Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.5% → 95.2%

Time: 14.5s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-305) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-305) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-305) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-305], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999996e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. remove-double-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. *-commutative 88.4%

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

      5. associate-*l/ 74.8%

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

      6. associate-/l* 93.3%

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

      7. fma-neg 93.3%

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

      8. remove-double-neg 93.3%

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

   3. Simplified 93.3%

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

   if -9.99999999999999996e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 2.8%

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

   3. Taylor expanded in z around inf 81.3%

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

      1. associate--l+ 81.3%

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

      2. distribute-lft-out-- 81.3%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. div-sub 81.3%

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

      7. associate-/l* 82.0%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-160} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-160) (not (<= t_1 0.0)))
     t_1
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-160) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-160)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - (x * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-160) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-160) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-160) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-160) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-160], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-160 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.6%

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

   if -2e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 10.8%

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

   3. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. distribute-lft-out-- 71.3%

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

      3. div-sub 71.3%

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

      4. mul-1-neg 71.3%

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

      5. unsub-neg 71.3%

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

      6. div-sub 71.3%

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

      7. associate-/l* 68.3%

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

      8. associate-/l* 74.2%

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

      9. distribute-rgt-out-- 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. distribute-frac-neg2 82.5%

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

   8. Simplified 82.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-160} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-160)
     t_1
     (if (<= t_1 0.0)
       (- t (* x (/ (- a y) z)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-160) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-160)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t - (x * ((a - y) / z))
    else
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-160) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-160:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t - (x * ((a - y) / z))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-160)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2e-160)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t - (x * ((a - y) / z));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-160], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-160

   1. Initial program 92.4%

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

   if -2e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 10.8%

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

   3. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. distribute-lft-out-- 71.3%

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

      3. div-sub 71.3%

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

      4. mul-1-neg 71.3%

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

      5. unsub-neg 71.3%

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

      6. div-sub 71.3%

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

      7. associate-/l* 68.3%

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

      8. associate-/l* 74.2%

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

      9. distribute-rgt-out-- 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. distribute-frac-neg2 82.5%

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

   8. Simplified 82.5%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.7%

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

      1. clear-num 90.6%

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

      2. un-div-inv 90.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 90.9%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-160}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* x (/ (- y a) z))))
   (if (<= z -1.8e-26)
     (+ x t)
     (if (<= z -2.1e-73)
       t_2
       (if (<= z 1.25e-208)
         (+ x (/ (* y t) a))
         (if (<= z 1.15e-70)
           t_1
           (if (<= z 4e-45)
             (* t (/ y (- a z)))
             (if (<= z 2.9e-7) t_1 (if (<= z 2.95e+162) t_2 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.8e-26) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = t_2;
	} else if (z <= 1.25e-208) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.15e-70) {
		tmp = t_1;
	} else if (z <= 4e-45) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.9e-7) {
		tmp = t_1;
	} else if (z <= 2.95e+162) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = x * ((y - a) / z)
    if (z <= (-1.8d-26)) then
        tmp = x + t
    else if (z <= (-2.1d-73)) then
        tmp = t_2
    else if (z <= 1.25d-208) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.15d-70) then
        tmp = t_1
    else if (z <= 4d-45) then
        tmp = t * (y / (a - z))
    else if (z <= 2.9d-7) then
        tmp = t_1
    else if (z <= 2.95d+162) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.8e-26) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = t_2;
	} else if (z <= 1.25e-208) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.15e-70) {
		tmp = t_1;
	} else if (z <= 4e-45) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.9e-7) {
		tmp = t_1;
	} else if (z <= 2.95e+162) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = x * ((y - a) / z)
	tmp = 0
	if z <= -1.8e-26:
		tmp = x + t
	elif z <= -2.1e-73:
		tmp = t_2
	elif z <= 1.25e-208:
		tmp = x + ((y * t) / a)
	elif z <= 1.15e-70:
		tmp = t_1
	elif z <= 4e-45:
		tmp = t * (y / (a - z))
	elif z <= 2.9e-7:
		tmp = t_1
	elif z <= 2.95e+162:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -1.8e-26)
		tmp = Float64(x + t);
	elseif (z <= -2.1e-73)
		tmp = t_2;
	elseif (z <= 1.25e-208)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.15e-70)
		tmp = t_1;
	elseif (z <= 4e-45)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.9e-7)
		tmp = t_1;
	elseif (z <= 2.95e+162)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -1.8e-26)
		tmp = x + t;
	elseif (z <= -2.1e-73)
		tmp = t_2;
	elseif (z <= 1.25e-208)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.15e-70)
		tmp = t_1;
	elseif (z <= 4e-45)
		tmp = t * (y / (a - z));
	elseif (z <= 2.9e-7)
		tmp = t_1;
	elseif (z <= 2.95e+162)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-26], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.1e-73], t$95$2, If[LessEqual[z, 1.25e-208], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-70], t$95$1, If[LessEqual[z, 4e-45], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-7], t$95$1, If[LessEqual[z, 2.95e+162], t$95$2, t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8000000000000001e-26

