Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 14

Speedup: 1.0×

• 35.1% 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: 35.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-54}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 13.5:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-54)
   (* y t)
   (if (<= t -5e-169) (* z x) (if (<= t 13.5) (* y (- x)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-54) {
		tmp = y * t;
	} else if (t <= -5e-169) {
		tmp = z * x;
	} else if (t <= 13.5) {
		tmp = y * -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 (t <= (-1.8d-54)) then
        tmp = y * t
    else if (t <= (-5d-169)) then
        tmp = z * x
    else if (t <= 13.5d0) then
        tmp = y * -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 (t <= -1.8e-54) {
		tmp = y * t;
	} else if (t <= -5e-169) {
		tmp = z * x;
	} else if (t <= 13.5) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-54:
		tmp = y * t
	elif t <= -5e-169:
		tmp = z * x
	elif t <= 13.5:
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-54)
		tmp = Float64(y * t);
	elseif (t <= -5e-169)
		tmp = Float64(z * x);
	elseif (t <= 13.5)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e-54)
		tmp = y * t;
	elseif (t <= -5e-169)
		tmp = z * x;
	elseif (t <= 13.5)
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e-54], N[(y * t), $MachinePrecision], If[LessEqual[t, -5e-169], N[(z * x), $MachinePrecision], If[LessEqual[t, 13.5], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.79999999999999988e-54 or 13.5 < t

   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 77.7%

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

      1. associate--l+ 77.7%

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

      2. +-commutative 77.7%

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

      3. mul-1-neg 77.7%

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

      4. unsub-neg 77.7%

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

      5. div-sub 79.3%

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

      6. unsub-neg 79.3%

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

      7. mul-1-neg 79.3%

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

      8. mul-1-neg 79.3%

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

      9. distribute-rgt-neg-in 79.3%

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

      10. sub-neg 79.3%

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

      11. +-commutative 79.3%

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

      12. distribute-neg-in 79.3%

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

      13. remove-double-neg 79.3%

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

      14. sub-neg 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in z around 0 48.3%

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

   7. Taylor expanded in t around inf 41.6%

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

      1. *-commutative 41.6%

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

   9. Simplified 41.6%

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

   if -1.79999999999999988e-54 < t < -5.0000000000000002e-169

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. sub-neg 74.9%

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

      4. +-commutative 74.9%

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

      5. distribute-neg-in 74.9%

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

      6. remove-double-neg 74.9%

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

      7. sub-neg 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in z around inf 49.8%

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

   7. Taylor expanded in z around inf 45.8%

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

   if -5.0000000000000002e-169 < t < 13.5

   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 89.2%

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

      1. associate--l+ 89.2%

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

      2. +-commutative 89.2%

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

      3. mul-1-neg 89.2%

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

      4. unsub-neg 89.2%

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

      5. div-sub 90.3%

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

      6. unsub-neg 90.3%

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

      7. mul-1-neg 90.3%

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

      8. mul-1-neg 90.3%

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

      9. distribute-rgt-neg-in 90.3%

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

      10. sub-neg 90.3%

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

      11. +-commutative 90.3%

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

      12. distribute-neg-in 90.3%

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

      13. remove-double-neg 90.3%

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

      14. sub-neg 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around inf 50.9%

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

   7. Taylor expanded in t around 0 43.6%

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

      1. neg-mul-1 43.6%

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

   9. Simplified 43.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-54}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 13.5:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-56} \lor \neg \left(t \leq 180000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.7e-56) (not (<= t 180000000.0)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.7e-56) || !(t <= 180000000.0)) {
		tmp = x + ((y - z) * t);
	} 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 <= (-3.7d-56)) .or. (.not. (t <= 180000000.0d0))) then
        tmp = x + ((y - z) * t)
    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 <= -3.7e-56) || !(t <= 180000000.0)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.7e-56) or not (t <= 180000000.0):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.7e-56) || !(t <= 180000000.0))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	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 <= -3.7e-56) || ~((t <= 180000000.0)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.7e-56], N[Not[LessEqual[t, 180000000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7000000000000002e-56 or 1.8e8 < 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 91.8%

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

   if -3.7000000000000002e-56 < t < 1.8e8

   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 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. sub-neg 84.2%

