Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 91.6%

Time: 21.8s

Alternatives: 26

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: 80.1% 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: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (<= t_1 -2e-82)
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if (t_1 <= -2e-82) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -2e-82)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-82], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-82

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*l/ 75.2%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.2%

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

      5. un-div-inv 95.5%

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

   4. Applied egg-rr 95.5%

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

   if -2e-82 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 15.8%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. distribute-lft-out-- 76.2%

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

      3. div-sub 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

      6. div-sub 76.2%

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

      7. associate-/l* 78.5%

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

      8. associate-/l* 85.6%

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

      9. distribute-rgt-out-- 85.6%

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

   5. Simplified 85.6%

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

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

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-*l/ 74.5%

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

      6. associate-/l* 93.4%

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

      7. fma-neg 93.4%

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

      8. remove-double-neg 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-233}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155} \lor \neg \left(a \leq 9 \cdot 10^{+172}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= a -1.75e-85)
     t_2
     (if (<= a -1.4e-132)
       t_1
       (if (<= a -2.5e-138)
         (* y (/ (- t x) a))
         (if (<= a -3.6e-233)
           (- t (/ (* y t) z))
           (if (<= a 3.4e-290)
             (* y (/ (- x t) z))
             (if (<= a 9.5e+56)
               t_1
               (if (<= a 1.9e+75)
                 t_2
                 (if (<= a 5.5e+76)
                   (* y (/ x (- z a)))
                   (if (<= a 2.8e+106)
                     t_2
                     (if (<= a 3.5e+119)
                       t_1
                       (if (or (<= a 1.6e+155) (not (<= a 9e+172)))
                         t_2
                         (/ t (/ a (- y z))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -1.75e-85) {
		tmp = t_2;
	} else if (a <= -1.4e-132) {
		tmp = t_1;
	} else if (a <= -2.5e-138) {
		tmp = y * ((t - x) / a);
	} else if (a <= -3.6e-233) {
		tmp = t - ((y * t) / z);
	} else if (a <= 3.4e-290) {
		tmp = y * ((x - t) / z);
	} else if (a <= 9.5e+56) {
		tmp = t_1;
	} else if (a <= 1.9e+75) {
		tmp = t_2;
	} else if (a <= 5.5e+76) {
		tmp = y * (x / (z - a));
	} else if (a <= 2.8e+106) {
		tmp = t_2;
	} else if (a <= 3.5e+119) {
		tmp = t_1;
	} else if ((a <= 1.6e+155) || !(a <= 9e+172)) {
		tmp = t_2;
	} else {
		tmp = t / (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) :: t_2
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    t_2 = x + ((y * t) / a)
    if (a <= (-1.75d-85)) then
        tmp = t_2
    else if (a <= (-1.4d-132)) then
        tmp = t_1
    else if (a <= (-2.5d-138)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-3.6d-233)) then
        tmp = t - ((y * t) / z)
    else if (a <= 3.4d-290) then
        tmp = y * ((x - t) / z)
    else if (a <= 9.5d+56) then
        tmp = t_1
    else if (a <= 1.9d+75) then
        tmp = t_2
    else if (a <= 5.5d+76) then
        tmp = y * (x / (z - a))
    else if (a <= 2.8d+106) then
        tmp = t_2
    else if (a <= 3.5d+119) then
        tmp = t_1
    else if ((a <= 1.6d+155) .or. (.not. (a <= 9d+172))) then
        tmp = t_2
    else
        tmp = t / (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 = t + (y * (x / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -1.75e-85) {
		tmp = t_2;
	} else if (a <= -1.4e-132) {
		tmp = t_1;
	} else if (a <= -2.5e-138) {
		tmp = y * ((t - x) / a);
	} else if (a <= -3.6e-233) {
		tmp = t - ((y * t) / z);
	} else if (a <= 3.4e-290) {
		tmp = y * ((x - t) / z);
	} else if (a <= 9.5e+56) {
		tmp = t_1;
	} else if (a <= 1.9e+75) {
		tmp = t_2;
	} else if (a <= 5.5e+76) {
		tmp = y * (x / (z - a));
	} else if (a <= 2.8e+106) {
		tmp = t_2;
	} else if (a <= 3.5e+119) {
		tmp = t_1;
	} else if ((a <= 1.6e+155) || !(a <= 9e+172)) {
		tmp = t_2;
	} else {
		tmp = t / (a / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if a <= -1.75e-85:
		tmp = t_2
	elif a <= -1.4e-132:
		tmp = t_1
	elif a <= -2.5e-138:
		tmp = y * ((t - x) / a)
	elif a <= -3.6e-233:
		tmp = t - ((y * t) / z)
	elif a <= 3.4e-290:
		tmp = y * ((x - t) / z)
	elif a <= 9.5e+56:
		tmp = t_1
	elif a <= 1.9e+75:
		tmp = t_2
	elif a <= 5.5e+76:
		tmp = y * (x / (z - a))
	elif a <= 2.8e+106:
		tmp = t_2
	elif a <= 3.5e+119:
		tmp = t_1
	elif (a <= 1.6e+155) or not (a <= 9e+172):
		tmp = t_2
	else:
		tmp = t / (a / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -1.75e-85)
		tmp = t_2;
	elseif (a <= -1.4e-132)
		tmp = t_1;
	elseif (a <= -2.5e-138)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -3.6e-233)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= 3.4e-290)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 9.5e+56)
		tmp = t_1;
	elseif (a <= 1.9e+75)
		tmp = t_2;
	elseif (a <= 5.5e+76)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (a <= 2.8e+106)
		tmp = t_2;
	elseif (a <= 3.5e+119)
		tmp = t_1;
	elseif ((a <= 1.6e+155) || !(a <= 9e+172))
		tmp = t_2;
	else
		tmp = Float64(t / Float64(a / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -1.75e-85)
		tmp = t_2;
	elseif (a <= -1.4e-132)
		tmp = t_1;
	elseif (a <= -2.5e-138)
		tmp = y * ((t - x) / a);
	elseif (a <= -3.6e-233)
		tmp = t - ((y * t) / z);
	elseif (a <= 3.4e-290)
		tmp = y * ((x - t) / z);
	elseif (a <= 9.5e+56)
		tmp = t_1;
	elseif (a <= 1.9e+75)
		tmp = t_2;
	elseif (a <= 5.5e+76)
		tmp = y * (x / (z - a));
	elseif (a <= 2.8e+106)
		tmp = t_2;
	elseif (a <= 3.5e+119)
		tmp = t_1;
	elseif ((a <= 1.6e+155) || ~((a <= 9e+172)))
		tmp = t_2;
	else
		tmp = t / (a / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e-85], t$95$2, If[LessEqual[a, -1.4e-132], t$95$1, If[LessEqual[a, -2.5e-138], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e-233], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-290], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+56], t$95$1, If[LessEqual[a, 1.9e+75], t$95$2, If[LessEqual[a, 5.5e+76], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+106], t$95$2, If[LessEqual[a, 3.5e+119], t$95$1, If[Or[LessEqual[a, 1.6e+155], N[Not[LessEqual[a, 9e+172]], $MachinePrecision]], t$95$2, N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.74999999999999989e-85 or 9.4999999999999997e56 < a < 1.9000000000000001e75 or 5.5000000000000001e76 < a < 2.79999999999999993e106 or 3.5000000000000001e119 < a < 1.60000000000000006e155 or 9.0000000000000004e172 < a

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*l/ 67.0%

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

      3. associate-*r/ 89.4%

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

      4. clear-num 89.3%

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

      5. un-div-inv 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in z around 0 75.3%

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

   6. Taylor expanded in t around inf 61.4%

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

   if -1.74999999999999989e-85 < a < -1.40000000000000001e-132 or 3.39999999999999984e-290 < a < 9.4999999999999997e56 or 2.79999999999999993e106 < a < 3.5000000000000001e119

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. distribute-lft-out-- 63.7%

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

      3. div-sub 65.0%

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

      4. mul-1-neg 65.0%

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

      5. unsub-neg 65.0%

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

      6. div-sub 63.7%

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

      7. associate-/l* 69.7%

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

      8. associate-/l* 65.8%

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

      9. distribute-rgt-out-- 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in y around inf 61.3%

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

      1. associate-*r/ 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in t around 0 59.4%

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

       1. neg-mul-1 59.4%

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

       2. distribute-neg-frac 59.4%

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

   11. Simplified 59.4%

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

   if -1.40000000000000001e-132 < a < -2.49999999999999994e-138

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. div-sub 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in a around inf 99.2%

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

   if -2.49999999999999994e-138 < a < -3.60000000000000007e-233

   1. Initial program 79.4%

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

   3. Taylor expanded in a around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. unsub-neg 56.2%

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

      3. associate-/l* 75.0%

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

      4. div-sub 75.0%

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

      5. sub-neg 75.0%

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

      6. *-inverses 75.0%

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

      7. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. sub-neg 72.7%

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

      3. metadata-eval 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

      5. +-commutative 72.7%

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

      6. distribute-neg-in 72.7%

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

      7. metadata-eval 72.7%

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

      8. sub-neg 72.7%

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

   8. Simplified 72.7%

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

   9. Taylor expanded in y around 0 72.8%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 72.8%

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

       2. associate-*r/ 72.7%

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

       3. unsub-neg 72.7%

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

       4. *-commutative 72.7%

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

       5. associate-*l/ 72.8%

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

   11. Simplified 72.8%

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

   if -3.60000000000000007e-233 < a < 3.39999999999999984e-290

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. div-sub 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in a around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/l* 73.3%

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

      3. distribute-rgt-neg-in 73.3%

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

      4. distribute-neg-frac2 73.3%

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

   8. Simplified 73.3%

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

   if 1.9000000000000001e75 < a < 5.5000000000000001e76

   1. Initial program 51.4%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   8. Simplified 100.0%

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

   if 1.60000000000000006e155 < a < 9.0000000000000004e172

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 75.8%

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

      3. associate-*r/ 99.6%

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

      4. clear-num 99.2%

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

      5. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. div-sub 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around 0 98.3%

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

   8. Taylor expanded in a around inf 98.3%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y - z}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-233}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155} \lor \neg \left(a \leq 9 \cdot 10^{+172}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-39}:\\ \;\;\;\;x + x \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+176} \lor \neg \left(x \leq 9.5 \cdot 10^{+181}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= x -1e+117)
     t_1
     (if (<= x -4.2e+73)
       (+ t (* y (/ x z)))
       (if (<= x -1.22e+24)
         (/ (* x y) (- z a))
         (if (<= x -7e-28)
           t_2
           (if (<= x -1.32e-39)
             (+ x (* x (/ z a)))
             (if (<= x 1.15e+57)
               t_2
               (if (or (<= x 1.3e+176) (not (<= x 9.5e+181)))
                 t_1
                 (* a (/ (- t x) z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -1e+117) {
		tmp = t_1;
	} else if (x <= -4.2e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -1.22e+24) {
		tmp = (x * y) / (z - a);
	} else if (x <= -7e-28) {
		tmp = t_2;
	} else if (x <= -1.32e-39) {
		tmp = x + (x * (z / a));
	} else if (x <= 1.15e+57) {
		tmp = t_2;
	} else if ((x <= 1.3e+176) || !(x <= 9.5e+181)) {
		tmp = t_1;
	} else {
		tmp = a * ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (x <= (-1d+117)) then
        tmp = t_1
    else if (x <= (-4.2d+73)) then
        tmp = t + (y * (x / z))
    else if (x <= (-1.22d+24)) then
        tmp = (x * y) / (z - a)
    else if (x <= (-7d-28)) then
        tmp = t_2
    else if (x <= (-1.32d-39)) then
        tmp = x + (x * (z / a))
    else if (x <= 1.15d+57) then
        tmp = t_2
    else if ((x <= 1.3d+176) .or. (.not. (x <= 9.5d+181))) then
        tmp = t_1
    else
        tmp = a * ((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 t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -1e+117) {
		tmp = t_1;
	} else if (x <= -4.2e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -1.22e+24) {
		tmp = (x * y) / (z - a);
	} else if (x <= -7e-28) {
		tmp = t_2;
	} else if (x <= -1.32e-39) {
		tmp = x + (x * (z / a));
	} else if (x <= 1.15e+57) {
		tmp = t_2;
	} else if ((x <= 1.3e+176) || !(x <= 9.5e+181)) {
		tmp = t_1;
	} else {
		tmp = a * ((t - x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -1e+117:
		tmp = t_1
	elif x <= -4.2e+73:
		tmp = t + (y * (x / z))
	elif x <= -1.22e+24:
		tmp = (x * y) / (z - a)
	elif x <= -7e-28:
		tmp = t_2
	elif x <= -1.32e-39:
		tmp = x + (x * (z / a))
	elif x <= 1.15e+57:
		tmp = t_2
	elif (x <= 1.3e+176) or not (x <= 9.5e+181):
		tmp = t_1
	else:
		tmp = a * ((t - x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -1e+117)
		tmp = t_1;
	elseif (x <= -4.2e+73)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (x <= -1.22e+24)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (x <= -7e-28)
		tmp = t_2;
	elseif (x <= -1.32e-39)
		tmp = Float64(x + Float64(x * Float64(z / a)));
	elseif (x <= 1.15e+57)
		tmp = t_2;
	elseif ((x <= 1.3e+176) || !(x <= 9.5e+181))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t - x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -1e+117)
		tmp = t_1;
	elseif (x <= -4.2e+73)
		tmp = t + (y * (x / z));
	elseif (x <= -1.22e+24)
		tmp = (x * y) / (z - a);
	elseif (x <= -7e-28)
		tmp = t_2;
	elseif (x <= -1.32e-39)
		tmp = x + (x * (z / a));
	elseif (x <= 1.15e+57)
		tmp = t_2;
	elseif ((x <= 1.3e+176) || ~((x <= 9.5e+181)))
		tmp = t_1;
	else
		tmp = a * ((t - x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * 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[x, -1e+117], t$95$1, If[LessEqual[x, -4.2e+73], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.22e+24], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-28], t$95$2, If[LessEqual[x, -1.32e-39], N[(x + N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+57], t$95$2, If[Or[LessEqual[x, 1.3e+176], N[Not[LessEqual[x, 9.5e+181]], $MachinePrecision]], t$95$1, N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.00000000000000005e117 or 1.1499999999999999e57 < x < 1.29999999999999995e176 or 9.50000000000000032e181 < x