   1. Initial program 81.4%

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

      1. clear-num 81.3%

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

      2. un-div-inv 81.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 81.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 67.6%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 48.1%

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

   if -1.8000000000000001e-26 < z < -2.0999999999999999e-73 or 2.8999999999999998e-7 < z < 2.95000000000000014e162

   1. Initial program 77.8%

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

   3. Taylor expanded in x around -inf 60.0%

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

      1. mul-1-neg 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in z around inf 51.1%

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

      1. associate-/l* 55.3%

         \[\leadsto -\color{blue}{x \cdot \frac{a + -1 \cdot y}{z}} \]

      2. neg-mul-1 55.3%

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

      3. unsub-neg 55.3%

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

   8. Simplified 55.3%

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

   if -2.0999999999999999e-73 < z < 1.24999999999999991e-208

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 94.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 78.4%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around 0 67.2%

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

   if 1.24999999999999991e-208 < z < 1.15e-70 or 3.99999999999999994e-45 < z < 2.8999999999999998e-7

   1. Initial program 90.1%

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

   3. Taylor expanded in x around -inf 72.0%

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

      1. mul-1-neg 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around 0 62.9%

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

   if 1.15e-70 < z < 3.99999999999999994e-45

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. div-sub 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in t around inf 52.3%

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

      1. associate-/l* 61.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if 2.95000000000000014e162 < z

   1. Initial program 55.4%

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

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* y (/ x z))))
   (if (<= z -5.4e-19)
     (+ x t)
     (if (<= z -2.1e-73)
       t_2
       (if (<= z 6.2e-201)
         (+ x (/ (* y t) a))
         (if (<= z 6.5e-71)
           t_1
           (if (<= z 1.8e-44)
             (* t (/ y (- a z)))
             (if (<= z 1.52e-6) t_1 (if (<= z 2.9e+162) t_2 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * (x / z);
	double tmp;
	if (z <= -5.4e-19) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = t_2;
	} else if (z <= 6.2e-201) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.5e-71) {
		tmp = t_1;
	} else if (z <= 1.8e-44) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.52e-6) {
		tmp = t_1;
	} else if (z <= 2.9e+162) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = y * (x / z)
    if (z <= (-5.4d-19)) then
        tmp = x + t
    else if (z <= (-2.1d-73)) then
        tmp = t_2
    else if (z <= 6.2d-201) then
        tmp = x + ((y * t) / a)
    else if (z <= 6.5d-71) then
        tmp = t_1
    else if (z <= 1.8d-44) then
        tmp = t * (y / (a - z))
    else if (z <= 1.52d-6) then
        tmp = t_1
    else if (z <= 2.9d+162) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * (x / z);
	double tmp;
	if (z <= -5.4e-19) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = t_2;
	} else if (z <= 6.2e-201) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.5e-71) {
		tmp = t_1;
	} else if (z <= 1.8e-44) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.52e-6) {
		tmp = t_1;
	} else if (z <= 2.9e+162) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = y * (x / z)
	tmp = 0
	if z <= -5.4e-19:
		tmp = x + t
	elif z <= -2.1e-73:
		tmp = t_2
	elif z <= 6.2e-201:
		tmp = x + ((y * t) / a)
	elif z <= 6.5e-71:
		tmp = t_1
	elif z <= 1.8e-44:
		tmp = t * (y / (a - z))
	elif z <= 1.52e-6:
		tmp = t_1
	elif z <= 2.9e+162:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -5.4e-19)
		tmp = Float64(x + t);
	elseif (z <= -2.1e-73)
		tmp = t_2;
	elseif (z <= 6.2e-201)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 6.5e-71)
		tmp = t_1;
	elseif (z <= 1.8e-44)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.52e-6)
		tmp = t_1;
	elseif (z <= 2.9e+162)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = y * (x / z);
	tmp = 0.0;
	if (z <= -5.4e-19)
		tmp = x + t;
	elseif (z <= -2.1e-73)
		tmp = t_2;
	elseif (z <= 6.2e-201)
		tmp = x + ((y * t) / a);
	elseif (z <= 6.5e-71)
		tmp = t_1;
	elseif (z <= 1.8e-44)
		tmp = t * (y / (a - z));
	elseif (z <= 1.52e-6)
		tmp = t_1;
	elseif (z <= 2.9e+162)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-19], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.1e-73], t$95$2, If[LessEqual[z, 6.2e-201], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-71], t$95$1, If[LessEqual[z, 1.8e-44], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e-6], t$95$1, If[LessEqual[z, 2.9e+162], t$95$2, t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.4000000000000002e-19

   1. Initial program 81.7%

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

      1. clear-num 81.6%

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

      2. un-div-inv 81.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 81.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 67.4%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 48.6%

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

   if -5.4000000000000002e-19 < z < -2.0999999999999999e-73 or 1.52000000000000006e-6 < z < 2.90000000000000006e162

   1. Initial program 77.6%

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

   3. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in a around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. distribute-neg-frac2 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in t around 0 48.3%

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

   if -2.0999999999999999e-73 < z < 6.1999999999999998e-201

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 94.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 78.4%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around 0 67.2%