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

      4. +-commutative 84.2%

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

      5. distribute-neg-in 84.2%

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

      6. remove-double-neg 84.2%

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

      7. sub-neg 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-56} \lor \neg \left(t \leq 180000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-53}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6.9e+44) t_1 (if (<= y 5.1e-53) (- x (* z t)) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.9e+44) {
		tmp = t_1;
	} else if (y <= 5.1e-53) {
		tmp = x - (z * t);
	} else {
		tmp = x + 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 <= (-6.9d+44)) then
        tmp = t_1
    else if (y <= 5.1d-53) then
        tmp = x - (z * t)
    else
        tmp = x + 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 <= -6.9e+44) {
		tmp = t_1;
	} else if (y <= 5.1e-53) {
		tmp = x - (z * t);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -6.9e+44:
		tmp = t_1
	elif y <= 5.1e-53:
		tmp = x - (z * t)
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -6.9e+44)
		tmp = t_1;
	elseif (y <= 5.1e-53)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = Float64(x + 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 <= -6.9e+44)
		tmp = t_1;
	elseif (y <= 5.1e-53)
		tmp = x - (z * t);
	else
		tmp = x + 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, -6.9e+44], t$95$1, If[LessEqual[y, 5.1e-53], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8999999999999997e44

   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 96.9%

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

      1. associate--l+ 96.9%

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

      2. +-commutative 96.9%

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

      3. mul-1-neg 96.9%

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

      4. unsub-neg 96.9%

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

      5. div-sub 96.9%

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

      6. unsub-neg 96.9%

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

      7. mul-1-neg 96.9%

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

      8. mul-1-neg 96.9%

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

      9. distribute-rgt-neg-in 96.9%

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

      10. sub-neg 96.9%

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

      11. +-commutative 96.9%

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

      12. distribute-neg-in 96.9%

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

      13. remove-double-neg 96.9%

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

      14. sub-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in y around inf 88.5%

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

   if -6.8999999999999997e44 < y < 5.10000000000000045e-53

   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 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in t around inf 68.0%

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

   if 5.10000000000000045e-53 < 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 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-53}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-55}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq 580000000:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-55)
   (- x (* z t))
   (if (<= t 580000000.0) (+ x (* x (- z y))) (+ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-55) {
		tmp = x - (z * t);
	} else if (t <= 580000000.0) {
		tmp = x + (x * (z - y));
	} 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) :: tmp
    if (t <= (-7d-55)) then
        tmp = x - (z * t)
    else if (t <= 580000000.0d0) then
        tmp = x + (x * (z - y))
    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 tmp;
	if (t <= -7e-55) {
		tmp = x - (z * t);
	} else if (t <= 580000000.0) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-55:
		tmp = x - (z * t)
	elif t <= 580000000.0:
		tmp = x + (x * (z - y))
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-55)
		tmp = Float64(x - Float64(z * t));
	elseif (t <= 580000000.0)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-55)
		tmp = x - (z * t);
	elseif (t <= 580000000.0)
		tmp = x + (x * (z - y));
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-55], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 580000000.0], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000051e-55

   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 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around inf 65.5%

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

   if -7.00000000000000051e-55 < t < 5.8e8

   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 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. sub-neg 84.2%

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

      4. +-commutative 84.2%

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

      5. distribute-neg-in 84.2%

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

      6. remove-double-neg 84.2%

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

      7. sub-neg 84.2%

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

   5. Simplified 84.2%

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

   if 5.8e8 < 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 90.7%

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

   4. Taylor expanded in y around inf 56.6%

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

Alternative 6: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+44} \lor \neg \left(y \leq 2.25 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.2e+44) (not (<= y 2.25e+16))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e+44) || !(y <= 2.25e+16)) {
		tmp = y * (t - x);
	} 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 <= (-8.2d+44)) .or. (.not. (y <= 2.25d+16))) then
        tmp = y * (t - x)
    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 <= -8.2e+44) || !(y <= 2.25e+16)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.2e+44) or not (y <= 2.25e+16):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.2e+44) || !(y <= 2.25e+16))
		tmp = Float64(y * Float64(t - x));
	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 <= -8.2e+44) || ~((y <= 2.25e+16)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.2e+44], N[Not[LessEqual[y, 2.25e+16]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999993e44 or 2.25e16 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. distribute-rgt-neg-in 97.6%