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*l/ 53.8%

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

      3. associate-*r/ 76.3%

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

      4. clear-num 76.2%

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

      5. un-div-inv 76.2%

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

   4. Applied egg-rr 76.2%

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

      1. div-sub 76.2%

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

   6. Applied egg-rr 76.2%

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

   7. Taylor expanded in t around 0 65.1%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 65.1%

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

      2. div-sub 65.1%

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

      3. distribute-neg-frac 65.1%

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

   9. Simplified 65.1%

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

   10. Taylor expanded in z around 0 43.7%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   11. Step-by-step derivation

       1. mul-1-neg 43.7%

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

       2. unsub-neg 43.7%

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

       3. associate-/l* 56.0%

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

   12. Simplified 56.0%

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

   if -1.00000000000000005e117 < x < -4.2000000000000003e73

   1. Initial program 36.7%

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

   3. Taylor expanded in z around inf 84.1%

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

      1. associate--l+ 84.1%

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

      2. distribute-lft-out-- 84.1%

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

      3. div-sub 84.1%

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

      4. mul-1-neg 84.1%

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

      5. unsub-neg 84.1%

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

      6. div-sub 84.1%

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

      7. associate-/l* 69.3%

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

      8. associate-/l* 66.7%

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

      9. distribute-rgt-out-- 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around inf 68.7%

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

      1. associate-*r/ 53.9%

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

   8. Simplified 53.9%

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

   9. Taylor expanded in t around 0 68.8%

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

       1. neg-mul-1 68.8%

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

       2. distribute-neg-frac 68.8%

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

   11. Simplified 68.8%

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

   if -4.2000000000000003e73 < x < -1.21999999999999996e24

   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 72.5%

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

      1. div-sub 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. mul-1-neg 58.6%

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

      3. distribute-lft-neg-out 58.6%

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

      4. *-commutative 58.6%

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

   8. Simplified 58.6%

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

   if -1.21999999999999996e24 < x < -6.9999999999999999e-28 or -1.31999999999999997e-39 < x < 1.1499999999999999e57

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 56.2%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   if -6.9999999999999999e-28 < x < -1.31999999999999997e-39

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. clear-num 99.2%

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

      5. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in y around 0 53.7%

      \[\leadsto x + \frac{t - x}{\color{blue}{-1 \cdot \frac{a}{z}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.7%

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

      2. neg-mul-1 53.7%

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

   8. Simplified 53.7%

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

   9. Taylor expanded in t around 0 53.7%

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

       1. associate-*r/ 53.7%

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

   11. Simplified 53.7%

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

   if 1.29999999999999995e176 < x < 9.50000000000000032e181

   1. Initial program 29.1%

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

   3. Taylor expanded in z around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. distribute-lft-out-- 74.6%

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

      3. div-sub 74.6%

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

      4. mul-1-neg 74.6%

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

      5. unsub-neg 74.6%

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

      6. div-sub 74.6%

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

      7. associate-/l* 75.7%

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

      8. associate-/l* 74.6%

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

      9. distribute-rgt-out-- 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf 43.5%

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

      1. associate-/l* 67.4%

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

   8. Simplified 67.4%

      \[\leadsto \color{blue}{a \cdot \frac{t - x}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+117}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-39}:\\ \;\;\;\;x + x \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+176} \lor \neg \left(x \leq 9.5 \cdot 10^{+181}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-226}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1200:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+151} \lor \neg \left(a \leq 9.5 \cdot 10^{+185}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t))) (t_2 (+ x (/ (* y t) a))))
   (if (<= a -1.15e-85)
     t_2
     (if (<= a -1.75e-226)
       (- t (/ (* y t) z))
       (if (<= a -1.45e-290)
         t_1
         (if (<= a 7.5e-291)
           (* y (/ (- x t) z))
           (if (<= a 5.4e-56)
             t_1
             (if (<= a 1200.0)
               (* t (- 1.0 (/ y z)))
               (if (or (<= a 1.12e+151) (not (<= a 9.5e+185)))
                 t_2
                 (/ t (/ a (- y z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -1.15e-85) {
		tmp = t_2;
	} else if (a <= -1.75e-226) {
		tmp = t - ((y * t) / z);
	} else if (a <= -1.45e-290) {
		tmp = t_1;
	} else if (a <= 7.5e-291) {
		tmp = y * ((x - t) / z);
	} else if (a <= 5.4e-56) {
		tmp = t_1;
	} else if (a <= 1200.0) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 1.12e+151) || !(a <= 9.5e+185)) {
		tmp = t_2;
	} else {
		tmp = t / (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) :: t_2
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    t_2 = x + ((y * t) / a)
    if (a <= (-1.15d-85)) then
        tmp = t_2
    else if (a <= (-1.75d-226)) then
        tmp = t - ((y * t) / z)
    else if (a <= (-1.45d-290)) then
        tmp = t_1
    else if (a <= 7.5d-291) then
        tmp = y * ((x - t) / z)
    else if (a <= 5.4d-56) then
        tmp = t_1
    else if (a <= 1200.0d0) then
        tmp = t * (1.0d0 - (y / z))
    else if ((a <= 1.12d+151) .or. (.not. (a <= 9.5d+185))) then
        tmp = t_2
    else
        tmp = t / (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 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -1.15e-85) {
		tmp = t_2;
	} else if (a <= -1.75e-226) {
		tmp = t - ((y * t) / z);
	} else if (a <= -1.45e-290) {
		tmp = t_1;
	} else if (a <= 7.5e-291) {
		tmp = y * ((x - t) / z);
	} else if (a <= 5.4e-56) {
		tmp = t_1;
	} else if (a <= 1200.0) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 1.12e+151) || !(a <= 9.5e+185)) {
		tmp = t_2;
	} else {
		tmp = t / (a / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	t_2 = x + ((y * t) / a)
	tmp = 0
	if a <= -1.15e-85:
		tmp = t_2
	elif a <= -1.75e-226:
		tmp = t - ((y * t) / z)
	elif a <= -1.45e-290:
		tmp = t_1
	elif a <= 7.5e-291:
		tmp = y * ((x - t) / z)
	elif a <= 5.4e-56:
		tmp = t_1
	elif a <= 1200.0:
		tmp = t * (1.0 - (y / z))
	elif (a <= 1.12e+151) or not (a <= 9.5e+185):
		tmp = t_2
	else:
		tmp = t / (a / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -1.15e-85)
		tmp = t_2;
	elseif (a <= -1.75e-226)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= -1.45e-290)
		tmp = t_1;
	elseif (a <= 7.5e-291)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 5.4e-56)
		tmp = t_1;
	elseif (a <= 1200.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif ((a <= 1.12e+151) || !(a <= 9.5e+185))
		tmp = t_2;
	else
		tmp = Float64(t / Float64(a / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -1.15e-85)
		tmp = t_2;
	elseif (a <= -1.75e-226)
		tmp = t - ((y * t) / z);
	elseif (a <= -1.45e-290)
		tmp = t_1;
	elseif (a <= 7.5e-291)
		tmp = y * ((x - t) / z);
	elseif (a <= 5.4e-56)
		tmp = t_1;
	elseif (a <= 1200.0)
		tmp = t * (1.0 - (y / z));
	elseif ((a <= 1.12e+151) || ~((a <= 9.5e+185)))
		tmp = t_2;
	else
		tmp = t / (a / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-85], t$95$2, If[LessEqual[a, -1.75e-226], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.45e-290], t$95$1, If[LessEqual[a, 7.5e-291], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-56], t$95$1, If[LessEqual[a, 1200.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.12e+151], N[Not[LessEqual[a, 9.5e+185]], $MachinePrecision]], t$95$2, N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.15e-85 or 1200 < a < 1.12000000000000004e151 or 9.4999999999999995e185 < a

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*l/ 66.6%

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

      3. associate-*r/ 86.9%

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

      4. clear-num 86.9%

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

      5. un-div-inv 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in z around 0 70.2%

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

   6. Taylor expanded in t around inf 56.9%

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

   if -1.15e-85 < a < -1.75e-226

   1. Initial program 76.7%

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

   3. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 59.9%

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

      4. div-sub 60.2%

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

      5. sub-neg 60.2%

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

      6. *-inverses 60.2%

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

      7. metadata-eval 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in x around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. sub-neg 59.0%

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

      3. metadata-eval 59.0%

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

      4. distribute-rgt-neg-in 59.0%

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

      5. +-commutative 59.0%

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

      6. distribute-neg-in 59.0%

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

      7. metadata-eval 59.0%

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

      8. sub-neg 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 59.0%

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

       2. associate-*r/ 59.0%

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

       3. unsub-neg 59.0%

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

       4. *-commutative 59.0%

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

       5. associate-*l/ 59.0%

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

   11. Simplified 59.0%

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

   if -1.75e-226 < a < -1.44999999999999997e-290 or 7.49999999999999981e-291 < a < 5.3999999999999999e-56

   1. Initial program 64.9%

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

   3. Taylor expanded in z around inf 77.7%

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

      1. associate--l+ 77.7%

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

      2. distribute-lft-out-- 77.7%

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

      3. div-sub 77.7%

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

      4. mul-1-neg 77.7%

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

      5. unsub-neg 77.7%

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

      6. div-sub 77.7%

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

      7. associate-/l* 80.0%

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

      8. associate-/l* 71.3%

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

      9. distribute-rgt-out-- 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 73.9%

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

      1. associate-*r/ 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in y around inf 53.2%

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

       1. distribute-lft-out-- 53.2%

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

       2. associate-*r/ 49.3%

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

       3. *-commutative 49.3%

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

       4. associate-/l* 57.1%

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

       5. associate-*r/ 55.0%

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

       6. *-commutative 55.0%

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

       7. associate-*r/ 59.0%

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

       8. distribute-rgt-out-- 61.0%

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

   11. Simplified 61.0%

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

   if -1.44999999999999997e-290 < a < 7.49999999999999981e-291

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.3%

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

      1. div-sub 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in a around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. associate-/l* 84.3%

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

      3. distribute-rgt-neg-in 84.3%

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

      4. distribute-neg-frac2 84.3%

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

   8. Simplified 84.3%

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

   if 5.3999999999999999e-56 < a < 1200

   1. Initial program 70.9%

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

   3. Taylor expanded in a around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-/l* 45.7%

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

      4. div-sub 45.7%

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

      5. sub-neg 45.7%

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

      6. *-inverses 45.7%

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

      7. metadata-eval 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in x around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. sub-neg 48.7%

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

      3. metadata-eval 48.7%

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

      4. distribute-rgt-neg-in 48.7%

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

      5. +-commutative 48.7%

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

      6. distribute-neg-in 48.7%

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

      7. metadata-eval 48.7%

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

      8. sub-neg 48.7%

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

   8. Simplified 48.7%

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

   if 1.12000000000000004e151 < a < 9.4999999999999995e185

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 63.9%

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

      3. associate-*r/ 99.6%

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

      4. clear-num 99.4%

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

      5. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. div-sub 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 74.9%

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

   8. Taylor expanded in a around inf 62.5%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y - z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-226}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1200:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+151} \lor \neg \left(a \leq 9.5 \cdot 10^{+185}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-286}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5500:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+153} \lor \neg \left(a \leq 6.2 \cdot 10^{+196}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t)))
        (t_2 (+ x (/ (* y t) a)))
        (t_3 (* t (- 1.0 (/ y z)))))
   (if (<= a -3.7e-85)
     t_2
     (if (<= a -4.2e-226)
       (- t (/ (* y t) z))
       (if (<= a -5.5e-291)
         t_1
         (if (<= a 2.5e-286)
           t_3
           (if (<= a 6.5e-18)
             t_1
             (if (<= a 5500.0)
               t_3
               (if (or (<= a 1.55e+153) (not (<= a 6.2e+196)))
                 t_2
                 (/ t (/ a (- y z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -3.7e-85) {
		tmp = t_2;
	} else if (a <= -4.2e-226) {
		tmp = t - ((y * t) / z);
	} else if (a <= -5.5e-291) {
		tmp = t_1;
	} else if (a <= 2.5e-286) {
		tmp = t_3;
	} else if (a <= 6.5e-18) {
		tmp = t_1;
	} else if (a <= 5500.0) {
		tmp = t_3;
	} else if ((a <= 1.55e+153) || !(a <= 6.2e+196)) {
		tmp = t_2;
	} else {
		tmp = t / (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    t_2 = x + ((y * t) / a)
    t_3 = t * (1.0d0 - (y / z))
    if (a <= (-3.7d-85)) then
        tmp = t_2
    else if (a <= (-4.2d-226)) then
        tmp = t - ((y * t) / z)
    else if (a <= (-5.5d-291)) then
        tmp = t_1
    else if (a <= 2.5d-286) then
        tmp = t_3
    else if (a <= 6.5d-18) then
        tmp = t_1
    else if (a <= 5500.0d0) then
        tmp = t_3
    else if ((a <= 1.55d+153) .or. (.not. (a <= 6.2d+196))) then
        tmp = t_2
    else
        tmp = t / (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 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -3.7e-85) {
		tmp = t_2;
	} else if (a <= -4.2e-226) {
		tmp = t - ((y * t) / z);
	} else if (a <= -5.5e-291) {
		tmp = t_1;
	} else if (a <= 2.5e-286) {
		tmp = t_3;
	} else if (a <= 6.5e-18) {
		tmp = t_1;
	} else if (a <= 5500.0) {
		tmp = t_3;
	} else if ((a <= 1.55e+153) || !(a <= 6.2e+196)) {
		tmp = t_2;
	} else {
		tmp = t / (a / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	t_2 = x + ((y * t) / a)
	t_3 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -3.7e-85:
		tmp = t_2
	elif a <= -4.2e-226:
		tmp = t - ((y * t) / z)
	elif a <= -5.5e-291:
		tmp = t_1
	elif a <= 2.5e-286:
		tmp = t_3
	elif a <= 6.5e-18:
		tmp = t_1
	elif a <= 5500.0:
		tmp = t_3
	elif (a <= 1.55e+153) or not (a <= 6.2e+196):
		tmp = t_2
	else:
		tmp = t / (a / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	t_3 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -3.7e-85)
		tmp = t_2;
	elseif (a <= -4.2e-226)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= -5.5e-291)
		tmp = t_1;
	elseif (a <= 2.5e-286)
		tmp = t_3;
	elseif (a <= 6.5e-18)
		tmp = t_1;
	elseif (a <= 5500.0)
		tmp = t_3;
	elseif ((a <= 1.55e+153) || !(a <= 6.2e+196))
		tmp = t_2;
	else
		tmp = Float64(t / Float64(a / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	t_2 = x + ((y * t) / a);
	t_3 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -3.7e-85)
		tmp = t_2;
	elseif (a <= -4.2e-226)
		tmp = t - ((y * t) / z);
	elseif (a <= -5.5e-291)
		tmp = t_1;
	elseif (a <= 2.5e-286)
		tmp = t_3;
	elseif (a <= 6.5e-18)
		tmp = t_1;
	elseif (a <= 5500.0)
		tmp = t_3;
	elseif ((a <= 1.55e+153) || ~((a <= 6.2e+196)))
		tmp = t_2;
	else
		tmp = t / (a / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e-85], t$95$2, If[LessEqual[a, -4.2e-226], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-291], t$95$1, If[LessEqual[a, 2.5e-286], t$95$3, If[LessEqual[a, 6.5e-18], t$95$1, If[LessEqual[a, 5500.0], t$95$3, If[Or[LessEqual[a, 1.55e+153], N[Not[LessEqual[a, 6.2e+196]], $MachinePrecision]], t$95$2, N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.69999999999999983e-85 or 5500 < a < 1.55e153 or 6.2000000000000002e196 < a

