Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 93.2%

Time: 35.3s

Alternatives: 31

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: 80.4% 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: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-280)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0) (+ t (* (/ x z) (- y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-280) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-280)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-280], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000028e-280

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. remove-double-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

      5. associate-*l/ 79.5%

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

      6. associate-/l* 94.9%

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

      7. fma-neg 94.9%

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

      8. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

   if -5.00000000000000028e-280 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. associate--l+ 86.4%

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

      2. distribute-lft-out-- 86.4%

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

      3. div-sub 86.4%

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

      4. mul-1-neg 86.4%

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

      5. unsub-neg 86.4%

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

      6. distribute-rgt-out-- 86.4%

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

      7. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

      1. clear-num 89.2%

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

      2. un-div-inv 89.3%

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

   7. Applied egg-rr 89.3%

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

   8. Taylor expanded in t around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. associate-*l/ 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

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

   1. Initial program 93.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 40.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+195}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -13000000000:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-156}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-252}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))))
   (if (<= a -1.75e+226)
     x
     (if (<= a -4.2e+195)
       (/ (- y z) (/ a t))
       (if (<= a -8.2e+87)
         x
         (if (<= a -13000000000.0)
           (* z (/ t (- z a)))
           (if (<= a -2.7e-96)
             (* y (/ t (- a z)))
             (if (<= a -4.1e-156)
               t
               (if (<= a 3.6e-295)
                 t_1
                 (if (<= a 3.7e-252)
                   t
                   (if (<= a 3.8e-91)
                     t_1
                     (if (<= a 2.9e+152) (* t (/ (- y z) a)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (a <= -1.75e+226) {
		tmp = x;
	} else if (a <= -4.2e+195) {
		tmp = (y - z) / (a / t);
	} else if (a <= -8.2e+87) {
		tmp = x;
	} else if (a <= -13000000000.0) {
		tmp = z * (t / (z - a));
	} else if (a <= -2.7e-96) {
		tmp = y * (t / (a - z));
	} else if (a <= -4.1e-156) {
		tmp = t;
	} else if (a <= 3.6e-295) {
		tmp = t_1;
	} else if (a <= 3.7e-252) {
		tmp = t;
	} else if (a <= 3.8e-91) {
		tmp = t_1;
	} else if (a <= 2.9e+152) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    if (a <= (-1.75d+226)) then
        tmp = x
    else if (a <= (-4.2d+195)) then
        tmp = (y - z) / (a / t)
    else if (a <= (-8.2d+87)) then
        tmp = x
    else if (a <= (-13000000000.0d0)) then
        tmp = z * (t / (z - a))
    else if (a <= (-2.7d-96)) then
        tmp = y * (t / (a - z))
    else if (a <= (-4.1d-156)) then
        tmp = t
    else if (a <= 3.6d-295) then
        tmp = t_1
    else if (a <= 3.7d-252) then
        tmp = t
    else if (a <= 3.8d-91) then
        tmp = t_1
    else if (a <= 2.9d+152) then
        tmp = t * ((y - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (a <= -1.75e+226) {
		tmp = x;
	} else if (a <= -4.2e+195) {
		tmp = (y - z) / (a / t);
	} else if (a <= -8.2e+87) {
		tmp = x;
	} else if (a <= -13000000000.0) {
		tmp = z * (t / (z - a));
	} else if (a <= -2.7e-96) {
		tmp = y * (t / (a - z));
	} else if (a <= -4.1e-156) {
		tmp = t;
	} else if (a <= 3.6e-295) {
		tmp = t_1;
	} else if (a <= 3.7e-252) {
		tmp = t;
	} else if (a <= 3.8e-91) {
		tmp = t_1;
	} else if (a <= 2.9e+152) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	tmp = 0
	if a <= -1.75e+226:
		tmp = x
	elif a <= -4.2e+195:
		tmp = (y - z) / (a / t)
	elif a <= -8.2e+87:
		tmp = x
	elif a <= -13000000000.0:
		tmp = z * (t / (z - a))
	elif a <= -2.7e-96:
		tmp = y * (t / (a - z))
	elif a <= -4.1e-156:
		tmp = t
	elif a <= 3.6e-295:
		tmp = t_1
	elif a <= 3.7e-252:
		tmp = t
	elif a <= 3.8e-91:
		tmp = t_1
	elif a <= 2.9e+152:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -1.75e+226)
		tmp = x;
	elseif (a <= -4.2e+195)
		tmp = Float64(Float64(y - z) / Float64(a / t));
	elseif (a <= -8.2e+87)
		tmp = x;
	elseif (a <= -13000000000.0)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= -2.7e-96)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (a <= -4.1e-156)
		tmp = t;
	elseif (a <= 3.6e-295)
		tmp = t_1;
	elseif (a <= 3.7e-252)
		tmp = t;
	elseif (a <= 3.8e-91)
		tmp = t_1;
	elseif (a <= 2.9e+152)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -1.75e+226)
		tmp = x;
	elseif (a <= -4.2e+195)
		tmp = (y - z) / (a / t);
	elseif (a <= -8.2e+87)
		tmp = x;
	elseif (a <= -13000000000.0)
		tmp = z * (t / (z - a));
	elseif (a <= -2.7e-96)
		tmp = y * (t / (a - z));
	elseif (a <= -4.1e-156)
		tmp = t;
	elseif (a <= 3.6e-295)
		tmp = t_1;
	elseif (a <= 3.7e-252)
		tmp = t;
	elseif (a <= 3.8e-91)
		tmp = t_1;
	elseif (a <= 2.9e+152)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+226], x, If[LessEqual[a, -4.2e+195], N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e+87], x, If[LessEqual[a, -13000000000.0], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-96], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e-156], t, If[LessEqual[a, 3.6e-295], t$95$1, If[LessEqual[a, 3.7e-252], t, If[LessEqual[a, 3.8e-91], t$95$1, If[LessEqual[a, 2.9e+152], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.7499999999999999e226 or -4.20000000000000019e195 < a < -8.1999999999999998e87 or 2.8999999999999998e152 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 56.2%