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

      10. sub-neg 97.6%

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

      11. +-commutative 97.6%

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

      12. distribute-neg-in 97.6%

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

      13. remove-double-neg 97.6%

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

      14. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 78.0%

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

   if -8.1999999999999993e44 < y < 2.25e16

   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 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in t around inf 64.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+44} \lor \neg \left(y \leq 2.25 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+45} \lor \neg \left(y \leq 2.2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e+45) (not (<= y 2.2e-12))) (* y (- t x)) (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+45) || !(y <= 2.2e-12)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3d+45)) .or. (.not. (y <= 2.2d-12))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+45) || !(y <= 2.2e-12)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e+45) or not (y <= 2.2e-12):
		tmp = y * (t - x)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e+45) || !(y <= 2.2e-12))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e+45) || ~((y <= 2.2e-12)))
		tmp = y * (t - x);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e+45], N[Not[LessEqual[y, 2.2e-12]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000011e45 or 2.19999999999999992e-12 < 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 97.7%

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

      1. associate--l+ 97.7%

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

      2. +-commutative 97.7%

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

      3. mul-1-neg 97.7%

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

      4. unsub-neg 97.7%

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

      5. div-sub 97.7%

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

      6. unsub-neg 97.7%

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

      7. mul-1-neg 97.7%

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

      8. mul-1-neg 97.7%

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

      9. distribute-rgt-neg-in 97.7%

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

      10. sub-neg 97.7%

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

      11. +-commutative 97.7%

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

      12. distribute-neg-in 97.7%

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

      13. remove-double-neg 97.7%

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

      14. sub-neg 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around inf 76.8%

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

   if -3.00000000000000011e45 < y < 2.19999999999999992e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. sub-neg 52.5%

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

      4. +-commutative 52.5%

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

      5. distribute-neg-in 52.5%

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

      6. remove-double-neg 52.5%

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

      7. sub-neg 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around inf 51.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+45} \lor \neg \left(y \leq 2.2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+44} \lor \neg \left(y \leq 2.3 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.6e+44) (not (<= y 2.3e-58))) (* y (- t x)) (* z (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.6e+44) || !(y <= 2.3e-58)) {
		tmp = y * (t - x);
	} else {
		tmp = 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 <= (-6.6d+44)) .or. (.not. (y <= 2.3d-58))) then
        tmp = y * (t - x)
    else
        tmp = 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 <= -6.6e+44) || !(y <= 2.3e-58)) {
		tmp = y * (t - x);
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.6e+44) or not (y <= 2.3e-58):
		tmp = y * (t - x)
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.6e+44) || !(y <= 2.3e-58))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.6e+44) || ~((y <= 2.3e-58)))
		tmp = y * (t - x);
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.6e+44], N[Not[LessEqual[y, 2.3e-58]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.60000000000000027e44 or 2.2999999999999999e-58 < 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 97.1%

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

      1. associate--l+ 97.1%

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

      2. +-commutative 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. div-sub 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. mul-1-neg 97.8%

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

      9. distribute-rgt-neg-in 97.8%

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

      10. sub-neg 97.8%

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

      11. +-commutative 97.8%

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

      12. distribute-neg-in 97.8%

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

      13. remove-double-neg 97.8%

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

      14. sub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around inf 73.3%

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

   if -6.60000000000000027e44 < y < 2.2999999999999999e-58

   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 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in t around inf 68.0%

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

   7. Taylor expanded in x around 0 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

   9. Simplified 46.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+44} \lor \neg \left(y \leq 2.3 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 36000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-111)
   (* z (- t))
   (if (<= t 36000000.0) (* x (- 1.0 y)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-111) {
		tmp = z * -t;
	} else if (t <= 36000000.0) {
		tmp = x * (1.0 - y);
	} 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 (t <= (-1.5d-111)) then
        tmp = z * -t
    else if (t <= 36000000.0d0) then
        tmp = x * (1.0d0 - y)
    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 (t <= -1.5e-111) {
		tmp = z * -t;
	} else if (t <= 36000000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-111:
		tmp = z * -t
	elif t <= 36000000.0:
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-111)
		tmp = Float64(z * Float64(-t));
	elseif (t <= 36000000.0)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-111)
		tmp = z * -t;
	elseif (t <= 36000000.0)
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-111], N[(z * (-t)), $MachinePrecision], If[LessEqual[t, 36000000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000004e-111