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-*l/ 67.1%

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

      3. associate-*r/ 86.9%

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

      4. clear-num 86.8%

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

      5. un-div-inv 86.8%

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

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in z around 0 70.7%

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

   6. Taylor expanded in t around inf 57.9%

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

   if -3.69999999999999983e-85 < a < -4.2000000000000003e-226

   1. Initial program 76.7%

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

   3. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 59.9%

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

      4. div-sub 60.2%

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

      5. sub-neg 60.2%

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

      6. *-inverses 60.2%

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

      7. metadata-eval 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in x around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. sub-neg 59.0%

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

      3. metadata-eval 59.0%

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

      4. distribute-rgt-neg-in 59.0%

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

      5. +-commutative 59.0%

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

      6. distribute-neg-in 59.0%

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

      7. metadata-eval 59.0%

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

      8. sub-neg 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 59.0%

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

       2. associate-*r/ 59.0%

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

       3. unsub-neg 59.0%

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

       4. *-commutative 59.0%

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

       5. associate-*l/ 59.0%

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

   11. Simplified 59.0%

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

   if -4.2000000000000003e-226 < a < -5.5000000000000002e-291 or 2.50000000000000018e-286 < a < 6.50000000000000008e-18

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. distribute-lft-out-- 74.5%

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

      3. div-sub 74.5%

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

      4. mul-1-neg 74.5%

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

      5. unsub-neg 74.5%

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

      6. div-sub 74.5%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 74.1%

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

      9. distribute-rgt-out-- 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in y around inf 53.7%

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

       1. distribute-lft-out-- 53.7%

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

       2. associate-*r/ 48.7%

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

       3. *-commutative 48.7%

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

       4. associate-/l* 57.0%

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

       5. associate-*r/ 55.3%

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

       6. *-commutative 55.3%

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

       7. associate-*r/ 58.6%

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

       8. distribute-rgt-out-- 62.0%

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

   11. Simplified 62.0%

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

   if -5.5000000000000002e-291 < a < 2.50000000000000018e-286 or 6.50000000000000008e-18 < a < 5500

   1. Initial program 66.2%

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

   3. Taylor expanded in a around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

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

      3. associate-/l* 44.3%

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

      4. div-sub 44.3%

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

      5. sub-neg 44.3%

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

      6. *-inverses 44.3%

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

      7. metadata-eval 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in x around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. sub-neg 60.3%

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

      3. metadata-eval 60.3%

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

      4. distribute-rgt-neg-in 60.3%

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

      5. +-commutative 60.3%

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

      6. distribute-neg-in 60.3%

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

      7. metadata-eval 60.3%

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

      8. sub-neg 60.3%

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

   8. Simplified 60.3%

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

   if 1.55e153 < a < 6.2000000000000002e196

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 52.1%

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

      3. associate-*r/ 99.6%

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

      4. clear-num 99.4%

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

      5. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. div-sub 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 87.2%

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

   8. Taylor expanded in a around inf 74.8%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y - z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5500:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+153} \lor \neg \left(a \leq 6.2 \cdot 10^{+196}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+156} \lor \neg \left(z \leq 1.6 \cdot 10^{+156}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* t (/ y (- a z)))))
   (if (<= z -1.7e+136)
     t_1
     (if (<= z -2.15e+67)
       (* x (/ (- y a) z))
       (if (<= z -1.82e-68)
         t_2
         (if (<= z -9.2e-245)
           x
           (if (<= z 6.2e-59)
             t_2
             (if (<= z 2.05e+71)
               x
               (if (or (<= z 1.56e+156) (not (<= z 1.6e+156)))
                 t_1
                 (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (z <= -1.7e+136) {
		tmp = t_1;
	} else if (z <= -2.15e+67) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.82e-68) {
		tmp = t_2;
	} else if (z <= -9.2e-245) {
		tmp = x;
	} else if (z <= 6.2e-59) {
		tmp = t_2;
	} else if (z <= 2.05e+71) {
		tmp = x;
	} else if ((z <= 1.56e+156) || !(z <= 1.6e+156)) {
		tmp = t_1;
	} else {
		tmp = t * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = t * (y / (a - z))
    if (z <= (-1.7d+136)) then
        tmp = t_1
    else if (z <= (-2.15d+67)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.82d-68)) then
        tmp = t_2
    else if (z <= (-9.2d-245)) then
        tmp = x
    else if (z <= 6.2d-59) then
        tmp = t_2
    else if (z <= 2.05d+71) then
        tmp = x
    else if ((z <= 1.56d+156) .or. (.not. (z <= 1.6d+156))) then
        tmp = t_1
    else
        tmp = t * (y / a)
    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 * (1.0 - (y / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (z <= -1.7e+136) {
		tmp = t_1;
	} else if (z <= -2.15e+67) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.82e-68) {
		tmp = t_2;
	} else if (z <= -9.2e-245) {
		tmp = x;
	} else if (z <= 6.2e-59) {
		tmp = t_2;
	} else if (z <= 2.05e+71) {
		tmp = x;
	} else if ((z <= 1.56e+156) || !(z <= 1.6e+156)) {
		tmp = t_1;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = t * (y / (a - z))
	tmp = 0
	if z <= -1.7e+136:
		tmp = t_1
	elif z <= -2.15e+67:
		tmp = x * ((y - a) / z)
	elif z <= -1.82e-68:
		tmp = t_2
	elif z <= -9.2e-245:
		tmp = x
	elif z <= 6.2e-59:
		tmp = t_2
	elif z <= 2.05e+71:
		tmp = x
	elif (z <= 1.56e+156) or not (z <= 1.6e+156):
		tmp = t_1
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.7e+136)
		tmp = t_1;
	elseif (z <= -2.15e+67)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.82e-68)
		tmp = t_2;
	elseif (z <= -9.2e-245)
		tmp = x;
	elseif (z <= 6.2e-59)
		tmp = t_2;
	elseif (z <= 2.05e+71)
		tmp = x;
	elseif ((z <= 1.56e+156) || !(z <= 1.6e+156))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -1.7e+136)
		tmp = t_1;
	elseif (z <= -2.15e+67)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.82e-68)
		tmp = t_2;
	elseif (z <= -9.2e-245)
		tmp = x;
	elseif (z <= 6.2e-59)
		tmp = t_2;
	elseif (z <= 2.05e+71)
		tmp = x;
	elseif ((z <= 1.56e+156) || ~((z <= 1.6e+156)))
		tmp = t_1;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+136], t$95$1, If[LessEqual[z, -2.15e+67], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.82e-68], t$95$2, If[LessEqual[z, -9.2e-245], x, If[LessEqual[z, 6.2e-59], t$95$2, If[LessEqual[z, 2.05e+71], x, If[Or[LessEqual[z, 1.56e+156], N[Not[LessEqual[z, 1.6e+156]], $MachinePrecision]], t$95$1, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.69999999999999998e136 or 2.0500000000000001e71 < z < 1.55999999999999992e156 or 1.60000000000000001e156 < z

   1. Initial program 59.3%

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

   3. Taylor expanded in a around 0 28.5%

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

      1. mul-1-neg 28.5%

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

      2. unsub-neg 28.5%

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

      3. associate-/l* 50.3%

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

      4. div-sub 50.4%

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

      5. sub-neg 50.4%

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

      6. *-inverses 50.4%

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

      7. metadata-eval 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in x around 0 59.4%

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

      1. mul-1-neg 59.4%

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

      2. sub-neg 59.4%

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

      3. metadata-eval 59.4%

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

      4. distribute-rgt-neg-in 59.4%

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

      5. +-commutative 59.4%

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

      6. distribute-neg-in 59.4%

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

      7. metadata-eval 59.4%

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

      8. sub-neg 59.4%

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

   8. Simplified 59.4%

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

   if -1.69999999999999998e136 < z < -2.1500000000000001e67

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf 46.5%

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

      1. associate--l+ 46.5%

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

      2. distribute-lft-out-- 46.5%

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

      3. div-sub 46.5%

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

      4. mul-1-neg 46.5%

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

      5. unsub-neg 46.5%

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

      6. div-sub 46.5%

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

      7. associate-/l* 54.1%

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

      8. associate-/l* 58.8%

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

      9. distribute-rgt-out-- 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in t around 0 38.9%

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

      1. associate-/l* 51.2%

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

   8. Simplified 51.2%

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

   if -2.1500000000000001e67 < z < -1.81999999999999994e-68 or -9.2000000000000007e-245 < z < 6.19999999999999998e-59

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 53.6%

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

      1. div-sub 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in t around inf 38.5%

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

      1. associate-/l* 43.9%

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

   8. Simplified 43.9%

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

   if -1.81999999999999994e-68 < z < -9.2000000000000007e-245 or 6.19999999999999998e-59 < z < 2.0500000000000001e71

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 42.7%

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

   if 1.55999999999999992e156 < z < 1.60000000000000001e156

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around inf 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+156} \lor \neg \left(z \leq 1.6 \cdot 10^{+156}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* t (/ y (- a z)))))
   (if (<= z -1.75e+39)
     t_1
     (if (<= z -3.5e-49)
       (/ t (/ a y))
       (if (<= z -2.05e-50)
         t
         (if (<= z 4.2e-296)
           x
           (if (<= z 1.6e-217)
             t_2
             (if (<= z 9.2e-217)
               (* x (/ y (- a)))
               (if (<= z 1.3e-56) t_2 (if (<= z 9.5e+63) x t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (z <= -1.75e+39) {
		tmp = t_1;
	} else if (z <= -3.5e-49) {
		tmp = t / (a / y);
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= 4.2e-296) {
		tmp = x;
	} else if (z <= 1.6e-217) {
		tmp = t_2;
	} else if (z <= 9.2e-217) {
		tmp = x * (y / -a);
	} else if (z <= 1.3e-56) {
		tmp = t_2;
	} else if (z <= 9.5e+63) {
		tmp = x;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = t * (y / (a - z))
    if (z <= (-1.75d+39)) then
        tmp = t_1
    else if (z <= (-3.5d-49)) then
        tmp = t / (a / y)
    else if (z <= (-2.05d-50)) then
        tmp = t
    else if (z <= 4.2d-296) then
        tmp = x
    else if (z <= 1.6d-217) then
        tmp = t_2
    else if (z <= 9.2d-217) then
        tmp = x * (y / -a)
    else if (z <= 1.3d-56) then
        tmp = t_2
    else if (z <= 9.5d+63) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (z <= -1.75e+39) {
		tmp = t_1;
	} else if (z <= -3.5e-49) {
		tmp = t / (a / y);
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= 4.2e-296) {
		tmp = x;
	} else if (z <= 1.6e-217) {
		tmp = t_2;
	} else if (z <= 9.2e-217) {
		tmp = x * (y / -a);
	} else if (z <= 1.3e-56) {
		tmp = t_2;
	} else if (z <= 9.5e+63) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = t * (y / (a - z))
	tmp = 0
	if z <= -1.75e+39:
		tmp = t_1
	elif z <= -3.5e-49:
		tmp = t / (a / y)
	elif z <= -2.05e-50:
		tmp = t
	elif z <= 4.2e-296:
		tmp = x
	elif z <= 1.6e-217:
		tmp = t_2
	elif z <= 9.2e-217:
		tmp = x * (y / -a)
	elif z <= 1.3e-56:
		tmp = t_2
	elif z <= 9.5e+63:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.75e+39)
		tmp = t_1;
	elseif (z <= -3.5e-49)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= 4.2e-296)
		tmp = x;
	elseif (z <= 1.6e-217)
		tmp = t_2;
	elseif (z <= 9.2e-217)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (z <= 1.3e-56)
		tmp = t_2;
	elseif (z <= 9.5e+63)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -1.75e+39)
		tmp = t_1;
	elseif (z <= -3.5e-49)
		tmp = t / (a / y);
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= 4.2e-296)
		tmp = x;
	elseif (z <= 1.6e-217)
		tmp = t_2;
	elseif (z <= 9.2e-217)
		tmp = x * (y / -a);
	elseif (z <= 1.3e-56)
		tmp = t_2;
	elseif (z <= 9.5e+63)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+39], t$95$1, If[LessEqual[z, -3.5e-49], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e-50], t, If[LessEqual[z, 4.2e-296], x, If[LessEqual[z, 1.6e-217], t$95$2, If[LessEqual[z, 9.2e-217], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-56], t$95$2, If[LessEqual[z, 9.5e+63], x, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.7500000000000001e39 or 9.5000000000000003e63 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in a around 0 29.5%