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

   if -1.7499999999999999e226 < a < -4.20000000000000019e195

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in a around inf 75.6%

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

      1. clear-num 75.8%

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

      2. un-div-inv 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -8.1999999999999998e87 < a < -1.3e10

   1. Initial program 67.5%

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

   3. Taylor expanded in x around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-/l* 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0 28.9%

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

      1. associate-*r/ 28.9%

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

      2. mul-1-neg 28.9%

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

      3. distribute-rgt-neg-out 28.9%

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

      4. associate-*l/ 41.7%

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

      5. *-commutative 41.7%

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

      6. distribute-lft-neg-out 41.7%

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

      7. distribute-rgt-neg-in 41.7%

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

      8. distribute-frac-neg2 41.7%

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

      9. sub-neg 41.7%

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

      10. distribute-neg-in 41.7%

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

      11. remove-double-neg 41.7%

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

   8. Simplified 41.7%

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

   if -1.3e10 < a < -2.7e-96

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in y around inf 47.8%

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

      1. associate-*l/ 47.9%

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

      2. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -2.7e-96 < a < -4.1000000000000002e-156 or 3.6000000000000001e-295 < a < 3.7000000000000001e-252

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 57.7%

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

   if -4.1000000000000002e-156 < a < 3.6000000000000001e-295 or 3.7000000000000001e-252 < a < 3.79999999999999978e-91