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

   if 6.1999999999999998e-201 < z < 6.50000000000000005e-71 or 1.7999999999999999e-44 < z < 1.52000000000000006e-6

   1. Initial program 90.1%

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

   3. Taylor expanded in x around -inf 72.0%

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

      1. mul-1-neg 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around 0 62.9%

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

   if 6.50000000000000005e-71 < z < 1.7999999999999999e-44

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. div-sub 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in t around inf 52.3%

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

      1. associate-/l* 61.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if 2.90000000000000006e162 < z

   1. Initial program 55.4%

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

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.05e+85)
     t_2
     (if (<= t -1e+37)
       t_1
       (if (<= t -7e-36)
         t_2
         (if (<= t -2.05e-138)
           t_1
           (if (<= t -7.4e-233)
             (* x (/ (- y a) z))
             (if (<= t 3.6e+24) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.05e+85) {
		tmp = t_2;
	} else if (t <= -1e+37) {
		tmp = t_1;
	} else if (t <= -7e-36) {
		tmp = t_2;
	} else if (t <= -2.05e-138) {
		tmp = t_1;
	} else if (t <= -7.4e-233) {
		tmp = x * ((y - a) / z);
	} else if (t <= 3.6e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-3.05d+85)) then
        tmp = t_2
    else if (t <= (-1d+37)) then
        tmp = t_1
    else if (t <= (-7d-36)) then
        tmp = t_2
    else if (t <= (-2.05d-138)) then
        tmp = t_1
    else if (t <= (-7.4d-233)) then
        tmp = x * ((y - a) / z)
    else if (t <= 3.6d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.05e+85) {
		tmp = t_2;
	} else if (t <= -1e+37) {
		tmp = t_1;
	} else if (t <= -7e-36) {
		tmp = t_2;
	} else if (t <= -2.05e-138) {
		tmp = t_1;
	} else if (t <= -7.4e-233) {
		tmp = x * ((y - a) / z);
	} else if (t <= 3.6e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.05e+85:
		tmp = t_2
	elif t <= -1e+37:
		tmp = t_1
	elif t <= -7e-36:
		tmp = t_2
	elif t <= -2.05e-138:
		tmp = t_1
	elif t <= -7.4e-233:
		tmp = x * ((y - a) / z)
	elif t <= 3.6e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.05e+85)
		tmp = t_2;
	elseif (t <= -1e+37)
		tmp = t_1;
	elseif (t <= -7e-36)
		tmp = t_2;
	elseif (t <= -2.05e-138)
		tmp = t_1;
	elseif (t <= -7.4e-233)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 3.6e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.05e+85)
		tmp = t_2;
	elseif (t <= -1e+37)
		tmp = t_1;
	elseif (t <= -7e-36)
		tmp = t_2;
	elseif (t <= -2.05e-138)
		tmp = t_1;
	elseif (t <= -7.4e-233)
		tmp = x * ((y - a) / z);
	elseif (t <= 3.6e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e+85], t$95$2, If[LessEqual[t, -1e+37], t$95$1, If[LessEqual[t, -7e-36], t$95$2, If[LessEqual[t, -2.05e-138], t$95$1, If[LessEqual[t, -7.4e-233], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+24], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.04999999999999991e85 or -9.99999999999999954e36 < t < -6.9999999999999999e-36 or 3.59999999999999983e24 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 76.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 76.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.04999999999999991e85 < t < -9.99999999999999954e36 or -6.9999999999999999e-36 < t < -2.05e-138 or -7.3999999999999996e-233 < t < 3.59999999999999983e24

   1. Initial program 80.6%

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

   3. Taylor expanded in x around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around 0 59.0%

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

   if -2.05e-138 < t < -7.3999999999999996e-233

   1. Initial program 63.8%

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

   3. Taylor expanded in x around -inf 77.6%

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

      1. mul-1-neg 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in z around inf 54.4%

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

      1. associate-/l* 68.0%

         \[\leadsto -\color{blue}{x \cdot \frac{a + -1 \cdot y}{z}} \]

      2. neg-mul-1 68.0%

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

      3. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-17)
   (+ x t)
   (if (<= z -2.1e-73)
     (* y (/ x z))
     (if (<= z 2.35e-139)
       (+ x (/ (* y t) a))
       (if (<= z 2.2e-65)
         (* y (/ (- t x) a))
         (if (<= z 7.2e+162) (* x (/ y z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-17) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = y * (x / z);
	} else if (z <= 2.35e-139) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.2e-65) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.2e+162) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d-17)) then
        tmp = x + t
    else if (z <= (-2.1d-73)) then
        tmp = y * (x / z)
    else if (z <= 2.35d-139) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.2d-65) then
        tmp = y * ((t - x) / a)
    else if (z <= 7.2d+162) then
        tmp = x * (y / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-17) {
		tmp = x + t;
	} else if (z <= -2.1e-73) {
		tmp = y * (x / z);
	} else if (z <= 2.35e-139) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.2e-65) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.2e+162) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-17:
		tmp = x + t
	elif z <= -2.1e-73:
		tmp = y * (x / z)
	elif z <= 2.35e-139:
		tmp = x + ((y * t) / a)
	elif z <= 2.2e-65:
		tmp = y * ((t - x) / a)
	elif z <= 7.2e+162:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-17)
		tmp = Float64(x + t);
	elseif (z <= -2.1e-73)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 2.35e-139)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.2e-65)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 7.2e+162)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e-17)
		tmp = x + t;
	elseif (z <= -2.1e-73)
		tmp = y * (x / z);
	elseif (z <= 2.35e-139)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.2e-65)
		tmp = y * ((t - x) / a);
	elseif (z <= 7.2e+162)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-17], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.1e-73], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-139], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-65], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+162], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.2e-17