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

      1. mul-1-neg 29.5%

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

      2. unsub-neg 29.5%

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

      3. associate-/l* 47.1%

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

      4. div-sub 47.2%

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

      5. sub-neg 47.2%

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

      6. *-inverses 47.2%

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

      7. metadata-eval 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in x around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. sub-neg 53.3%

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

      3. metadata-eval 53.3%

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

      4. distribute-rgt-neg-in 53.3%

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

      5. +-commutative 53.3%

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

      6. distribute-neg-in 53.3%

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

      7. metadata-eval 53.3%

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

      8. sub-neg 53.3%

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

   8. Simplified 53.3%

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

   if -1.7500000000000001e39 < z < -3.50000000000000006e-49

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 48.7%

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

      1. div-sub 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in a around inf 41.4%

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

   7. Taylor expanded in t around inf 26.0%

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

      1. associate-/l* 40.1%

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

   9. Simplified 40.1%

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

       1. clear-num 40.1%

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

       2. un-div-inv 40.3%

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

   11. Applied egg-rr 40.3%

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

   if -3.50000000000000006e-49 < z < -2.04999999999999993e-50

   1. Initial program 7.6%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -2.04999999999999993e-50 < z < 4.1999999999999999e-296 or 1.29999999999999998e-56 < z < 9.5000000000000003e63

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 41.5%

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

   if 4.1999999999999999e-296 < z < 1.6000000000000001e-217 or 9.20000000000000019e-217 < z < 1.29999999999999998e-56

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. div-sub 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in t around inf 43.1%

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

      1. associate-/l* 48.6%

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

   8. Simplified 48.6%

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

   if 1.6000000000000001e-217 < z < 9.20000000000000019e-217

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. div-sub 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in a around inf 98.4%

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

   7. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \color{blue}{-x \cdot \frac{y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-82} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (or (<= t_1 -2e-82) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) / (a - z)) * (z - y))
    if ((t_1 <= (-2d-82)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    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 t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if (t_1 <= -2e-82) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	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)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if ((t_1 <= -2e-82) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-82], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $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 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-82 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 74.8%

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

      3. associate-*r/ 94.3%

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

      4. clear-num 94.2%

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

      5. un-div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

   if -2e-82 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 15.8%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. distribute-lft-out-- 76.2%

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

      3. div-sub 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

      6. div-sub 76.2%

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

      7. associate-/l* 78.5%

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

      8. associate-/l* 85.6%

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

      9. distribute-rgt-out-- 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-82} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-82} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (or (<= t_1 -2e-82) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) / (a - z)) * (z - y))
    if ((t_1 <= (-2d-82)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    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 t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if (t_1 <= -2e-82) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if ((t_1 <= -2e-82) || !(t_1 <= 0.0))
		tmp = t_1;
	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)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if ((t_1 <= -2e-82) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-82], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, 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)))) < -2e-82 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

   if -2e-82 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 15.8%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. distribute-lft-out-- 76.2%

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

      3. div-sub 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

      6. div-sub 76.2%

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

      7. associate-/l* 78.5%

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

      8. associate-/l* 85.6%

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

      9. distribute-rgt-out-- 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-82} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0\right):\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -80:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.65 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -80.0)
     x
     (if (<= a -2.7e-269)
       t_1
       (if (<= a -3.65e-292)
         (/ (* x y) z)
         (if (<= a 1.05e-118)
           t_1
           (if (<= a 3.4e-56)
             (/ x (/ z y))
             (if (<= a 2.1e+57)
               t_1
               (if (<= a 7.6e+154)
                 x
                 (if (<= a 6.6e+158) (* z (/ t (- a))) (/ t (/ a y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -80.0) {
		tmp = x;
	} else if (a <= -2.7e-269) {
		tmp = t_1;
	} else if (a <= -3.65e-292) {
		tmp = (x * y) / z;
	} else if (a <= 1.05e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 2.1e+57) {
		tmp = t_1;
	} else if (a <= 7.6e+154) {
		tmp = x;
	} else if (a <= 6.6e+158) {
		tmp = z * (t / -a);
	} else {
		tmp = t / (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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-80.0d0)) then
        tmp = x
    else if (a <= (-2.7d-269)) then
        tmp = t_1
    else if (a <= (-3.65d-292)) then
        tmp = (x * y) / z
    else if (a <= 1.05d-118) then
        tmp = t_1
    else if (a <= 3.4d-56) then
        tmp = x / (z / y)
    else if (a <= 2.1d+57) then
        tmp = t_1
    else if (a <= 7.6d+154) then
        tmp = x
    else if (a <= 6.6d+158) then
        tmp = z * (t / -a)
    else
        tmp = t / (a / y)
    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 * (1.0 - (y / z));
	double tmp;
	if (a <= -80.0) {
		tmp = x;
	} else if (a <= -2.7e-269) {
		tmp = t_1;
	} else if (a <= -3.65e-292) {
		tmp = (x * y) / z;
	} else if (a <= 1.05e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 2.1e+57) {
		tmp = t_1;
	} else if (a <= 7.6e+154) {
		tmp = x;
	} else if (a <= 6.6e+158) {
		tmp = z * (t / -a);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -80.0:
		tmp = x
	elif a <= -2.7e-269:
		tmp = t_1
	elif a <= -3.65e-292:
		tmp = (x * y) / z
	elif a <= 1.05e-118:
		tmp = t_1
	elif a <= 3.4e-56:
		tmp = x / (z / y)
	elif a <= 2.1e+57:
		tmp = t_1
	elif a <= 7.6e+154:
		tmp = x
	elif a <= 6.6e+158:
		tmp = z * (t / -a)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -80.0)
		tmp = x;
	elseif (a <= -2.7e-269)
		tmp = t_1;
	elseif (a <= -3.65e-292)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 1.05e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.1e+57)
		tmp = t_1;
	elseif (a <= 7.6e+154)
		tmp = x;
	elseif (a <= 6.6e+158)
		tmp = Float64(z * Float64(t / Float64(-a)));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -80.0)
		tmp = x;
	elseif (a <= -2.7e-269)
		tmp = t_1;
	elseif (a <= -3.65e-292)
		tmp = (x * y) / z;
	elseif (a <= 1.05e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = x / (z / y);
	elseif (a <= 2.1e+57)
		tmp = t_1;
	elseif (a <= 7.6e+154)
		tmp = x;
	elseif (a <= 6.6e+158)
		tmp = z * (t / -a);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -80.0], x, If[LessEqual[a, -2.7e-269], t$95$1, If[LessEqual[a, -3.65e-292], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.05e-118], t$95$1, If[LessEqual[a, 3.4e-56], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+57], t$95$1, If[LessEqual[a, 7.6e+154], x, If[LessEqual[a, 6.6e+158], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -80 or 2.09999999999999991e57 < a < 7.5999999999999996e154

   1. Initial program 85.7%

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

   3. Taylor expanded in a around inf 46.2%

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

   if -80 < a < -2.70000000000000015e-269 or -3.6499999999999999e-292 < a < 1.05e-118 or 3.39999999999999982e-56 < a < 2.09999999999999991e57

   1. Initial program 71.3%

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

   3. Taylor expanded in a around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

      3. associate-/l* 52.2%

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

      4. div-sub 52.2%

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

      5. sub-neg 52.2%

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

      6. *-inverses 52.2%

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

      7. metadata-eval 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in x around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. sub-neg 52.8%

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

      3. metadata-eval 52.8%

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

      4. distribute-rgt-neg-in 52.8%

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

      5. +-commutative 52.8%

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

      6. distribute-neg-in 52.8%

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

      7. metadata-eval 52.8%

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

      8. sub-neg 52.8%

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

   8. Simplified 52.8%

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

   if -2.70000000000000015e-269 < a < -3.6499999999999999e-292

   1. Initial program 75.7%

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

   3. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 76.4%

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

      4. div-sub 76.4%

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

      5. sub-neg 76.4%

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

      6. *-inverses 76.4%

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

      7. metadata-eval 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around -inf 63.6%

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

   if 1.05e-118 < a < 3.39999999999999982e-56

   1. Initial program 63.5%

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

   3. Taylor expanded in a around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. unsub-neg 45.7%

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

      3. associate-/l* 54.4%

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

      4. div-sub 54.5%

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

      5. sub-neg 54.5%

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

      6. *-inverses 54.5%

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

      7. metadata-eval 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around -inf 48.4%

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

      1. associate-/l* 56.8%

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

   8. Simplified 56.8%

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

      1. clear-num 56.6%

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

      2. un-div-inv 56.9%

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

   10. Applied egg-rr 56.9%

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

   if 7.5999999999999996e154 < a < 6.60000000000000035e158

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 67.8%

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

      3. associate-*r/ 99.5%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. div-sub 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0 97.7%

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

   8. Taylor expanded in a around inf 64.7%

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

   9. Taylor expanded in y around 0 65.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-*r/ 65.1%

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

       2. mul-1-neg 65.1%

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

       3. distribute-rgt-neg-out 65.1%

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

       4. associate-*l/ 65.3%

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

       5. *-commutative 65.3%

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

       6. distribute-lft-neg-out 65.3%

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

       7. distribute-rgt-neg-in 65.3%

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

       8. distribute-neg-frac2 65.3%

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

   11. Simplified 65.3%

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

   if 6.60000000000000035e158 < a

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 48.0%

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

      1. div-sub 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in a around inf 48.0%

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

   7. Taylor expanded in t around inf 27.8%

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

      1. associate-/l* 43.6%

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

   9. Simplified 43.6%

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

       1. clear-num 43.6%

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

       2. un-div-inv 43.6%

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

   11. Applied egg-rr 43.6%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 11: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= z -5.2e+258)
     t_1
     (if (<= z -2.2e+191)
       (* (/ (- t x) z) (- a y))
       (if (<= z -1.55e+119)
         t_1
         (if (<= z -3.6e-47)
           t_2
           (if (<= z -4.7e-71)
             (* y (/ (- t x) (- a z)))
             (if (<= z -4e-121)
               t_2
               (if (<= z 1.42e+72)
                 (+ x (/ (- t x) (/ a y)))
                 (* t (/ (- y z) (- a z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (z <= -5.2e+258) {
		tmp = t_1;
	} else if (z <= -2.2e+191) {
		tmp = ((t - x) / z) * (a - y);
	} else if (z <= -1.55e+119) {
		tmp = t_1;
	} else if (z <= -3.6e-47) {
		tmp = t_2;
	} else if (z <= -4.7e-71) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -4e-121) {
		tmp = t_2;
	} else if (z <= 1.42e+72) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * ((y - z) / (a - 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) :: t_2
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    t_2 = x + (t * ((y - z) / a))
    if (z <= (-5.2d+258)) then
        tmp = t_1
    else if (z <= (-2.2d+191)) then
        tmp = ((t - x) / z) * (a - y)
    else if (z <= (-1.55d+119)) then
        tmp = t_1
    else if (z <= (-3.6d-47)) then
        tmp = t_2
    else if (z <= (-4.7d-71)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= (-4d-121)) then
        tmp = t_2
    else if (z <= 1.42d+72) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t * ((y - z) / (a - 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 = t + (y * (x / z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (z <= -5.2e+258) {
		tmp = t_1;
	} else if (z <= -2.2e+191) {
		tmp = ((t - x) / z) * (a - y);
	} else if (z <= -1.55e+119) {
		tmp = t_1;
	} else if (z <= -3.6e-47) {
		tmp = t_2;
	} else if (z <= -4.7e-71) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -4e-121) {
		tmp = t_2;
	} else if (z <= 1.42e+72) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	t_2 = x + (t * ((y - z) / a))
	tmp = 0
	if z <= -5.2e+258:
		tmp = t_1
	elif z <= -2.2e+191:
		tmp = ((t - x) / z) * (a - y)
	elif z <= -1.55e+119:
		tmp = t_1
	elif z <= -3.6e-47:
		tmp = t_2
	elif z <= -4.7e-71:
		tmp = y * ((t - x) / (a - z))
	elif z <= -4e-121:
		tmp = t_2
	elif z <= 1.42e+72:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (z <= -5.2e+258)
		tmp = t_1;
	elseif (z <= -2.2e+191)
		tmp = Float64(Float64(Float64(t - x) / z) * Float64(a - y));
	elseif (z <= -1.55e+119)
		tmp = t_1;
	elseif (z <= -3.6e-47)
		tmp = t_2;
	elseif (z <= -4.7e-71)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= -4e-121)
		tmp = t_2;
	elseif (z <= 1.42e+72)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	t_2 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (z <= -5.2e+258)
		tmp = t_1;
	elseif (z <= -2.2e+191)
		tmp = ((t - x) / z) * (a - y);
	elseif (z <= -1.55e+119)
		tmp = t_1;
	elseif (z <= -3.6e-47)
		tmp = t_2;
	elseif (z <= -4.7e-71)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= -4e-121)
		tmp = t_2;
	elseif (z <= 1.42e+72)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+258], t$95$1, If[LessEqual[z, -2.2e+191], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e+119], t$95$1, If[LessEqual[z, -3.6e-47], t$95$2, If[LessEqual[z, -4.7e-71], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-121], t$95$2, If[LessEqual[z, 1.42e+72], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.20000000000000021e258 or -2.2e191 < z < -1.54999999999999998e119