   1. Initial program 68.6%

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

   3. Taylor expanded in y around -inf 65.9%

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

   4. Taylor expanded in a around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate-/l* 62.8%

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

      3. div-sub 62.8%

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

      4. distribute-rgt-neg-in 62.8%

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

      5. div-sub 62.8%

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

   6. Simplified 62.8%

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

   if 3.79999999999999978e-91 < a < 2.8999999999999998e152

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+195}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -13000000000:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-156}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-252}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.05 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-88}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x z) (- y a)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -3.2e+84)
     t_2
     (if (<= a -5.2e+70)
       t_1
       (if (<= a -5.1e+36)
         t_2
         (if (<= a -1.75e-17)
           (+ t (* (- t x) (/ a z)))
           (if (<= a -4.05e-97)
             (* y (/ (- t x) (- a z)))
             (if (<= a 3.4e-88)
               (+ t (/ (- x t) (/ z y)))
               (if (<= a 2.7e-15)
                 (+ x (/ (* y (- t x)) a))
                 (if (<= a 8.2e+65) t_1 (- x (* (/ y a) (- x t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x / z) * (y - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3.2e+84) {
		tmp = t_2;
	} else if (a <= -5.2e+70) {
		tmp = t_1;
	} else if (a <= -5.1e+36) {
		tmp = t_2;
	} else if (a <= -1.75e-17) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -4.05e-97) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.4e-88) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 2.7e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8.2e+65) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x / z) * (y - a))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-3.2d+84)) then
        tmp = t_2
    else if (a <= (-5.2d+70)) then
        tmp = t_1
    else if (a <= (-5.1d+36)) then
        tmp = t_2
    else if (a <= (-1.75d-17)) then
        tmp = t + ((t - x) * (a / z))
    else if (a <= (-4.05d-97)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 3.4d-88) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 2.7d-15) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 8.2d+65) then
        tmp = t_1
    else
        tmp = x - ((y / a) * (x - 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 + ((x / z) * (y - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3.2e+84) {
		tmp = t_2;
	} else if (a <= -5.2e+70) {
		tmp = t_1;
	} else if (a <= -5.1e+36) {
		tmp = t_2;
	} else if (a <= -1.75e-17) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -4.05e-97) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.4e-88) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 2.7e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8.2e+65) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x / z) * (y - a))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -3.2e+84:
		tmp = t_2
	elif a <= -5.2e+70:
		tmp = t_1
	elif a <= -5.1e+36:
		tmp = t_2
	elif a <= -1.75e-17:
		tmp = t + ((t - x) * (a / z))
	elif a <= -4.05e-97:
		tmp = y * ((t - x) / (a - z))
	elif a <= 3.4e-88:
		tmp = t + ((x - t) / (z / y))
	elif a <= 2.7e-15:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 8.2e+65:
		tmp = t_1
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x / z) * Float64(y - a)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -3.2e+84)
		tmp = t_2;
	elseif (a <= -5.2e+70)
		tmp = t_1;
	elseif (a <= -5.1e+36)
		tmp = t_2;
	elseif (a <= -1.75e-17)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(a / z)));
	elseif (a <= -4.05e-97)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 3.4e-88)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 2.7e-15)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 8.2e+65)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x / z) * (y - a));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -3.2e+84)
		tmp = t_2;
	elseif (a <= -5.2e+70)
		tmp = t_1;
	elseif (a <= -5.1e+36)
		tmp = t_2;
	elseif (a <= -1.75e-17)
		tmp = t + ((t - x) * (a / z));
	elseif (a <= -4.05e-97)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 3.4e-88)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 2.7e-15)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 8.2e+65)
		tmp = t_1;
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+84], t$95$2, If[LessEqual[a, -5.2e+70], t$95$1, If[LessEqual[a, -5.1e+36], t$95$2, If[LessEqual[a, -1.75e-17], N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.05e-97], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-88], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-15], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+65], t$95$1, N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.2000000000000001e84 or -5.2000000000000001e70 < a < -5.09999999999999973e36

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 62.4%

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

      1. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   if -3.2000000000000001e84 < a < -5.2000000000000001e70 or 2.70000000000000009e-15 < a < 8.2000000000000003e65

   1. Initial program 55.6%

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

   3. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. distribute-lft-out-- 62.8%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. distribute-rgt-out-- 62.8%

