {
		tmp = x + t_1;
	} else if (y <= 6e+52) {
		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 <= -1.8:
		tmp = x + t_1
	elif y <= 6e+52:
		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 <= -1.8)
		tmp = Float64(x + t_1);
	elseif (y <= 6e+52)
		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 <= -1.8)
		tmp = x + t_1;
	elseif (y <= 6e+52)
		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, -1.8], N[(x + t$95$1), $MachinePrecision], If[LessEqual[y, 6e+52], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000004

   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 83.1%

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

      1. *-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -1.80000000000000004 < y < 6e52

   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 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

   5. Simplified 92.5%

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

   if 6e52 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 83.2%

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

      1. associate-*r* 83.2%

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

      2. neg-mul-1 83.2%

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

      3. associate--l+ 83.2%

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

      4. mul-1-neg 83.2%

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

      5. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around -inf 90.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \lor \neg \left(y \leq 6 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.8) (not (<= y 6e+16))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.8) || !(y <= 6e+16)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	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 <= (-7.8d0)) .or. (.not. (y <= 6d+16))) then
        tmp = y * (t - x)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.8) || !(y <= 6e+16)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.8) or not (y <= 6e+16):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.8) || !(y <= 6e+16))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.8) || ~((y <= 6e+16)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.8], N[Not[LessEqual[y, 6e+16]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.79999999999999982 or 6e16 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 85.3%

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

      1. associate-*r* 85.3%

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

      2. neg-mul-1 85.3%

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

      3. associate--l+ 85.3%

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

      4. mul-1-neg 85.3%

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

      5. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in y around -inf 82.9%

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

   if -7.79999999999999982 < y < 6e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around 0 59.0%

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

      1. +-commutative 59.0%

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

   8. Simplified 59.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \lor \neg \left(y \leq 6 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -90000.0) (* y (- x)) (if (<= y 1.1e+68) (* x (+ z 1.0)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -90000.0) {
		tmp = y * -x;
	} else if (y <= 1.1e+68) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-90000.0d0)) then
        tmp = y * -x
    else if (y <= 1.1d+68) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -90000.0) {
		tmp = y * -x;
	} else if (y <= 1.1e+68) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -90000.0:
		tmp = y * -x
	elif y <= 1.1e+68:
		tmp = x * (z + 1.0)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -90000.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= 1.1e+68)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -90000.0)
		tmp = y * -x;
	elseif (y <= 1.1e+68)
		tmp = x * (z + 1.0);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -90000.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, 1.1e+68], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. neg-mul-1 49.1%

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

   8. Simplified 49.1%

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

   if -9e4 < y < 1.09999999999999994e68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in y around 0 56.6%

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

      1. +-commutative 56.6%

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

   8. Simplified 56.6%

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

   if 1.09999999999999994e68 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 81.9%

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

      1. associate-*r* 81.9%

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

      2. neg-mul-1 81.9%

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

      3. associate--l+ 81.9%

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

      4. mul-1-neg 81.9%

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

      5. *-commutative 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in y around -inf 92.7%

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

   7. Taylor expanded in t around inf 56.9%

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

      1. *-commutative 56.9%

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

   9. Simplified 56.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-52} \lor \neg \left(y \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-52) (not (<= y 3.6e+15))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-52) || !(y <= 3.6e+15)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.05d-52)) .or. (.not. (y <= 3.6d+15))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-52) || !(y <= 3.6e+15)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-52) or not (y <= 3.6e+15):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-52) || !(y <= 3.6e+15))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-52) || ~((y <= 3.6e+15)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-52], N[Not[LessEqual[y, 3.6e+15]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.0499999999999999e-52 or 3.6e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 86.4%

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

      1. associate-*r* 86.4%

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

      2. neg-mul-1 86.4%

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

      3. associate--l+ 86.4%

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

      4. mul-1-neg 86.4%

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

      5. *-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around -inf 77.9%

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

   7. Taylor expanded in t around inf 43.2%

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

      1. *-commutative 43.2%

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

   9. Simplified 43.2%

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

   if -1.0499999999999999e-52 < y < 3.6e15

   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 45.9%

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

      1. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in y around 0 40.3%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-52} \lor \neg \left(y \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+45} \lor \neg \left(z \leq 13000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e+45) (not (<= z 13000000.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+45) || !(z <= 13000000.0)) {
		tmp = z * x;
	} 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 <= (-3.2d+45)) .or. (.not. (z <= 13000000.0d0))) then
        tmp = z * x
    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 <= -3.2e+45) || !(z <= 13000000.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+45) or not (z <= 13000000.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+45) || !(z <= 13000000.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e+45) || ~((z <= 13000000.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+45], N[Not[LessEqual[z, 13000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000003e45 or 1.3e7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around inf 40.3%

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

   if -3.2000000000000003e45 < z < 1.3e7

   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 88.4%

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

      1. *-commutative 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 33.6%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+45} \lor \neg \left(z \leq 13000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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. Add Preprocessing

Alternative 15: 18.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 63.4%

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

   1. *-commutative 63.4%

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

5. Simplified 63.4%

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

6. Taylor expanded in y around 0 20.1%

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

Developer Target 1: 96.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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