   1. Initial program 57.2%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. distribute-lft-out-- 68.9%

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

      3. div-sub 68.9%

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

      4. mul-1-neg 68.9%

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

      5. unsub-neg 68.9%

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

      6. div-sub 68.9%

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

      7. associate-/l* 79.1%

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

      8. associate-/l* 92.9%

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

      9. distribute-rgt-out-- 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 88.3%

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

   8. Simplified 88.3%

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

   9. Taylor expanded in t around 0 81.3%

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

       1. neg-mul-1 81.3%

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

       2. distribute-neg-frac 81.3%

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

   11. Simplified 81.3%

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

   if -5.20000000000000021e258 < z < -2.2e191

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 48.7%

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

      1. associate--l+ 48.7%

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

      2. distribute-lft-out-- 48.7%

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

      3. div-sub 48.7%

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

      4. mul-1-neg 48.7%

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

      5. unsub-neg 48.7%

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

      6. div-sub 48.7%

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

      7. associate-/l* 70.6%

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

      8. associate-/l* 87.7%

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

      9. distribute-rgt-out-- 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around 0 37.5%

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

      1. associate-*r/ 37.5%

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

      2. neg-mul-1 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

      4. associate-*l/ 70.6%

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

      5. distribute-rgt-neg-out 70.6%

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

      6. sub-neg 70.6%

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

      7. distribute-lft-out 70.6%

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

      8. associate-*l/ 48.7%

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

      9. associate-*r/ 70.6%

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

      10. +-commutative 70.6%

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

      11. *-commutative 70.6%

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

      12. distribute-lft-neg-out 70.6%

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

      13. associate-/l* 53.5%

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

      14. mul-1-neg 53.5%

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

      15. distribute-neg-in 53.5%

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

      16. mul-1-neg 53.5%

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

      17. remove-double-neg 53.5%

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

   8. Simplified 70.6%

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

   if -1.54999999999999998e119 < z < -3.59999999999999991e-47 or -4.69999999999999996e-71 < z < -3.9999999999999999e-121

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 83.4%

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

      3. associate-*r/ 92.9%

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

      4. clear-num 92.8%

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

      5. un-div-inv 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in a around inf 69.7%

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

   6. Taylor expanded in t around inf 59.9%

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

      1. associate-*r/ 65.2%

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

   8. Simplified 65.2%

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

   if -3.59999999999999991e-47 < z < -4.69999999999999996e-71

   1. Initial program 78.4%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. div-sub 81.5%

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

   5. Simplified 81.5%

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

   if -3.9999999999999999e-121 < z < 1.41999999999999997e72

   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. *-commutative 90.7%

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

      2. associate-*l/ 84.7%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 95.1%

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

      5. un-div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in z around 0 76.7%

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

   if 1.41999999999999997e72 < z

   1. Initial program 58.9%

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

   3. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 64.1%

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

   5. Simplified 64.1%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+258}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-121}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+189}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-59} \lor \neg \left(z \leq 4 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -5.2e+258)
     t_1
     (if (<= z -1.7e+189)
       (* (/ (- t x) z) (- a y))
       (if (<= z -6.4e+119)
         t_1
         (if (<= z -2.8e-47)
           (+ x (* t (/ (- y z) a)))
           (if (or (<= z -8.5e-59) (not (<= z 4e+71)))
             (* t (/ (- y z) (- a z)))
             (+ x (* y (/ (- t x) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -5.2e+258) {
		tmp = t_1;
	} else if (z <= -1.7e+189) {
		tmp = ((t - x) / z) * (a - y);
	} else if (z <= -6.4e+119) {
		tmp = t_1;
	} else if (z <= -2.8e-47) {
		tmp = x + (t * ((y - z) / a));
	} else if ((z <= -8.5e-59) || !(z <= 4e+71)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / 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) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-5.2d+258)) then
        tmp = t_1
    else if (z <= (-1.7d+189)) then
        tmp = ((t - x) / z) * (a - y)
    else if (z <= (-6.4d+119)) then
        tmp = t_1
    else if (z <= (-2.8d-47)) then
        tmp = x + (t * ((y - z) / a))
    else if ((z <= (-8.5d-59)) .or. (.not. (z <= 4d+71))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * ((t - x) / a))
    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 * (x / z));
	double tmp;
	if (z <= -5.2e+258) {
		tmp = t_1;
	} else if (z <= -1.7e+189) {
		tmp = ((t - x) / z) * (a - y);
	} else if (z <= -6.4e+119) {
		tmp = t_1;
	} else if (z <= -2.8e-47) {
		tmp = x + (t * ((y - z) / a));
	} else if ((z <= -8.5e-59) || !(z <= 4e+71)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -5.2e+258:
		tmp = t_1
	elif z <= -1.7e+189:
		tmp = ((t - x) / z) * (a - y)
	elif z <= -6.4e+119:
		tmp = t_1
	elif z <= -2.8e-47:
		tmp = x + (t * ((y - z) / a))
	elif (z <= -8.5e-59) or not (z <= 4e+71):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -5.2e+258)
		tmp = t_1;
	elseif (z <= -1.7e+189)
		tmp = Float64(Float64(Float64(t - x) / z) * Float64(a - y));
	elseif (z <= -6.4e+119)
		tmp = t_1;
	elseif (z <= -2.8e-47)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif ((z <= -8.5e-59) || !(z <= 4e+71))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -5.2e+258)
		tmp = t_1;
	elseif (z <= -1.7e+189)
		tmp = ((t - x) / z) * (a - y);
	elseif (z <= -6.4e+119)
		tmp = t_1;
	elseif (z <= -2.8e-47)
		tmp = x + (t * ((y - z) / a));
	elseif ((z <= -8.5e-59) || ~((z <= 4e+71)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+258], t$95$1, If[LessEqual[z, -1.7e+189], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e+119], t$95$1, If[LessEqual[z, -2.8e-47], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.5e-59], N[Not[LessEqual[z, 4e+71]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.20000000000000021e258 or -1.69999999999999992e189 < z < -6.39999999999999979e119

   1. Initial program 57.2%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. distribute-lft-out-- 68.9%

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

      3. div-sub 68.9%

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

      4. mul-1-neg 68.9%

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

      5. unsub-neg 68.9%

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

      6. div-sub 68.9%

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

      7. associate-/l* 79.1%

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

      8. associate-/l* 92.9%

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

      9. distribute-rgt-out-- 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 88.3%

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

   8. Simplified 88.3%

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

   9. Taylor expanded in t around 0 81.3%

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

       1. neg-mul-1 81.3%

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

       2. distribute-neg-frac 81.3%

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

   11. Simplified 81.3%

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

   if -5.20000000000000021e258 < z < -1.69999999999999992e189

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 48.7%

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

      1. associate--l+ 48.7%

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

      2. distribute-lft-out-- 48.7%

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

      3. div-sub 48.7%

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

      4. mul-1-neg 48.7%

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

      5. unsub-neg 48.7%

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

      6. div-sub 48.7%

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

      7. associate-/l* 70.6%

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

      8. associate-/l* 87.7%

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

      9. distribute-rgt-out-- 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around 0 37.5%

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

      1. associate-*r/ 37.5%

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

      2. neg-mul-1 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

      4. associate-*l/ 70.6%

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

      5. distribute-rgt-neg-out 70.6%

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

      6. sub-neg 70.6%

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

      7. distribute-lft-out 70.6%

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

      8. associate-*l/ 48.7%

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

      9. associate-*r/ 70.6%

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

      10. +-commutative 70.6%

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

      11. *-commutative 70.6%

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

      12. distribute-lft-neg-out 70.6%

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

      13. associate-/l* 53.5%

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

      14. mul-1-neg 53.5%

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

      15. distribute-neg-in 53.5%

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

      16. mul-1-neg 53.5%

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

      17. remove-double-neg 53.5%

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

   8. Simplified 70.6%

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

   if -6.39999999999999979e119 < z < -2.79999999999999993e-47

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 90.8%

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

      4. clear-num 90.7%

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

      5. un-div-inv 90.8%

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

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in a around inf 64.2%

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

   6. Taylor expanded in t around inf 51.2%

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

      1. associate-*r/ 58.0%

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

   8. Simplified 58.0%

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

   if -2.79999999999999993e-47 < z < -8.49999999999999933e-59 or 4.0000000000000002e71 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in x around 0 46.8%

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

      1. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   if -8.49999999999999933e-59 < z < 4.0000000000000002e71

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 74.3%

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

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+258}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+189}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-59} \lor \neg \left(z \leq 4 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-224}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-288}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2200:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t)))
        (t_2 (+ x (/ (* y t) a)))
        (t_3 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.7e-85)
     t_2
     (if (<= a -1.55e-224)
       (- t (/ (* y t) z))
       (if (<= a -7.4e-290)
         t_1
         (if (<= a 1.55e-288)
           t_3
           (if (<= a 6.6e-18) t_1 (if (<= a 2200.0) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.7e-85) {
		tmp = t_2;
	} else if (a <= -1.55e-224) {
		tmp = t - ((y * t) / z);
	} else if (a <= -7.4e-290) {
		tmp = t_1;
	} else if (a <= 1.55e-288) {
		tmp = t_3;
	} else if (a <= 6.6e-18) {
		tmp = t_1;
	} else if (a <= 2200.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    t_2 = x + ((y * t) / a)
    t_3 = t * (1.0d0 - (y / z))
    if (a <= (-1.7d-85)) then
        tmp = t_2
    else if (a <= (-1.55d-224)) then
        tmp = t - ((y * t) / z)
    else if (a <= (-7.4d-290)) then
        tmp = t_1
    else if (a <= 1.55d-288) then
        tmp = t_3
    else if (a <= 6.6d-18) then
        tmp = t_1
    else if (a <= 2200.0d0) then
        tmp = t_3
    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 = (y / z) * (x - t);
	double t_2 = x + ((y * t) / a);
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.7e-85) {
		tmp = t_2;
	} else if (a <= -1.55e-224) {
		tmp = t - ((y * t) / z);
	} else if (a <= -7.4e-290) {
		tmp = t_1;
	} else if (a <= 1.55e-288) {
		tmp = t_3;
	} else if (a <= 6.6e-18) {
		tmp = t_1;
	} else if (a <= 2200.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	t_2 = x + ((y * t) / a)
	t_3 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.7e-85:
		tmp = t_2
	elif a <= -1.55e-224:
		tmp = t - ((y * t) / z)
	elif a <= -7.4e-290:
		tmp = t_1
	elif a <= 1.55e-288:
		tmp = t_3
	elif a <= 6.6e-18:
		tmp = t_1
	elif a <= 2200.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	t_3 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.7e-85)
		tmp = t_2;
	elseif (a <= -1.55e-224)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= -7.4e-290)
		tmp = t_1;
	elseif (a <= 1.55e-288)
		tmp = t_3;
	elseif (a <= 6.6e-18)
		tmp = t_1;
	elseif (a <= 2200.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	t_2 = x + ((y * t) / a);
	t_3 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.7e-85)
		tmp = t_2;
	elseif (a <= -1.55e-224)
		tmp = t - ((y * t) / z);
	elseif (a <= -7.4e-290)
		tmp = t_1;
	elseif (a <= 1.55e-288)
		tmp = t_3;
	elseif (a <= 6.6e-18)
		tmp = t_1;
	elseif (a <= 2200.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e-85], t$95$2, If[LessEqual[a, -1.55e-224], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.4e-290], t$95$1, If[LessEqual[a, 1.55e-288], t$95$3, If[LessEqual[a, 6.6e-18], t$95$1, If[LessEqual[a, 2200.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7e-85 or 2200 < a

   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. *-commutative 83.0%

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

      2. associate-*l/ 66.2%

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

      3. associate-*r/ 87.5%

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

      4. clear-num 87.5%

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

      5. un-div-inv 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in z around 0 69.7%

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

   6. Taylor expanded in t around inf 55.7%

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

   if -1.7e-85 < a < -1.55000000000000004e-224

   1. Initial program 76.7%

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

   3. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 59.9%

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

      4. div-sub 60.2%

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

      5. sub-neg 60.2%

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

      6. *-inverses 60.2%

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

      7. metadata-eval 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in x around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. sub-neg 59.0%

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

      3. metadata-eval 59.0%

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

      4. distribute-rgt-neg-in 59.0%

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

      5. +-commutative 59.0%

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

      6. distribute-neg-in 59.0%

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

      7. metadata-eval 59.0%

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

      8. sub-neg 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 59.0%

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

       2. associate-*r/ 59.0%

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

       3. unsub-neg 59.0%

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

       4. *-commutative 59.0%

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

       5. associate-*l/ 59.0%

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

   11. Simplified 59.0%

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

   if -1.55000000000000004e-224 < a < -7.39999999999999954e-290 or 1.54999999999999992e-288 < a < 6.6000000000000003e-18

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. distribute-lft-out-- 74.5%

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

      3. div-sub 74.5%

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

      4. mul-1-neg 74.5%

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

      5. unsub-neg 74.5%

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

      6. div-sub 74.5%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 74.1%

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

      9. distribute-rgt-out-- 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in y around inf 53.7%

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

       1. distribute-lft-out-- 53.7%

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

       2. associate-*r/ 48.7%

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

       3. *-commutative 48.7%

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

       4. associate-/l* 57.0%

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

       5. associate-*r/ 55.3%

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

       6. *-commutative 55.3%

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

       7. associate-*r/ 58.6%

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

       8. distribute-rgt-out-- 62.0%

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

   11. Simplified 62.0%

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

   if -7.39999999999999954e-290 < a < 1.54999999999999992e-288 or 6.6000000000000003e-18 < a < 2200