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

      7. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

      1. clear-num 70.7%

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

      2. un-div-inv 70.8%

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

   7. Applied egg-rr 70.8%

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

   8. Taylor expanded in t around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. associate-*l/ 67.5%

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

      3. distribute-rgt-neg-in 67.5%

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

   10. Simplified 67.5%

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

   if -5.09999999999999973e36 < a < -1.7500000000000001e-17

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 67.9%

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

      7. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around 0 67.8%

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

      1. neg-mul-1 67.8%

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

      2. distribute-neg-frac 67.8%

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

   8. Simplified 67.8%

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

   if -1.7500000000000001e-17 < a < -4.05000000000000004e-97

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. div-sub 93.8%

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

   5. Simplified 93.8%

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

   if -4.05000000000000004e-97 < a < 3.39999999999999975e-88

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. distribute-rgt-out-- 82.2%

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

      7. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

      1. clear-num 84.7%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in y around inf 81.5%

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

   if 3.39999999999999975e-88 < a < 2.70000000000000009e-15

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 87.0%

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

   if 8.2000000000000003e65 < a

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. remove-double-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

      5. associate-*l/ 67.0%

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

      6. associate-/l* 97.3%

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

      7. fma-neg 97.3%

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

      8. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

      1. fma-undefine 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around 0 74.7%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 7 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.05 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-88}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+73}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-88}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2e+85)
     t_1
     (if (<= a -9e+73)
       (+ t (* (/ x z) (- y a)))
       (if (<= a -1.9e+29)
         t_1
         (if (<= a -6.5e-19)
           (+ t (* (- t x) (/ a z)))
           (if (<= a -7.4e-94)
             (* y (/ (- t x) (- a z)))
             (if (<= a 8.2e-88)
               (+ t (/ (- x t) (/ z y)))
               (if (<= a 4e-15)
                 (+ x (/ (* y (- t x)) a))
                 (if (<= a 1.55e+66)
                   (+ t (/ (* x (- y a)) z))
                   (- x (* (/ y a) (- x t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2e+85) {
		tmp = t_1;
	} else if (a <= -9e+73) {
		tmp = t + ((x / z) * (y - a));
	} else if (a <= -1.9e+29) {
		tmp = t_1;
	} else if (a <= -6.5e-19) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -7.4e-94) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 8.2e-88) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 4e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.55e+66) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((t - x) / a))
    if (a <= (-2d+85)) then
        tmp = t_1
    else if (a <= (-9d+73)) then
        tmp = t + ((x / z) * (y - a))
    else if (a <= (-1.9d+29)) then
        tmp = t_1
    else if (a <= (-6.5d-19)) then
        tmp = t + ((t - x) * (a / z))
    else if (a <= (-7.4d-94)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 8.2d-88) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 4d-15) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 1.55d+66) then
        tmp = t + ((x * (y - a)) / z)
    else
        tmp = x - ((y / a) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2e+85) {
		tmp = t_1;
	} else if (a <= -9e+73) {
		tmp = t + ((x / z) * (y - a));
	} else if (a <= -1.9e+29) {
		tmp = t_1;
	} else if (a <= -6.5e-19) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -7.4e-94) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 8.2e-88) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 4e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.55e+66) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2e+85:
		tmp = t_1
	elif a <= -9e+73:
		tmp = t + ((x / z) * (y - a))
	elif a <= -1.9e+29:
		tmp = t_1
	elif a <= -6.5e-19:
		tmp = t + ((t - x) * (a / z))
	elif a <= -7.4e-94:
		tmp = y * ((t - x) / (a - z))
	elif a <= 8.2e-88:
		tmp = t + ((x - t) / (z / y))
	elif a <= 4e-15:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 1.55e+66:
		tmp = t + ((x * (y - a)) / z)
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2e+85)
		tmp = t_1;
	elseif (a <= -9e+73)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (a <= -1.9e+29)
		tmp = t_1;
	elseif (a <= -6.5e-19)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(a / z)));
	elseif (a <= -7.4e-94)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 8.2e-88)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 4e-15)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 1.55e+66)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2e+85)
		tmp = t_1;
	elseif (a <= -9e+73)
		tmp = t + ((x / z) * (y - a));
	elseif (a <= -1.9e+29)
		tmp = t_1;
	elseif (a <= -6.5e-19)
		tmp = t + ((t - x) * (a / z));
	elseif (a <= -7.4e-94)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 8.2e-88)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 4e-15)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 1.55e+66)
		tmp = t + ((x * (y - a)) / z);
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+85], t$95$1, If[LessEqual[a, -9e+73], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e+29], t$95$1, If[LessEqual[a, -6.5e-19], N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.4e-94], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-88], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-15], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+66], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -2e85 or -8.99999999999999969e73 < a < -1.89999999999999985e29