   1. Initial program 81.7%

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

      1. clear-num 81.6%

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

      2. un-div-inv 81.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 81.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 67.4%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 48.6%

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

   if -2.2e-17 < z < -2.0999999999999999e-73

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. div-sub 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. distribute-neg-frac2 69.0%

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

   8. Simplified 69.0%

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

   9. Taylor expanded in t around 0 58.7%

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

   if -2.0999999999999999e-73 < z < 2.35000000000000014e-139

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. un-div-inv 93.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 93.9%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 76.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around 0 65.7%

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

   if 2.35000000000000014e-139 < z < 2.20000000000000021e-65

   1. Initial program 86.7%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. div-sub 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in a around inf 61.6%

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

   if 2.20000000000000021e-65 < z < 7.19999999999999987e162

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 46.9%

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

      1. div-sub 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in a around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-neg-frac2 47.5%

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

   8. Simplified 47.5%

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

   9. Taylor expanded in t around 0 33.8%

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

       1. associate-/l* 38.1%

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

   11. Simplified 38.1%

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

   if 7.19999999999999987e162 < z

   1. Initial program 55.4%

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

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 72000000000000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8e+46)
     t_1
     (if (<= z -1.02e-66)
       (* y (/ (- t x) (- a z)))
       (if (<= z 72000000000000.0)
         (+ x (* y (/ (- t x) a)))
         (if (<= z 2e+139) (* x (/ (- y a) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+46) {
		tmp = t_1;
	} else if (z <= -1.02e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 72000000000000.0) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2e+139) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-8d+46)) then
        tmp = t_1
    else if (z <= (-1.02d-66)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 72000000000000.0d0) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 2d+139) then
        tmp = x * ((y - a) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+46) {
		tmp = t_1;
	} else if (z <= -1.02e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 72000000000000.0) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2e+139) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -8e+46:
		tmp = t_1
	elif z <= -1.02e-66:
		tmp = y * ((t - x) / (a - z))
	elif z <= 72000000000000.0:
		tmp = x + (y * ((t - x) / a))
	elif z <= 2e+139:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8e+46)
		tmp = t_1;
	elseif (z <= -1.02e-66)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 72000000000000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 2e+139)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -8e+46)
		tmp = t_1;
	elseif (z <= -1.02e-66)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 72000000000000.0)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 2e+139)
		tmp = x * ((y - a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+46], t$95$1, If[LessEqual[z, -1.02e-66], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 72000000000000.0], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+139], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9999999999999999e46 or 2.00000000000000007e139 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in x around 0 37.0%

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

      1. associate-/l* 65.9%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -7.9999999999999999e46 < z < -1.01999999999999996e-66

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. div-sub 71.8%

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

   5. Simplified 71.8%

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

   if -1.01999999999999996e-66 < z < 7.2e13

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0 69.5%

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

      1. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

   if 7.2e13 < z < 2.00000000000000007e139

   1. Initial program 62.1%

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

   3. Taylor expanded in x around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 61.3%

         \[\leadsto -\color{blue}{x \cdot \frac{a + -1 \cdot y}{z}} \]

      2. neg-mul-1 61.3%

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

      3. unsub-neg 61.3%

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

   8. Simplified 61.3%

      \[\leadsto -\color{blue}{x \cdot \frac{a - y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 72000000000000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-52} \lor \neg \left(a \leq 2.7 \cdot 10^{-65}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -3.5e+107)
     t_1
     (if (<= a -2e+55)
       t
       (if (or (<= a -2e-52) (not (<= a 2.7e-65))) t_1 (* y (/ (- x t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -3.5e+107) {
		tmp = t_1;
	} else if (a <= -2e+55) {
		tmp = t;
	} else if ((a <= -2e-52) || !(a <= 2.7e-65)) {
		tmp = t_1;
	} else {
		tmp = y * ((x - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-3.5d+107)) then
        tmp = t_1
    else if (a <= (-2d+55)) then
        tmp = t
    else if ((a <= (-2d-52)) .or. (.not. (a <= 2.7d-65))) then
        tmp = t_1
    else
        tmp = y * ((x - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -3.5e+107) {
		tmp = t_1;
	} else if (a <= -2e+55) {
		tmp = t;
	} else if ((a <= -2e-52) || !(a <= 2.7e-65)) {
		tmp = t_1;
	} else {
		tmp = y * ((x - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -3.5e+107:
		tmp = t_1
	elif a <= -2e+55:
		tmp = t
	elif (a <= -2e-52) or not (a <= 2.7e-65):
		tmp = t_1
	else:
		tmp = y * ((x - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -3.5e+107)
		tmp = t_1;
	elseif (a <= -2e+55)
		tmp = t;
	elseif ((a <= -2e-52) || !(a <= 2.7e-65))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -3.5e+107)
		tmp = t_1;
	elseif (a <= -2e+55)
		tmp = t;
	elseif ((a <= -2e-52) || ~((a <= 2.7e-65)))
		tmp = t_1;
	else
		tmp = y * ((x - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+107], t$95$1, If[LessEqual[a, -2e+55], t, If[Or[LessEqual[a, -2e-52], N[Not[LessEqual[a, 2.7e-65]], $MachinePrecision]], t$95$1, N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4999999999999997e107 or -2.00000000000000002e55 < a < -2e-52 or 2.6999999999999999e-65 < a