   1. Initial program 66.2%

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

   3. Taylor expanded in a around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 44.3%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 44.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 44.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 44.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 44.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   5. Simplified 44.3%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   6. Taylor expanded in x around 0 60.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\frac{y}{z} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 60.3%

         \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]

      2. sub-neg 60.3%

         \[\leadsto -t \cdot \color{blue}{\left(\frac{y}{z} + \left(-1\right)\right)} \]

      3. metadata-eval 60.3%

         \[\leadsto -t \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      4. distribute-rgt-neg-in 60.3%

         \[\leadsto \color{blue}{t \cdot \left(-\left(\frac{y}{z} + -1\right)\right)} \]

      5. +-commutative 60.3%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-1 + \frac{y}{z}\right)}\right) \]

      6. distribute-neg-in 60.3%

         \[\leadsto t \cdot \color{blue}{\left(\left(--1\right) + \left(-\frac{y}{z}\right)\right)} \]

      7. metadata-eval 60.3%

         \[\leadsto t \cdot \left(\color{blue}{1} + \left(-\frac{y}{z}\right)\right) \]

      8. sub-neg 60.3%

         \[\leadsto t \cdot \color{blue}{\left(1 - \frac{y}{z}\right)} \]

   8. Simplified 60.3%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-224}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 2200:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-289}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 112:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (/ (* y t) a)))
        (t_3 (* (/ y z) (- x t))))
   (if (<= a -1.7e-86)
     t_2
     (if (<= a -1.15e-235)
       t_1
       (if (<= a -1.2e-289)
         t_3
         (if (<= a 9e-286)
           t_1
           (if (<= a 5.2e-25) t_3 (if (<= a 112.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double t_3 = (y / z) * (x - t);
	double tmp;
	if (a <= -1.7e-86) {
		tmp = t_2;
	} else if (a <= -1.15e-235) {
		tmp = t_1;
	} else if (a <= -1.2e-289) {
		tmp = t_3;
	} else if (a <= 9e-286) {
		tmp = t_1;
	} else if (a <= 5.2e-25) {
		tmp = t_3;
	} else if (a <= 112.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + ((y * t) / a)
    t_3 = (y / z) * (x - t)
    if (a <= (-1.7d-86)) then
        tmp = t_2
    else if (a <= (-1.15d-235)) then
        tmp = t_1
    else if (a <= (-1.2d-289)) then
        tmp = t_3
    else if (a <= 9d-286) then
        tmp = t_1
    else if (a <= 5.2d-25) then
        tmp = t_3
    else if (a <= 112.0d0) 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 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double t_3 = (y / z) * (x - t);
	double tmp;
	if (a <= -1.7e-86) {
		tmp = t_2;
	} else if (a <= -1.15e-235) {
		tmp = t_1;
	} else if (a <= -1.2e-289) {
		tmp = t_3;
	} else if (a <= 9e-286) {
		tmp = t_1;
	} else if (a <= 5.2e-25) {
		tmp = t_3;
	} else if (a <= 112.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + ((y * t) / a)
	t_3 = (y / z) * (x - t)
	tmp = 0
	if a <= -1.7e-86:
		tmp = t_2
	elif a <= -1.15e-235:
		tmp = t_1
	elif a <= -1.2e-289:
		tmp = t_3
	elif a <= 9e-286:
		tmp = t_1
	elif a <= 5.2e-25:
		tmp = t_3
	elif a <= 112.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	t_3 = Float64(Float64(y / z) * Float64(x - t))
	tmp = 0.0
	if (a <= -1.7e-86)
		tmp = t_2;
	elseif (a <= -1.15e-235)
		tmp = t_1;
	elseif (a <= -1.2e-289)
		tmp = t_3;
	elseif (a <= 9e-286)
		tmp = t_1;
	elseif (a <= 5.2e-25)
		tmp = t_3;
	elseif (a <= 112.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + ((y * t) / a);
	t_3 = (y / z) * (x - t);
	tmp = 0.0;
	if (a <= -1.7e-86)
		tmp = t_2;
	elseif (a <= -1.15e-235)
		tmp = t_1;
	elseif (a <= -1.2e-289)
		tmp = t_3;
	elseif (a <= 9e-286)
		tmp = t_1;
	elseif (a <= 5.2e-25)
		tmp = t_3;
	elseif (a <= 112.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e-86], t$95$2, If[LessEqual[a, -1.15e-235], t$95$1, If[LessEqual[a, -1.2e-289], t$95$3, If[LessEqual[a, 9e-286], t$95$1, If[LessEqual[a, 5.2e-25], t$95$3, If[LessEqual[a, 112.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e-86 or 112 < a

   1. Initial program 83.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 83.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 66.5%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 87.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 87.6%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 87.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 87.6%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 69.3%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   6. Taylor expanded in t around inf 55.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

   if -1.7e-86 < a < -1.14999999999999999e-235 or -1.19999999999999997e-289 < a < 9.0000000000000001e-286 or 5.2e-25 < a < 112

   1. Initial program 74.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 47.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)} \]

      2. unsub-neg 47.9%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 54.6%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 54.7%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 54.7%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 54.7%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 54.7%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   5. Simplified 54.7%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   6. Taylor expanded in x around 0 59.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\frac{y}{z} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]

      2. sub-neg 59.1%

         \[\leadsto -t \cdot \color{blue}{\left(\frac{y}{z} + \left(-1\right)\right)} \]

      3. metadata-eval 59.1%

         \[\leadsto -t \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      4. distribute-rgt-neg-in 59.1%

         \[\leadsto \color{blue}{t \cdot \left(-\left(\frac{y}{z} + -1\right)\right)} \]

      5. +-commutative 59.1%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-1 + \frac{y}{z}\right)}\right) \]

      6. distribute-neg-in 59.1%

         \[\leadsto t \cdot \color{blue}{\left(\left(--1\right) + \left(-\frac{y}{z}\right)\right)} \]

      7. metadata-eval 59.1%

         \[\leadsto t \cdot \left(\color{blue}{1} + \left(-\frac{y}{z}\right)\right) \]

      8. sub-neg 59.1%

         \[\leadsto t \cdot \color{blue}{\left(1 - \frac{y}{z}\right)} \]

   8. Simplified 59.1%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if -1.14999999999999999e-235 < a < -1.19999999999999997e-289 or 9.0000000000000001e-286 < a < 5.2e-25

   1. Initial program 69.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 75.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 75.0%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 74.9%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 74.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 74.9%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 75.0%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 82.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 74.4%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 82.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 82.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in y around inf 71.6%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 78.8%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 78.8%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in y around inf 53.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)} \]
   10. Step-by-step derivation

       1. distribute-lft-out-- 53.0%

          \[\leadsto \color{blue}{y \cdot \frac{x}{z} - y \cdot \frac{t}{z}} \]

       2. associate-*r/ 47.7%

          \[\leadsto \color{blue}{\frac{y \cdot x}{z}} - y \cdot \frac{t}{z} \]

       3. *-commutative 47.7%

          \[\leadsto \frac{\color{blue}{x \cdot y}}{z} - y \cdot \frac{t}{z} \]

       4. associate-/l* 56.4%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} - y \cdot \frac{t}{z} \]

       5. associate-*r/ 54.6%

          \[\leadsto x \cdot \frac{y}{z} - \color{blue}{\frac{y \cdot t}{z}} \]

       6. *-commutative 54.6%

          \[\leadsto x \cdot \frac{y}{z} - \frac{\color{blue}{t \cdot y}}{z} \]

       7. associate-*r/ 58.1%

          \[\leadsto x \cdot \frac{y}{z} - \color{blue}{t \cdot \frac{y}{z}} \]

       8. distribute-rgt-out-- 61.8%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(x - t\right)} \]

   11. Simplified 61.8%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(x - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 112:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ t_2 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))) (t_2 (+ t (* y (/ (- x t) z)))))
   (if (<= z -1.55e+119)
     t_2
     (if (<= z -3.4e-7)
       t_1
       (if (<= z -4.7e-71)
         (* y (/ (- t x) (- a z)))
         (if (<= z -1.5e-123)
           t_1
           (if (<= z 1.7e-50) (+ x (/ (- t x) (/ a y))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double t_2 = t + (y * ((x - t) / z));
	double tmp;
	if (z <= -1.55e+119) {
		tmp = t_2;
	} else if (z <= -3.4e-7) {
		tmp = t_1;
	} else if (z <= -4.7e-71) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.5e-123) {
		tmp = t_1;
	} else if (z <= 1.7e-50) {
		tmp = x + ((t - x) / (a / y));
	} 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 + (t * ((y - z) / a))
    t_2 = t + (y * ((x - t) / z))
    if (z <= (-1.55d+119)) then
        tmp = t_2
    else if (z <= (-3.4d-7)) then
        tmp = t_1
    else if (z <= (-4.7d-71)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= (-1.5d-123)) then
        tmp = t_1
    else if (z <= 1.7d-50) then
        tmp = x + ((t - x) / (a / y))
    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 + (t * ((y - z) / a));
	double t_2 = t + (y * ((x - t) / z));
	double tmp;
	if (z <= -1.55e+119) {
		tmp = t_2;
	} else if (z <= -3.4e-7) {
		tmp = t_1;
	} else if (z <= -4.7e-71) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.5e-123) {
		tmp = t_1;
	} else if (z <= 1.7e-50) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	t_2 = t + (y * ((x - t) / z))
	tmp = 0
	if z <= -1.55e+119:
		tmp = t_2
	elif z <= -3.4e-7:
		tmp = t_1
	elif z <= -4.7e-71:
		tmp = y * ((t - x) / (a - z))
	elif z <= -1.5e-123:
		tmp = t_1
	elif z <= 1.7e-50:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	t_2 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (z <= -1.55e+119)
		tmp = t_2;
	elseif (z <= -3.4e-7)
		tmp = t_1;
	elseif (z <= -4.7e-71)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= -1.5e-123)
		tmp = t_1;
	elseif (z <= 1.7e-50)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	t_2 = t + (y * ((x - t) / z));
	tmp = 0.0;
	if (z <= -1.55e+119)
		tmp = t_2;
	elseif (z <= -3.4e-7)
		tmp = t_1;
	elseif (z <= -4.7e-71)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= -1.5e-123)
		tmp = t_1;
	elseif (z <= 1.7e-50)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+119], t$95$2, If[LessEqual[z, -3.4e-7], t$95$1, If[LessEqual[z, -4.7e-71], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-123], t$95$1, If[LessEqual[z, 1.7e-50], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.54999999999999998e119 or 1.70000000000000007e-50 < z

   1. Initial program 63.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 59.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 59.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 59.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 59.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 59.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 59.1%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 70.3%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 76.6%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 76.6%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 76.6%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in y around inf 56.5%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 67.7%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 67.7%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   if -1.54999999999999998e119 < z < -3.39999999999999974e-7 or -4.69999999999999996e-71 < z < -1.49999999999999992e-123

   1. Initial program 81.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 81.2%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 82.6%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 91.2%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 91.1%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 91.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 91.1%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in a around inf 68.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   6. Taylor expanded in t around inf 62.8%

      \[\leadsto x + \color{blue}{\frac{t \cdot \left(y - z\right)}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 66.2%

         \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a}} \]

   8. Simplified 66.2%

      \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a}} \]

   if -3.39999999999999974e-7 < z < -4.69999999999999996e-71

   1. Initial program 90.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 68.6%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 68.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -1.49999999999999992e-123 < z < 1.70000000000000007e-50

   1. Initial program 91.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 87.4%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 96.4%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 96.4%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 96.7%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 96.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 81.4%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-123}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 10^{+152}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= x -2.3e+118)
     t_1
     (if (<= x -7.8e+73)
       (+ t (* y (/ x z)))
       (if (<= x -2.05e-69)
         (* y (/ (- t x) (- a z)))
         (if (<= x 2.6e+55)
           (* t (/ (- y z) (- a z)))
           (if (<= x 1e+152) (* (- t x) (/ y (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -2.3e+118) {
		tmp = t_1;
	} else if (x <= -7.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -2.05e-69) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 2.6e+55) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1e+152) {
		tmp = (t - 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 = x - (x * (y / a))
    if (x <= (-2.3d+118)) then
        tmp = t_1
    else if (x <= (-7.8d+73)) then
        tmp = t + (y * (x / z))
    else if (x <= (-2.05d-69)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 2.6d+55) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 1d+152) then
        tmp = (t - 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 = x - (x * (y / a));
	double tmp;
	if (x <= -2.3e+118) {
		tmp = t_1;
	} else if (x <= -7.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -2.05e-69) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 2.6e+55) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1e+152) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if x <= -2.3e+118:
		tmp = t_1
	elif x <= -7.8e+73:
		tmp = t + (y * (x / z))
	elif x <= -2.05e-69:
		tmp = y * ((t - x) / (a - z))
	elif x <= 2.6e+55:
		tmp = t * ((y - z) / (a - z))
	elif x <= 1e+152:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -2.3e+118)
		tmp = t_1;
	elseif (x <= -7.8e+73)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (x <= -2.05e-69)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 2.6e+55)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 1e+152)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (x <= -2.3e+118)
		tmp = t_1;
	elseif (x <= -7.8e+73)
		tmp = t + (y * (x / z));
	elseif (x <= -2.05e-69)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 2.6e+55)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 1e+152)
		tmp = (t - 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[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+118], t$95$1, If[LessEqual[x, -7.8e+73], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.05e-69], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+55], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+152], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.30000000000000016e118 or 1e152 < x

   1. Initial program 70.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 52.8%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 73.5%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 73.5%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 73.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 73.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]
   5. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   6. Applied egg-rr 73.5%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   7. Taylor expanded in t around 0 64.9%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto x + \color{blue}{\left(-\frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}\right)} \]

      2. div-sub 64.9%

         \[\leadsto x + \left(-\frac{x}{\color{blue}{\frac{a - z}{y - z}}}\right) \]

      3. distribute-neg-frac 64.9%

         \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

   9. Simplified 64.9%

      \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

   10. Taylor expanded in z around 0 44.2%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   11. Step-by-step derivation