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 62.4%

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

      1. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   if -2e85 < a < -8.99999999999999969e73

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. associate--l+ 56.0%

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

      2. distribute-lft-out-- 56.0%

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

      3. div-sub 56.0%

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

      4. mul-1-neg 56.0%

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

      5. unsub-neg 56.0%

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

      6. distribute-rgt-out-- 56.0%

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

      7. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

      1. clear-num 77.5%

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

      2. un-div-inv 77.7%

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

   7. Applied egg-rr 77.7%

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

   8. Taylor expanded in t around 0 58.0%

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

      1. mul-1-neg 58.0%

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

      2. associate-*l/ 68.7%

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

      3. distribute-rgt-neg-in 68.7%

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

   10. Simplified 68.7%

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

   if -1.89999999999999985e29 < a < -6.5000000000000001e-19

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 67.9%

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

      7. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around 0 67.8%

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

      1. neg-mul-1 67.8%

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

      2. distribute-neg-frac 67.8%

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

   8. Simplified 67.8%

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

   if -6.5000000000000001e-19 < a < -7.3999999999999996e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. div-sub 93.8%

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

   5. Simplified 93.8%

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

   if -7.3999999999999996e-94 < a < 8.2000000000000002e-88

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. distribute-rgt-out-- 82.2%

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

      7. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

      1. clear-num 84.7%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in y around inf 81.5%

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

   if 8.2000000000000002e-88 < a < 4.0000000000000003e-15

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 87.0%

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

   if 4.0000000000000003e-15 < a < 1.55000000000000009e66

   1. Initial program 54.9%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. distribute-lft-out-- 66.9%

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

      3. div-sub 66.9%

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

      4. mul-1-neg 66.9%

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

      5. unsub-neg 66.9%

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

      6. distribute-rgt-out-- 66.9%

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

      7. associate-/l* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in t around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-lft-neg-out 66.9%

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

   8. Simplified 66.9%

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

   if 1.55000000000000009e66 < a

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. remove-double-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