   1. Initial program 86.7%

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

      1. clear-num 86.7%

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

      2. un-div-inv 86.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 86.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 76.7%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around 0 57.9%

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

   if -3.4999999999999997e107 < a < -2.00000000000000002e55

   1. Initial program 83.6%

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

   3. Taylor expanded in z around inf 49.3%

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

   if -2e-52 < a < 2.6999999999999999e-65

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. div-sub 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in a around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. distribute-neg-frac2 55.8%

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

   8. Simplified 55.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+107}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-52} \lor \neg \left(a \leq 2.7 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+122} \lor \neg \left(y \leq -5.9 \cdot 10^{+28} \lor \neg \left(y \leq -2.2 \cdot 10^{-52}\right) \land y \leq 4.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.2e+122)
         (not (or (<= y -5.9e+28) (and (not (<= y -2.2e-52)) (<= y 4.2e+61)))))
   (* x (/ y z))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.2e+122) || !((y <= -5.9e+28) || (!(y <= -2.2e-52) && (y <= 4.2e+61)))) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.2d+122)) .or. (.not. (y <= (-5.9d+28)) .or. (.not. (y <= (-2.2d-52))) .and. (y <= 4.2d+61))) then
        tmp = x * (y / z)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.2e+122) || !((y <= -5.9e+28) || (!(y <= -2.2e-52) && (y <= 4.2e+61)))) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.2e+122) or not ((y <= -5.9e+28) or (not (y <= -2.2e-52) and (y <= 4.2e+61))):
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.2e+122) || !((y <= -5.9e+28) || (!(y <= -2.2e-52) && (y <= 4.2e+61))))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.2e+122) || ~(((y <= -5.9e+28) || (~((y <= -2.2e-52)) && (y <= 4.2e+61)))))
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.2e+122], N[Not[Or[LessEqual[y, -5.9e+28], And[N[Not[LessEqual[y, -2.2e-52]], $MachinePrecision], LessEqual[y, 4.2e+61]]]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000032e122 or -5.9000000000000002e28 < y < -2.20000000000000009e-52 or 4.2000000000000002e61 < y

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. div-sub 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in a around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-neg-frac2 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in t around 0 40.7%

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

       1. associate-/l* 46.5%

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

   11. Simplified 46.5%

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

   if -4.20000000000000032e122 < y < -5.9000000000000002e28 or -2.20000000000000009e-52 < y < 4.2000000000000002e61

   1. Initial program 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 82.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 76.7%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 51.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+122} \lor \neg \left(y \leq -5.9 \cdot 10^{+28} \lor \neg \left(y \leq -2.2 \cdot 10^{-52}\right) \land y \leq 4.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{+28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.5e+91)
   (* y (/ (- t x) a))
   (if (<= y -1.06e+28)
     (+ x t)
     (if (<= y -2.2e-52)
       (* y (/ x z))
       (if (<= y 3.6e+63) (+ x t) (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+91) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.06e+28) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 3.6e+63) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-9.5d+91)) then
        tmp = y * ((t - x) / a)
    else if (y <= (-1.06d+28)) then
        tmp = x + t
    else if (y <= (-2.2d-52)) then
        tmp = y * (x / z)
    else if (y <= 3.6d+63) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+91) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.06e+28) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 3.6e+63) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e+91:
		tmp = y * ((t - x) / a)
	elif y <= -1.06e+28:
		tmp = x + t
	elif y <= -2.2e-52:
		tmp = y * (x / z)
	elif y <= 3.6e+63:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e+91)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (y <= -1.06e+28)
		tmp = Float64(x + t);
	elseif (y <= -2.2e-52)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3.6e+63)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e+91)
		tmp = y * ((t - x) / a);
	elseif (y <= -1.06e+28)
		tmp = x + t;
	elseif (y <= -2.2e-52)
		tmp = y * (x / z);
	elseif (y <= 3.6e+63)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e+91], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.06e+28], N[(x + t), $MachinePrecision], If[LessEqual[y, -2.2e-52], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+63], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5000000000000001e91