       1. mul-1-neg 44.2%

          \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

       2. unsub-neg 44.2%

          \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

       3. associate-/l* 55.9%

          \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   12. Simplified 55.9%

       \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -2.30000000000000016e118 < x < -7.8000000000000002e73

   1. Initial program 36.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 84.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 84.1%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 69.3%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 66.7%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 67.6%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in y around inf 68.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.9%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 53.9%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in t around 0 68.8%

      \[\leadsto t - y \cdot \color{blue}{\left(-1 \cdot \frac{x}{z}\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 68.8%

          \[\leadsto t - y \cdot \color{blue}{\left(-\frac{x}{z}\right)} \]

       2. distribute-neg-frac 68.8%

          \[\leadsto t - y \cdot \color{blue}{\frac{-x}{z}} \]

   11. Simplified 68.8%

       \[\leadsto t - y \cdot \color{blue}{\frac{-x}{z}} \]

   if -7.8000000000000002e73 < x < -2.04999999999999995e-69

   1. Initial program 90.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 60.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 60.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -2.04999999999999995e-69 < x < 2.6e55

   1. Initial program 81.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 60.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.4%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 2.6e55 < x < 1e152

   1. Initial program 75.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 75.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 51.6%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 75.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 75.6%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 75.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 75.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in y around inf 56.1%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 60.3%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 36.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. *-rgt-identity 36.6%

         \[\leadsto \frac{y \cdot \left(t - x\right)}{\color{blue}{\left(a - z\right) \cdot 1}} \]

      4. times-frac 60.3%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \frac{t - x}{1}} \]

      5. /-rgt-identity 60.3%

         \[\leadsto \frac{y}{a - z} \cdot \color{blue}{\left(t - x\right)} \]

   7. Simplified 60.3%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+118}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 10^{+152}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= x -6.4e+117)
     t_1
     (if (<= x -6.8e+73)
       (+ t (* y (/ x z)))
       (if (<= x -5.8e-70)
         t_2
         (if (<= x 1.75e+55)
           (* t (/ (- y z) (- a z)))
           (if (<= x 9.5e+152) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -6.4e+117) {
		tmp = t_1;
	} else if (x <= -6.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -5.8e-70) {
		tmp = t_2;
	} else if (x <= 1.75e+55) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 9.5e+152) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = y * ((t - x) / (a - z))
    if (x <= (-6.4d+117)) then
        tmp = t_1
    else if (x <= (-6.8d+73)) then
        tmp = t + (y * (x / z))
    else if (x <= (-5.8d-70)) then
        tmp = t_2
    else if (x <= 1.75d+55) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 9.5d+152) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -6.4e+117) {
		tmp = t_1;
	} else if (x <= -6.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -5.8e-70) {
		tmp = t_2;
	} else if (x <= 1.75e+55) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 9.5e+152) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if x <= -6.4e+117:
		tmp = t_1
	elif x <= -6.8e+73:
		tmp = t + (y * (x / z))
	elif x <= -5.8e-70:
		tmp = t_2
	elif x <= 1.75e+55:
		tmp = t * ((y - z) / (a - z))
	elif x <= 9.5e+152:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (x <= -6.4e+117)
		tmp = t_1;
	elseif (x <= -6.8e+73)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (x <= -5.8e-70)
		tmp = t_2;
	elseif (x <= 1.75e+55)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 9.5e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (x <= -6.4e+117)
		tmp = t_1;
	elseif (x <= -6.8e+73)
		tmp = t + (y * (x / z));
	elseif (x <= -5.8e-70)
		tmp = t_2;
	elseif (x <= 1.75e+55)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 9.5e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+117], t$95$1, If[LessEqual[x, -6.8e+73], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-70], t$95$2, If[LessEqual[x, 1.75e+55], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+152], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.4000000000000001e117 or 9.49999999999999916e152 < x

   1. Initial program 70.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 52.8%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 73.5%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 73.5%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 73.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 73.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]
   5. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   6. Applied egg-rr 73.5%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   7. Taylor expanded in t around 0 64.9%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto x + \color{blue}{\left(-\frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}\right)} \]

      2. div-sub 64.9%

         \[\leadsto x + \left(-\frac{x}{\color{blue}{\frac{a - z}{y - z}}}\right) \]

      3. distribute-neg-frac 64.9%

         \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

   9. Simplified 64.9%

      \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

   10. Taylor expanded in z around 0 44.2%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   11. Step-by-step derivation

       1. mul-1-neg 44.2%

          \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

       2. unsub-neg 44.2%

          \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

       3. associate-/l* 55.9%

          \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   12. Simplified 55.9%

       \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -6.4000000000000001e117 < x < -6.8000000000000003e73

   1. Initial program 36.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 84.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 84.1%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 69.3%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 66.7%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 67.6%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in y around inf 68.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.9%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 53.9%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in t around 0 68.8%

      \[\leadsto t - y \cdot \color{blue}{\left(-1 \cdot \frac{x}{z}\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 68.8%

          \[\leadsto t - y \cdot \color{blue}{\left(-\frac{x}{z}\right)} \]

       2. distribute-neg-frac 68.8%

          \[\leadsto t - y \cdot \color{blue}{\frac{-x}{z}} \]

   11. Simplified 68.8%

       \[\leadsto t - y \cdot \color{blue}{\frac{-x}{z}} \]

   if -6.8000000000000003e73 < x < -5.79999999999999943e-70 or 1.75000000000000005e55 < x < 9.49999999999999916e152

   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 58.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 60.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 60.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -5.79999999999999943e-70 < x < 1.75000000000000005e55

   1. Initial program 81.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 60.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.4%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+117}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;y \leq -2500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= y -2500000000000.0)
     t_1
     (if (<= y -1.35e-33)
       (* t (- 1.0 (/ y z)))
       (if (<= y 2e-31)
         x
         (if (<= y 7.1e+115)
           t_1
           (if (<= y 5.6e+164) (* (/ y z) (- x t)) (* t (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (y <= -2500000000000.0) {
		tmp = t_1;
	} else if (y <= -1.35e-33) {
		tmp = t * (1.0 - (y / z));
	} else if (y <= 2e-31) {
		tmp = x;
	} else if (y <= 7.1e+115) {
		tmp = t_1;
	} else if (y <= 5.6e+164) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t * (y / (a - 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 = y * ((t - x) / a)
    if (y <= (-2500000000000.0d0)) then
        tmp = t_1
    else if (y <= (-1.35d-33)) then
        tmp = t * (1.0d0 - (y / z))
    else if (y <= 2d-31) then
        tmp = x
    else if (y <= 7.1d+115) then
        tmp = t_1
    else if (y <= 5.6d+164) then
        tmp = (y / z) * (x - t)
    else
        tmp = t * (y / (a - 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 = y * ((t - x) / a);
	double tmp;
	if (y <= -2500000000000.0) {
		tmp = t_1;
	} else if (y <= -1.35e-33) {
		tmp = t * (1.0 - (y / z));
	} else if (y <= 2e-31) {
		tmp = x;
	} else if (y <= 7.1e+115) {
		tmp = t_1;
	} else if (y <= 5.6e+164) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if y <= -2500000000000.0:
		tmp = t_1
	elif y <= -1.35e-33:
		tmp = t * (1.0 - (y / z))
	elif y <= 2e-31:
		tmp = x
	elif y <= 7.1e+115:
		tmp = t_1
	elif y <= 5.6e+164:
		tmp = (y / z) * (x - t)
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (y <= -2500000000000.0)
		tmp = t_1;
	elseif (y <= -1.35e-33)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (y <= 2e-31)
		tmp = x;
	elseif (y <= 7.1e+115)
		tmp = t_1;
	elseif (y <= 5.6e+164)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (y <= -2500000000000.0)
		tmp = t_1;
	elseif (y <= -1.35e-33)
		tmp = t * (1.0 - (y / z));
	elseif (y <= 2e-31)
		tmp = x;
	elseif (y <= 7.1e+115)
		tmp = t_1;
	elseif (y <= 5.6e+164)
		tmp = (y / z) * (x - t);
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2500000000000.0], t$95$1, If[LessEqual[y, -1.35e-33], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-31], x, If[LessEqual[y, 7.1e+115], t$95$1, If[LessEqual[y, 5.6e+164], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.5e12 or 2e-31 < y < 7.0999999999999997e115

   1. Initial program 80.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 66.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 44.3%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   if -2.5e12 < y < -1.35e-33

   1. Initial program 71.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 19.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 19.7%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)} \]

      2. unsub-neg 19.7%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 36.5%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 36.5%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 36.5%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 36.5%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 36.5%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   5. Simplified 36.5%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   6. Taylor expanded in x around 0 58.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\frac{y}{z} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.1%

         \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]

      2. sub-neg 58.1%

         \[\leadsto -t \cdot \color{blue}{\left(\frac{y}{z} + \left(-1\right)\right)} \]

      3. metadata-eval 58.1%

         \[\leadsto -t \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      4. distribute-rgt-neg-in 58.1%

         \[\leadsto \color{blue}{t \cdot \left(-\left(\frac{y}{z} + -1\right)\right)} \]

      5. +-commutative 58.1%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-1 + \frac{y}{z}\right)}\right) \]

      6. distribute-neg-in 58.1%

         \[\leadsto t \cdot \color{blue}{\left(\left(--1\right) + \left(-\frac{y}{z}\right)\right)} \]

      7. metadata-eval 58.1%

         \[\leadsto t \cdot \left(\color{blue}{1} + \left(-\frac{y}{z}\right)\right) \]

      8. sub-neg 58.1%

         \[\leadsto t \cdot \color{blue}{\left(1 - \frac{y}{z}\right)} \]

   8. Simplified 58.1%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if -1.35e-33 < y < 2e-31

   1. Initial program 73.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.6%

      \[\leadsto \color{blue}{x} \]

   if 7.0999999999999997e115 < y < 5.6000000000000004e164

   1. Initial program 87.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 75.8%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 75.8%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 76.2%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 76.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 76.2%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 75.8%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 76.0%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 76.0%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 76.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in y around inf 75.9%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 76.1%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 76.1%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in y around inf 76.1%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)} \]
   10. Step-by-step derivation

       1. distribute-lft-out-- 76.1%

          \[\leadsto \color{blue}{y \cdot \frac{x}{z} - y \cdot \frac{t}{z}} \]

       2. associate-*r/ 75.9%

          \[\leadsto \color{blue}{\frac{y \cdot x}{z}} - y \cdot \frac{t}{z} \]

       3. *-commutative 75.9%

          \[\leadsto \frac{\color{blue}{x \cdot y}}{z} - y \cdot \frac{t}{z} \]

       4. associate-/l* 75.9%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} - y \cdot \frac{t}{z} \]

       5. associate-*r/ 75.9%

          \[\leadsto x \cdot \frac{y}{z} - \color{blue}{\frac{y \cdot t}{z}} \]

       6. *-commutative 75.9%

          \[\leadsto x \cdot \frac{y}{z} - \frac{\color{blue}{t \cdot y}}{z} \]

       7. associate-*r/ 75.9%

          \[\leadsto x \cdot \frac{y}{z} - \color{blue}{t \cdot \frac{y}{z}} \]

       8. distribute-rgt-out-- 75.9%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(x - t\right)} \]

   11. Simplified 75.9%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(x - t\right)} \]

   if 5.6000000000000004e164 < y

   1. Initial program 88.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 82.5%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in t around inf 49.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 59.0%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 59.0%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 19: 44.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -5e+136)
     t_1
     (if (<= z -6.1e+63)
       (* x (/ (- y a) z))
       (if (<= z -6.3e-68)
         (* t (/ y (- a z)))
         (if (<= z -6.2e-173)
           x
           (if (<= z 3.1e-44) (* y (/ (- t x) a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -5e+136) {
		tmp = t_1;
	} else if (z <= -6.1e+63) {
		tmp = x * ((y - a) / z);
	} else if (z <= -6.3e-68) {
		tmp = t * (y / (a - z));
	} else if (z <= -6.2e-173) {
		tmp = x;
	} else if (z <= 3.1e-44) {
		tmp = y * ((t - x) / a);
	} 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 * (1.0d0 - (y / z))
    if (z <= (-5d+136)) then
        tmp = t_1
    else if (z <= (-6.1d+63)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-6.3d-68)) then
        tmp = t * (y / (a - z))
    else if (z <= (-6.2d-173)) then
        tmp = x
    else if (z <= 3.1d-44) then
        tmp = y * ((t - x) / a)
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -5e+136) {
		tmp = t_1;
	} else if (z <= -6.1e+63) {
		tmp = x * ((y - a) / z);
	} else if (z <= -6.3e-68) {
		tmp = t * (y / (a - z));
	} else if (z <= -6.2e-173) {
		tmp = x;
	} else if (z <= 3.1e-44) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -5e+136:
		tmp = t_1
	elif z <= -6.1e+63:
		tmp = x * ((y - a) / z)
	elif z <= -6.3e-68:
		tmp = t * (y / (a - z))
	elif z <= -6.2e-173:
		tmp = x
	elif z <= 3.1e-44:
		tmp = y * ((t - x) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5e+136)
		tmp = t_1;
	elseif (z <= -6.1e+63)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -6.3e-68)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -6.2e-173)
		tmp = x;
	elseif (z <= 3.1e-44)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -5e+136)
		tmp = t_1;
	elseif (z <= -6.1e+63)
		tmp = x * ((y - a) / z);
	elseif (z <= -6.3e-68)
		tmp = t * (y / (a - z));
	elseif (z <= -6.2e-173)
		tmp = x;
	elseif (z <= 3.1e-44)
		tmp = y * ((t - x) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+136], t$95$1, If[LessEqual[z, -6.1e+63], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.3e-68], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-173], x, If[LessEqual[z, 3.1e-44], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.0000000000000002e136 or 3.09999999999999984e-44 < z