   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 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around inf 63.4%

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

   7. Taylor expanded in x around 0 54.3%

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

      1. associate-*r* 54.3%

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

      2. neg-mul-1 54.3%

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

   9. Simplified 54.3%

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

   if -1.50000000000000004e-111 < t < 3.6e7

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-rgt-neg-in 86.3%

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

      3. sub-neg 86.3%

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

      4. +-commutative 86.3%

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

      5. distribute-neg-in 86.3%

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

      6. remove-double-neg 86.3%

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

      7. sub-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in z around 0 57.6%

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

      1. *-rgt-identity 57.6%

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

      2. mul-1-neg 57.6%

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

      3. distribute-rgt-neg-in 57.6%

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

      4. distribute-lft-in 57.6%

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

      5. unsub-neg 57.6%

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

   8. Simplified 57.6%

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

   if 3.6e7 < t

   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 76.9%

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

      1. associate--l+ 76.9%

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

      2. +-commutative 76.9%

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

      3. mul-1-neg 76.9%

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

      4. unsub-neg 76.9%

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

      5. div-sub 80.3%

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

      6. unsub-neg 80.3%

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

      7. mul-1-neg 80.3%

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

      8. mul-1-neg 80.3%

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

      9. distribute-rgt-neg-in 80.3%

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

      10. sub-neg 80.3%

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

      11. +-commutative 80.3%

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

      12. distribute-neg-in 80.3%

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

      13. remove-double-neg 80.3%

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

      14. sub-neg 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in z around 0 52.7%

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

   7. Taylor expanded in t around inf 48.8%

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

      1. *-commutative 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 36000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 10:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.3e-111) (* z (- t)) (if (<= t 10.0) (* y (- x)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3e-111) {
		tmp = z * -t;
	} else if (t <= 10.0) {
		tmp = y * -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 (t <= (-1.3d-111)) then
        tmp = z * -t
    else if (t <= 10.0d0) then
        tmp = y * -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 (t <= -1.3e-111) {
		tmp = z * -t;
	} else if (t <= 10.0) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.3e-111:
		tmp = z * -t
	elif t <= 10.0:
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.3e-111)
		tmp = Float64(z * Float64(-t));
	elseif (t <= 10.0)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.3e-111)
		tmp = z * -t;
	elseif (t <= 10.0)
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.3e-111], N[(z * (-t)), $MachinePrecision], If[LessEqual[t, 10.0], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.29999999999999991e-111

   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 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around inf 63.4%

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

   7. Taylor expanded in x around 0 54.3%

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

      1. associate-*r* 54.3%

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

      2. neg-mul-1 54.3%

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

   9. Simplified 54.3%

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

   if -1.29999999999999991e-111 < t < 10

   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 87.8%

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

      1. associate--l+ 87.8%

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

      2. +-commutative 87.8%

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

      3. mul-1-neg 87.8%

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

      4. unsub-neg 87.8%

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

      5. div-sub 90.8%

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

      6. unsub-neg 90.8%

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

      7. mul-1-neg 90.8%

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

      8. mul-1-neg 90.8%

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

      9. distribute-rgt-neg-in 90.8%

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

      10. sub-neg 90.8%

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

      11. +-commutative 90.8%

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

      12. distribute-neg-in 90.8%

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

      13. remove-double-neg 90.8%

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

      14. sub-neg 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in y around inf 50.9%

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

   7. Taylor expanded in t around 0 42.7%

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

      1. neg-mul-1 42.7%

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

   9. Simplified 42.7%

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

   if 10 < t

   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 76.9%

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

      1. associate--l+ 76.9%

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

      2. +-commutative 76.9%

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

      3. mul-1-neg 76.9%

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

      4. unsub-neg 76.9%

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

      5. div-sub 80.3%

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

      6. unsub-neg 80.3%

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

      7. mul-1-neg 80.3%

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

      8. mul-1-neg 80.3%

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

      9. distribute-rgt-neg-in 80.3%

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

      10. sub-neg 80.3%

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

      11. +-commutative 80.3%

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

      12. distribute-neg-in 80.3%

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

      13. remove-double-neg 80.3%

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

      14. sub-neg 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in z around 0 52.7%