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. div-sub 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around inf 54.5%

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

   if -9.5000000000000001e91 < y < -1.0600000000000001e28 or -2.20000000000000009e-52 < y < 3.59999999999999999e63

   1. Initial program 81.3%

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

      1. clear-num 81.2%

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

      2. un-div-inv 81.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 81.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 75.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 52.5%

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

   if -1.0600000000000001e28 < y < -2.20000000000000009e-52

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in a around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-neg-frac2 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in t around 0 53.9%

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

   if 3.59999999999999999e63 < y

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 68.1%

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

      1. div-sub 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-neg-frac2 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in t around 0 40.3%

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

       1. associate-/l* 43.8%

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

   11. Simplified 43.8%

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

Alternative 12: 38.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+27}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+54}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.4e+96)
   (* t (/ y (- a z)))
   (if (<= y -6.8e+27)
     (+ x t)
     (if (<= y -2.2e-52)
       (* y (/ x z))
       (if (<= y 1.16e+54) (+ x t) (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.4e+96) {
		tmp = t * (y / (a - z));
	} else if (y <= -6.8e+27) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 1.16e+54) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.4d+96)) then
        tmp = t * (y / (a - z))
    else if (y <= (-6.8d+27)) then
        tmp = x + t
    else if (y <= (-2.2d-52)) then
        tmp = y * (x / z)
    else if (y <= 1.16d+54) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.4e+96) {
		tmp = t * (y / (a - z));
	} else if (y <= -6.8e+27) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 1.16e+54) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.4e+96:
		tmp = t * (y / (a - z))
	elif y <= -6.8e+27:
		tmp = x + t
	elif y <= -2.2e-52:
		tmp = y * (x / z)
	elif y <= 1.16e+54:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.4e+96)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= -6.8e+27)
		tmp = Float64(x + t);
	elseif (y <= -2.2e-52)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.16e+54)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.4e+96)
		tmp = t * (y / (a - z));
	elseif (y <= -6.8e+27)
		tmp = x + t;
	elseif (y <= -2.2e-52)
		tmp = y * (x / z);
	elseif (y <= 1.16e+54)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.4e+96], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e+27], N[(x + t), $MachinePrecision], If[LessEqual[y, -2.2e-52], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+54], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.40000000000000044e96

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. div-sub 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around inf 38.4%

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

      1. associate-/l* 47.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if -5.40000000000000044e96 < y < -6.8e27 or -2.20000000000000009e-52 < y < 1.1600000000000001e54

   1. Initial program 81.5%

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

      1. clear-num 81.5%

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

      2. un-div-inv 81.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 81.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 75.5%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 52.4%

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

   if -6.8e27 < y < -2.20000000000000009e-52

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in a around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-neg-frac2 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in t around 0 53.9%

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

   if 1.1600000000000001e54 < y

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 68.1%

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

      1. div-sub 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-neg-frac2 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in t around 0 40.3%

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

       1. associate-/l* 43.8%

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

   11. Simplified 43.8%

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

Alternative 13: 36.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= y -1e+123)
     t_1
     (if (<= y -7.6e+28)
       (+ x t)
       (if (<= y -2.2e-52) (* y (/ x z)) (if (<= y 1.05e+58) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -1e+123) {
		tmp = t_1;
	} else if (y <= -7.6e+28) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 1.05e+58) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (y <= (-1d+123)) then
        tmp = t_1
    else if (y <= (-7.6d+28)) then
        tmp = x + t
    else if (y <= (-2.2d-52)) then
        tmp = y * (x / z)
    else if (y <= 1.05d+58) then
        tmp = 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 a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -1e+123) {
		tmp = t_1;
	} else if (y <= -7.6e+28) {
		tmp = x + t;
	} else if (y <= -2.2e-52) {
		tmp = y * (x / z);
	} else if (y <= 1.05e+58) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if y <= -1e+123:
		tmp = t_1
	elif y <= -7.6e+28:
		tmp = x + t
	elif y <= -2.2e-52:
		tmp = y * (x / z)
	elif y <= 1.05e+58:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -1e+123)
		tmp = t_1;
	elseif (y <= -7.6e+28)
		tmp = Float64(x + t);
	elseif (y <= -2.2e-52)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.05e+58)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (y <= -1e+123)
		tmp = t_1;
	elseif (y <= -7.6e+28)
		tmp = x + t;
	elseif (y <= -2.2e-52)
		tmp = y * (x / z);
	elseif (y <= 1.05e+58)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+123], t$95$1, If[LessEqual[y, -7.6e+28], N[(x + t), $MachinePrecision], If[LessEqual[y, -2.2e-52], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+58], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999978e122 or 1.05000000000000006e58 < y

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. div-sub 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in a around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. distribute-neg-frac2 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in t around 0 38.4%

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

       1. associate-/l* 45.2%

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

   11. Simplified 45.2%

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

   if -9.99999999999999978e122 < y < -7.5999999999999998e28 or -2.20000000000000009e-52 < y < 1.05000000000000006e58

   1. Initial program 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 82.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 76.7%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 51.4%