   1. Initial program 64.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 29.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 29.5%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)} \]

      2. unsub-neg 29.5%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 47.3%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 47.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 47.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 47.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 47.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   6. Taylor expanded in x around 0 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\frac{y}{z} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]

      2. sub-neg 53.2%

         \[\leadsto -t \cdot \color{blue}{\left(\frac{y}{z} + \left(-1\right)\right)} \]

      3. metadata-eval 53.2%

         \[\leadsto -t \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      4. distribute-rgt-neg-in 53.2%

         \[\leadsto \color{blue}{t \cdot \left(-\left(\frac{y}{z} + -1\right)\right)} \]

      5. +-commutative 53.2%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-1 + \frac{y}{z}\right)}\right) \]

      6. distribute-neg-in 53.2%

         \[\leadsto t \cdot \color{blue}{\left(\left(--1\right) + \left(-\frac{y}{z}\right)\right)} \]

      7. metadata-eval 53.2%

         \[\leadsto t \cdot \left(\color{blue}{1} + \left(-\frac{y}{z}\right)\right) \]

      8. sub-neg 53.2%

         \[\leadsto t \cdot \color{blue}{\left(1 - \frac{y}{z}\right)} \]

   8. Simplified 53.2%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if -5.0000000000000002e136 < z < -6.09999999999999968e63

   1. Initial program 63.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 46.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 46.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 46.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 46.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 46.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 46.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 46.5%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 54.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 58.8%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 58.8%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 58.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in t around 0 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 51.2%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   8. Simplified 51.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -6.09999999999999968e63 < z < -6.2999999999999998e-68

   1. Initial program 81.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 50.0%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in t around inf 31.5%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 40.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if -6.2999999999999998e-68 < z < -6.20000000000000011e-173

   1. Initial program 83.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{x} \]

   if -6.20000000000000011e-173 < z < 3.09999999999999984e-44

   1. Initial program 92.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 56.6%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 56.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 48.8%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 20: 34.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -6.6e+150)
     t
     (if (<= z -3.6e-50)
       t_1
       (if (<= z -2.05e-50)
         t
         (if (<= z -1.2e-246)
           x
           (if (<= z 5.3e-55) t_1 (if (<= z 2e+86) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -6.6e+150) {
		tmp = t;
	} else if (z <= -3.6e-50) {
		tmp = t_1;
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= -1.2e-246) {
		tmp = x;
	} else if (z <= 5.3e-55) {
		tmp = t_1;
	} else if (z <= 2e+86) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-6.6d+150)) then
        tmp = t
    else if (z <= (-3.6d-50)) then
        tmp = t_1
    else if (z <= (-2.05d-50)) then
        tmp = t
    else if (z <= (-1.2d-246)) then
        tmp = x
    else if (z <= 5.3d-55) then
        tmp = t_1
    else if (z <= 2d+86) 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 t_1 = t * (y / a);
	double tmp;
	if (z <= -6.6e+150) {
		tmp = t;
	} else if (z <= -3.6e-50) {
		tmp = t_1;
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= -1.2e-246) {
		tmp = x;
	} else if (z <= 5.3e-55) {
		tmp = t_1;
	} else if (z <= 2e+86) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -6.6e+150:
		tmp = t
	elif z <= -3.6e-50:
		tmp = t_1
	elif z <= -2.05e-50:
		tmp = t
	elif z <= -1.2e-246:
		tmp = x
	elif z <= 5.3e-55:
		tmp = t_1
	elif z <= 2e+86:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -6.6e+150)
		tmp = t;
	elseif (z <= -3.6e-50)
		tmp = t_1;
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= -1.2e-246)
		tmp = x;
	elseif (z <= 5.3e-55)
		tmp = t_1;
	elseif (z <= 2e+86)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -6.6e+150)
		tmp = t;
	elseif (z <= -3.6e-50)
		tmp = t_1;
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= -1.2e-246)
		tmp = x;
	elseif (z <= 5.3e-55)
		tmp = t_1;
	elseif (z <= 2e+86)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+150], t, If[LessEqual[z, -3.6e-50], t$95$1, If[LessEqual[z, -2.05e-50], t, If[LessEqual[z, -1.2e-246], x, If[LessEqual[z, 5.3e-55], t$95$1, If[LessEqual[z, 2e+86], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999962e150 or -3.59999999999999979e-50 < z < -2.04999999999999993e-50 or 2e86 < z

   1. Initial program 56.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.3%

      \[\leadsto \color{blue}{t} \]

   if -6.59999999999999962e150 < z < -3.59999999999999979e-50 or -1.1999999999999999e-246 < z < 5.3000000000000003e-55

   1. Initial program 86.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 53.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 57.5%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 57.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 45.5%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 29.6%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 36.6%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 36.6%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if -2.04999999999999993e-50 < z < -1.1999999999999999e-246 or 5.3000000000000003e-55 < z < 2e86

   1. Initial program 90.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z - y}}\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -7.5e+42)
     t_1
     (if (<= z -2.9e-186)
       (+ x (/ (- x t) (/ a (- z y))))
       (if (<= z -2.85e-186)
         (* x (/ y (- a)))
         (if (<= z 7.5e+63) (+ x (* (- t x) (/ (- y z) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -7.5e+42) {
		tmp = t_1;
	} else if (z <= -2.9e-186) {
		tmp = x + ((x - t) / (a / (z - y)));
	} else if (z <= -2.85e-186) {
		tmp = x * (y / -a);
	} else if (z <= 7.5e+63) {
		tmp = x + ((t - x) * ((y - z) / a));
	} 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 + (((t - x) / z) * (a - y))
    if (z <= (-7.5d+42)) then
        tmp = t_1
    else if (z <= (-2.9d-186)) then
        tmp = x + ((x - t) / (a / (z - y)))
    else if (z <= (-2.85d-186)) then
        tmp = x * (y / -a)
    else if (z <= 7.5d+63) then
        tmp = x + ((t - x) * ((y - z) / a))
    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 + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -7.5e+42) {
		tmp = t_1;
	} else if (z <= -2.9e-186) {
		tmp = x + ((x - t) / (a / (z - y)));
	} else if (z <= -2.85e-186) {
		tmp = x * (y / -a);
	} else if (z <= 7.5e+63) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -7.5e+42:
		tmp = t_1
	elif z <= -2.9e-186:
		tmp = x + ((x - t) / (a / (z - y)))
	elif z <= -2.85e-186:
		tmp = x * (y / -a)
	elif z <= 7.5e+63:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -7.5e+42)
		tmp = t_1;
	elseif (z <= -2.9e-186)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(a / Float64(z - y))));
	elseif (z <= -2.85e-186)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (z <= 7.5e+63)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -7.5e+42)
		tmp = t_1;
	elseif (z <= -2.9e-186)
		tmp = x + ((x - t) / (a / (z - y)));
	elseif (z <= -2.85e-186)
		tmp = x * (y / -a);
	elseif (z <= 7.5e+63)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+42], t$95$1, If[LessEqual[z, -2.9e-186], N[(x + N[(N[(x - t), $MachinePrecision] / N[(a / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.85e-186], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+63], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.50000000000000041e42 or 7.5000000000000005e63 < z

   1. Initial program 61.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 61.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 61.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 61.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 61.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 61.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 61.3%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 73.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 80.2%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 80.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   if -7.50000000000000041e42 < z < -2.90000000000000019e-186

   1. Initial program 84.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 86.6%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 94.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 94.8%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 95.0%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 95.0%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in a around inf 74.4%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   if -2.90000000000000019e-186 < z < -2.85000000000000001e-186

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 0.0%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around 0 5.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 5.3%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a}} \]

      2. associate-/l* 100.0%

         \[\leadsto -\color{blue}{x \cdot \frac{y}{a}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{-x \cdot \frac{y}{a}} \]

   if -2.85000000000000001e-186 < z < 7.5000000000000005e63

   1. Initial program 91.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 69.9%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 83.2%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   5. Simplified 83.2%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z - y}}\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 34.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+150)
   t
   (if (<= z -4.5e-67)
     (/ t (/ a y))
     (if (<= z -2.15e-246)
       x
       (if (<= z 5.3e-55) (* t (/ y a)) (if (<= z 1.55e+97) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+150) {
		tmp = t;
	} else if (z <= -4.5e-67) {
		tmp = t / (a / y);
	} else if (z <= -2.15e-246) {
		tmp = x;
	} else if (z <= 5.3e-55) {
		tmp = t * (y / a);
	} else if (z <= 1.55e+97) {
		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 <= (-6.6d+150)) then
        tmp = t
    else if (z <= (-4.5d-67)) then
        tmp = t / (a / y)
    else if (z <= (-2.15d-246)) then
        tmp = x
    else if (z <= 5.3d-55) then
        tmp = t * (y / a)
    else if (z <= 1.55d+97) 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 <= -6.6e+150) {
		tmp = t;
	} else if (z <= -4.5e-67) {
		tmp = t / (a / y);
	} else if (z <= -2.15e-246) {
		tmp = x;
	} else if (z <= 5.3e-55) {
		tmp = t * (y / a);
	} else if (z <= 1.55e+97) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+150:
		tmp = t
	elif z <= -4.5e-67:
		tmp = t / (a / y)
	elif z <= -2.15e-246:
		tmp = x
	elif z <= 5.3e-55:
		tmp = t * (y / a)
	elif z <= 1.55e+97:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+150)
		tmp = t;
	elseif (z <= -4.5e-67)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= -2.15e-246)
		tmp = x;
	elseif (z <= 5.3e-55)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.55e+97)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+150)
		tmp = t;
	elseif (z <= -4.5e-67)
		tmp = t / (a / y);
	elseif (z <= -2.15e-246)
		tmp = x;
	elseif (z <= 5.3e-55)
		tmp = t * (y / a);
	elseif (z <= 1.55e+97)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+150], t, If[LessEqual[z, -4.5e-67], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-246], x, If[LessEqual[z, 5.3e-55], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+97], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.59999999999999962e150 or 1.54999999999999991e97 < z

   1. Initial program 56.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.8%

      \[\leadsto \color{blue}{t} \]

   if -6.59999999999999962e150 < z < -4.50000000000000015e-67

   1. Initial program 77.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 49.2%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 30.2%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 22.8%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 30.6%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 30.6%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num 30.6%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv 30.7%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr 30.7%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -4.50000000000000015e-67 < z < -2.14999999999999996e-246 or 5.3000000000000003e-55 < z < 1.54999999999999991e97

   1. Initial program 90.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.7%

      \[\leadsto \color{blue}{x} \]

   if -2.14999999999999996e-246 < z < 5.3000000000000003e-55

   1. Initial program 90.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 61.6%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 53.4%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 40.1%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 40.1%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128} \lor \neg \left(z \leq 4100\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+128) (not (<= z 4100.0)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+128) || !(z <= 4100.0)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / 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 ((z <= (-2.2d+128)) .or. (.not. (z <= 4100.0d0))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) * ((y - z) / 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 ((z <= -2.2e+128) || !(z <= 4100.0)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+128) or not (z <= 4100.0):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+128) || !(z <= 4100.0))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e+128) || ~((z <= 4100.0)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+128], N[Not[LessEqual[z, 4100.0]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000017e128 or 4100 < z

   1. Initial program 61.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 61.8%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 61.8%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 61.8%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 61.8%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 61.8%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 61.8%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 73.6%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 80.7%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      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 58.6%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 70.4%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 70.4%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   if -2.20000000000000017e128 < z < 4100

   1. Initial program 88.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 66.7%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.3%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   5. Simplified 77.3%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128} \lor \neg \left(z \leq 4100\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+136) t (if (<= z 4.8e+60) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+136) {
		tmp = t;
	} else if (z <= 4.8e+60) {
		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 <= (-2d+136)) then
        tmp = t
    else if (z <= 4.8d+60) 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 <= -2e+136) {
		tmp = t;
	} else if (z <= 4.8e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+136:
		tmp = t
	elif z <= 4.8e+60:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+136)
		tmp = t;
	elseif (z <= 4.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+136)
		tmp = t;
	elseif (z <= 4.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+136], t, If[LessEqual[z, 4.8e+60], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000012e136 or 4.8e60 < z

   1. Initial program 60.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 47.2%

      \[\leadsto \color{blue}{t} \]

   if -2.00000000000000012e136 < z < 4.8e60

   1. Initial program 87.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 32.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 24.4% 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 78.3%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 21.3%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Alternative 26: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 78.3%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 78.3%

      \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

   2. associate-*l/ 67.3%

      \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

   3. associate-*r/ 83.8%

      \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

   4. clear-num 83.7%

      \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

   5. un-div-inv 83.8%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

4. Applied egg-rr 83.8%

   \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]
5. Step-by-step derivation

   1. div-sub 83.4%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

6. Applied egg-rr 83.4%

   \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

7. Taylor expanded in t around 0 42.1%

   \[\leadsto x + \color{blue}{-1 \cdot \frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}} \]
8. Step-by-step derivation

   1. mul-1-neg 42.1%

      \[\leadsto x + \color{blue}{\left(-\frac{x}{\frac{a}{y - z} - \frac{z}{y - z}}\right)} \]

   2. div-sub 41.8%

      \[\leadsto x + \left(-\frac{x}{\color{blue}{\frac{a - z}{y - z}}}\right) \]

   3. distribute-neg-frac 41.8%

      \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

9. Simplified 41.8%

   \[\leadsto x + \color{blue}{\frac{-x}{\frac{a - z}{y - z}}} \]

10. Taylor expanded in z around inf 2.8%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
11. Step-by-step derivation

    1. mul-1-neg 2.8%

       \[\leadsto x + \color{blue}{\left(-x\right)} \]

    2. sub-neg 2.8%

       \[\leadsto \color{blue}{x - x} \]

    3. +-inverses 2.8%

       \[\leadsto \color{blue}{0} \]

12. Simplified 2.8%

    \[\leadsto \color{blue}{0} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(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)))))