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

   7. Taylor expanded in t around inf 48.8%

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

      1. *-commutative 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 10:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+100} \lor \neg \left(z \leq 2.9 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+100) (not (<= z 2.9e+77))) (* z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+100) || !(z <= 2.9e+77)) {
		tmp = z * 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 ((z <= (-6.2d+100)) .or. (.not. (z <= 2.9d+77))) then
        tmp = z * 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 ((z <= -6.2e+100) || !(z <= 2.9e+77)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+100) or not (z <= 2.9e+77):
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+100) || !(z <= 2.9e+77))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+100) || ~((z <= 2.9e+77)))
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+100], N[Not[LessEqual[z, 2.9e+77]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000014e100 or 2.9000000000000002e77 < 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 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-rgt-neg-in 48.6%

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

      3. sub-neg 48.6%

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

      4. +-commutative 48.6%

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

      5. distribute-neg-in 48.6%

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

      6. remove-double-neg 48.6%

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

      7. sub-neg 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in z around inf 44.0%

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

   7. Taylor expanded in z around inf 44.0%

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

   if -6.20000000000000014e100 < z < 2.9000000000000002e77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. associate--l+ 84.7%

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

      2. +-commutative 84.7%

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

      3. mul-1-neg 84.7%

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

      4. unsub-neg 84.7%

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

      5. div-sub 84.9%

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

      6. unsub-neg 84.9%

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

      7. mul-1-neg 84.9%

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

      8. mul-1-neg 84.9%

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

      9. distribute-rgt-neg-in 84.9%

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

      10. sub-neg 84.9%

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

      11. +-commutative 84.9%

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

      12. distribute-neg-in 84.9%

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

      13. remove-double-neg 84.9%

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

      14. sub-neg 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in z around 0 72.7%

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

   7. Taylor expanded in t around inf 36.8%

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

      1. *-commutative 36.8%

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

   9. Simplified 36.8%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+100} \lor \neg \left(z \leq 2.9 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-11) (not (<= z 1.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-11) || !(z <= 1.0)) {
		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 <= (-1.8d-11)) .or. (.not. (z <= 1.0d0))) 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 <= -1.8e-11) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-11) or not (z <= 1.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-11) || !(z <= 1.0))
		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 <= -1.8e-11) || ~((z <= 1.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-11], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-11 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 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-in 49.9%

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

      3. sub-neg 49.9%

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

      4. +-commutative 49.9%

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

      5. distribute-neg-in 49.9%

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

      6. remove-double-neg 49.9%

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

      7. sub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in z around inf 38.0%

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

   7. Taylor expanded in z around inf 37.6%

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

   if -1.79999999999999992e-11 < z < 1

   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 86.5%

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

      1. associate--l+ 86.5%

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

      2. +-commutative 86.5%

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

      3. mul-1-neg 86.5%

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

      4. unsub-neg 86.5%

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

      5. div-sub 86.7%

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

      6. unsub-neg 86.7%

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

      7. mul-1-neg 86.7%

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

      8. mul-1-neg 86.7%

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

      9. distribute-rgt-neg-in 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. distribute-neg-in 86.7%

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

      13. remove-double-neg 86.7%

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

      14. sub-neg 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in z around 0 78.5%

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

   7. Taylor expanded in y around 0 25.1%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 14: 17.0% 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 81.7%

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

   1. associate--l+ 81.7%

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

   2. +-commutative 81.7%

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

   3. mul-1-neg 81.7%

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

   4. unsub-neg 81.7%

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

   5. div-sub 84.2%

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

   6. unsub-neg 84.2%

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

   7. mul-1-neg 84.2%

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

   8. mul-1-neg 84.2%

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

   9. distribute-rgt-neg-in 84.2%

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

   10. sub-neg 84.2%

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

   11. +-commutative 84.2%

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

   12. distribute-neg-in 84.2%

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

   13. remove-double-neg 84.2%

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

   14. sub-neg 84.2%

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

5. Simplified 84.2%

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

6. Taylor expanded in z around 0 53.0%

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

7. Taylor expanded in y around 0 13.1%

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

Developer Target 1: 96.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024146 
(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))))