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

   if -7.5999999999999998e28 < y < -2.20000000000000009e-52

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in a around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-neg-frac2 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in t around 0 53.9%

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

Alternative 14: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e+218)
   (* x (/ (- y a) z))
   (if (<= x -1e-73)
     (* y (/ (- t x) (- a z)))
     (if (<= x 1.5e+119) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e+218) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1e-73) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.5e+119) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.75d+218)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-1d-73)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 1.5d+119) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e+218) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1e-73) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.5e+119) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.75e+218:
		tmp = x * ((y - a) / z)
	elif x <= -1e-73:
		tmp = y * ((t - x) / (a - z))
	elif x <= 1.5e+119:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e+218)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -1e-73)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 1.5e+119)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.75e+218)
		tmp = x * ((y - a) / z);
	elseif (x <= -1e-73)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 1.5e+119)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e+218], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-73], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+119], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7500000000000001e218

   1. Initial program 56.6%

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

   3. Taylor expanded in x around -inf 68.8%

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

      1. mul-1-neg 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in z around inf 50.0%

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

      1. associate-/l* 60.4%

         \[\leadsto -\color{blue}{x \cdot \frac{a + -1 \cdot y}{z}} \]

      2. neg-mul-1 60.4%

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

      3. unsub-neg 60.4%

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

   8. Simplified 60.4%

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

   if -1.7500000000000001e218 < x < -9.99999999999999997e-74

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. div-sub 57.9%

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

   5. Simplified 57.9%

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

   if -9.99999999999999997e-74 < x < 1.50000000000000001e119

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 54.6%

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

      1. associate-/l* 67.8%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 1.50000000000000001e119 < x

   1. Initial program 85.0%

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

   3. Taylor expanded in x around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around 0 63.8%

      \[\leadsto -\color{blue}{x \cdot \left(\frac{y}{a} - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-55} \lor \neg \left(a \leq 1.5 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e-55) (not (<= a 1.5e-65)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-55) || !(a <= 1.5e-65)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.5d-55)) .or. (.not. (a <= 1.5d-65))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-55) || !(a <= 1.5e-65)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e-55) or not (a <= 1.5e-65):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e-55) || !(a <= 1.5e-65))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e-55) || ~((a <= 1.5e-65)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e-55], N[Not[LessEqual[a, 1.5e-65]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.50000000000000023e-55 or 1.49999999999999999e-65 < a

   1. Initial program 86.5%

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

      1. clear-num 86.6%

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

      2. un-div-inv 86.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 86.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 74.5%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -7.50000000000000023e-55 < a < 1.49999999999999999e-65

   1. Initial program 77.8%

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

      1. clear-num 77.6%

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

      2. un-div-inv 78.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 78.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. associate-*r/ 80.4%

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

      3. associate-*r/ 80.4%

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

      4. mul-1-neg 80.4%

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

      5. div-sub 81.3%

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

      6. mul-1-neg 81.3%

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

      7. distribute-lft-out-- 81.3%

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

      8. associate-*r/ 81.3%

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

      9. mul-1-neg 81.3%

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

      10. unsub-neg 81.3%

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

      11. distribute-rgt-out-- 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-55} \lor \neg \left(a \leq 1.5 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-37} \lor \neg \left(a \leq 1.82 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e-37) (not (<= a 1.82e-65)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (* (/ (- t x) z) (- a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e-37) || !(a <= 1.82e-65)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.4d-37)) .or. (.not. (a <= 1.82d-65))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e-37) || !(a <= 1.82e-65)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.4e-37) or not (a <= 1.82e-65):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.4e-37) || !(a <= 1.82e-65))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.4e-37) || ~((a <= 1.82e-65)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.4e-37], N[Not[LessEqual[a, 1.82e-65]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.39999999999999991e-37 or 1.82e-65 < a

   1. Initial program 87.4%

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

      1. clear-num 87.4%

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

      2. un-div-inv 87.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 87.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 74.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -2.39999999999999991e-37 < a < 1.82e-65

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 80.4%

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

      4. mul-1-neg 80.4%

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

      5. unsub-neg 80.4%

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

      6. div-sub 79.4%

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

      7. associate-/l* 79.4%

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

      8. associate-/l* 73.7%

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

      9. distribute-rgt-out-- 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-37} \lor \neg \left(a \leq 1.82 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-49} \lor \neg \left(a \leq 1.25 \cdot 10^{-66}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.5e-49) (not (<= a 1.25e-66)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-49) || !(a <= 1.25e-66)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.5d-49)) .or. (.not. (a <= 1.25d-66))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-49) || !(a <= 1.25e-66)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.5e-49) or not (a <= 1.25e-66):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.5e-49) || !(a <= 1.25e-66))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.5e-49) || ~((a <= 1.25e-66)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.5e-49], N[Not[LessEqual[a, 1.25e-66]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5e-49 or 1.2499999999999999e-66 < a

   1. Initial program 86.3%

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

      1. clear-num 86.4%

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

      2. un-div-inv 86.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 86.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 74.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -1.5e-49 < a < 1.2499999999999999e-66

   1. Initial program 78.2%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. associate--l+ 79.8%

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

      2. distribute-lft-out-- 79.8%

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

      3. div-sub 80.7%

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

      4. mul-1-neg 80.7%

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

      5. unsub-neg 80.7%

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

      6. div-sub 79.8%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 73.8%

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

      9. distribute-rgt-out-- 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 77.0%

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

      1. associate-*r/ 79.0%

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

   8. Simplified 79.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-49} \lor \neg \left(a \leq 1.25 \cdot 10^{-66}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+88} \lor \neg \left(a \leq 3.7 \cdot 10^{+49}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e+88) (not (<= a 3.7e+49)))
   (+ x (/ (- y z) (/ a t)))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+88) || !(a <= 3.7e+49)) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d+88)) .or. (.not. (a <= 3.7d+49))) then
        tmp = x + ((y - z) / (a / t))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+88) || !(a <= 3.7e+49)) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e+88) or not (a <= 3.7e+49):
		tmp = x + ((y - z) / (a / t))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e+88) || !(a <= 3.7e+49))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e+88) || ~((a <= 3.7e+49)))
		tmp = x + ((y - z) / (a / t));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e+88], N[Not[LessEqual[a, 3.7e+49]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e88 or 3.70000000000000018e49 < a

   1. Initial program 85.6%

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

      1. clear-num 85.7%

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

      2. un-div-inv 85.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 85.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 77.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in a around inf 72.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a}{t}}} \]

   if -2.6000000000000001e88 < a < 3.70000000000000018e49

   1. Initial program 81.4%

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

   3. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.7%

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

      4. mul-1-neg 68.7%

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

      5. unsub-neg 68.7%

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

      6. div-sub 68.0%

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

      7. associate-/l* 70.4%

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

      8. associate-/l* 69.0%

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

      9. distribute-rgt-out-- 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around inf 66.7%

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

      1. associate-*r/ 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+88} \lor \neg \left(a \leq 3.7 \cdot 10^{+49}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+115} \lor \neg \left(y \leq 4.25 \cdot 10^{+167}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.45e+115) (not (<= y 4.25e+167))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+115) || !(y <= 4.25e+167)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.45d+115)) .or. (.not. (y <= 4.25d+167))) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+115) || !(y <= 4.25e+167)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.45e+115) or not (y <= 4.25e+167):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.45e+115) || !(y <= 4.25e+167))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.45e+115) || ~((y <= 4.25e+167)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.45e+115], N[Not[LessEqual[y, 4.25e+167]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000002e115 or 4.25000000000000003e167 < y

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. div-sub 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. clear-num 40.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a - z}{t}}} \]

      2. div-inv 41.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t}}} \]

      3. div-inv 41.0%

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

      4. div-inv 41.0%

         \[\leadsto \frac{y}{\color{blue}{\frac{a - z}{t}}} \]

      5. sub-neg 41.0%

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

      6. +-commutative 41.0%

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

      7. add-sqr-sqrt 24.9%

         \[\leadsto \frac{y}{\frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}} + a}{t}} \]

      8. sqrt-unprod 35.4%

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

      9. sqr-neg 35.4%

         \[\leadsto \frac{y}{\frac{\sqrt{\color{blue}{z \cdot z}} + a}{t}} \]

      10. sqrt-unprod 11.7%

          \[\leadsto \frac{y}{\frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}} + a}{t}} \]

      11. add-sqr-sqrt 32.6%

          \[\leadsto \frac{y}{\frac{\color{blue}{z} + a}{t}} \]

   8. Applied egg-rr 32.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{z + a}{t}}} \]

   9. Taylor expanded in z around 0 29.0%

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

       1. associate-/l* 36.7%

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

   11. Simplified 36.7%

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

   if -1.45000000000000002e115 < y < 4.25000000000000003e167

   1. Initial program 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Applied egg-rr 82.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in t around inf 69.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 44.4%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+115} \lor \neg \left(y \leq 4.25 \cdot 10^{+167}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e-6) t (if (<= z 2.35e+57) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-6) {
		tmp = t;
	} else if (z <= 2.35e+57) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.2d-6)) then
        tmp = t
    else if (z <= 2.35d+57) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-6) {
		tmp = t;
	} else if (z <= 2.35e+57) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e-6:
		tmp = t
	elif z <= 2.35e+57:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e-6)
		tmp = t;
	elseif (z <= 2.35e+57)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e-6)
		tmp = t;
	elseif (z <= 2.35e+57)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e-6], t, If[LessEqual[z, 2.35e+57], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999999e-6 or 2.3500000000000001e57 < z

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf 42.8%

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

   if -6.1999999999999999e-6 < z < 2.3500000000000001e57

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 32.1%

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

Alternative 21: 33.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 83.0%

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

   1. clear-num 83.0%

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

   2. un-div-inv 83.2%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

4. Applied egg-rr 83.2%

   \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

5. Taylor expanded in t around inf 62.8%

   \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

6. Taylor expanded in z around inf 34.5%

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

Alternative 22: 24.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in z around inf 21.8%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))