      5. associate-*l/ 67.0%

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

      6. associate-/l* 97.3%

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

      7. fma-neg 97.3%

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

      8. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

      1. fma-undefine 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around 0 74.7%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 8 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+85}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+73}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-88}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-18}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-90}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) a))))
   (if (<= a -2.05e+83)
     t_1
     (if (<= a -7.6e+73)
       (+ t (* (/ x z) (- y a)))
       (if (<= a -8.5e+27)
         t_1
         (if (<= a -1.35e-18)
           (+ t (* (- t x) (/ a z)))
           (if (<= a -4.5e-94)
             (* y (/ (- t x) (- a z)))
             (if (<= a 5.6e-90)
               (+ t (/ (- x t) (/ z y)))
               (if (<= a 2.2e-15)
                 (+ x (/ (* y (- t x)) a))
                 (if (<= a 8.2e+65)
                   (+ t (/ (* x (- y a)) z))
                   (- x (* (/ y a) (- x t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / a);
	double tmp;
	if (a <= -2.05e+83) {
		tmp = t_1;
	} else if (a <= -7.6e+73) {
		tmp = t + ((x / z) * (y - a));
	} else if (a <= -8.5e+27) {
		tmp = t_1;
	} else if (a <= -1.35e-18) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -4.5e-94) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.6e-90) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 2.2e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8.2e+65) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / a)
    if (a <= (-2.05d+83)) then
        tmp = t_1
    else if (a <= (-7.6d+73)) then
        tmp = t + ((x / z) * (y - a))
    else if (a <= (-8.5d+27)) then
        tmp = t_1
    else if (a <= (-1.35d-18)) then
        tmp = t + ((t - x) * (a / z))
    else if (a <= (-4.5d-94)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.6d-90) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 2.2d-15) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 8.2d+65) then
        tmp = t + ((x * (y - a)) / z)
    else
        tmp = x - ((y / a) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / a);
	double tmp;
	if (a <= -2.05e+83) {
		tmp = t_1;
	} else if (a <= -7.6e+73) {
		tmp = t + ((x / z) * (y - a));
	} else if (a <= -8.5e+27) {
		tmp = t_1;
	} else if (a <= -1.35e-18) {
		tmp = t + ((t - x) * (a / z));
	} else if (a <= -4.5e-94) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.6e-90) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 2.2e-15) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8.2e+65) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / a)
	tmp = 0
	if a <= -2.05e+83:
		tmp = t_1
	elif a <= -7.6e+73:
		tmp = t + ((x / z) * (y - a))
	elif a <= -8.5e+27:
		tmp = t_1
	elif a <= -1.35e-18:
		tmp = t + ((t - x) * (a / z))
	elif a <= -4.5e-94:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.6e-90:
		tmp = t + ((x - t) / (z / y))
	elif a <= 2.2e-15:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 8.2e+65:
		tmp = t + ((x * (y - a)) / z)
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / a))
	tmp = 0.0
	if (a <= -2.05e+83)
		tmp = t_1;
	elseif (a <= -7.6e+73)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (a <= -8.5e+27)
		tmp = t_1;
	elseif (a <= -1.35e-18)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(a / z)));
	elseif (a <= -4.5e-94)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.6e-90)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 2.2e-15)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 8.2e+65)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / a);
	tmp = 0.0;
	if (a <= -2.05e+83)
		tmp = t_1;
	elseif (a <= -7.6e+73)
		tmp = t + ((x / z) * (y - a));
	elseif (a <= -8.5e+27)
		tmp = t_1;
	elseif (a <= -1.35e-18)
		tmp = t + ((t - x) * (a / z));
	elseif (a <= -4.5e-94)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.6e-90)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 2.2e-15)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 8.2e+65)
		tmp = t + ((x * (y - a)) / z);
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e+83], t$95$1, If[LessEqual[a, -7.6e+73], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e+27], t$95$1, If[LessEqual[a, -1.35e-18], N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.5e-94], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-90], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-15], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+65], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -2.05e83 or -7.60000000000000044e73 < a < -8.5e27

   1. Initial program 92.5%

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

   3. Taylor expanded in a around inf 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   if -2.05e83 < a < -7.60000000000000044e73

   1. Initial program 58.1%

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

   3. Taylor expanded in z around inf 57.7%

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

      1. associate--l+ 57.7%

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

      2. distribute-lft-out-- 57.7%

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

      3. div-sub 57.7%

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

      4. mul-1-neg 57.7%

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

      5. unsub-neg 57.7%

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

      6. distribute-rgt-out-- 57.7%

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

      7. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.5%

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

   7. Applied egg-rr 85.5%

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

   8. Taylor expanded in t around 0 59.6%

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

      1. mul-1-neg 59.6%

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

      2. associate-*l/ 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

   10. Simplified 73.4%

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

   if -8.5e27 < a < -1.34999999999999994e-18

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 67.9%

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

      7. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around 0 67.8%

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

      1. neg-mul-1 67.8%

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

      2. distribute-neg-frac 67.8%

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

   8. Simplified 67.8%

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

   if -1.34999999999999994e-18 < a < -4.5000000000000002e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. div-sub 93.8%

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

   5. Simplified 93.8%

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

   if -4.5000000000000002e-94 < a < 5.5999999999999998e-90

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. distribute-rgt-out-- 82.2%

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

      7. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

      1. clear-num 84.7%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in y around inf 81.5%

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

   if 5.5999999999999998e-90 < a < 2.19999999999999986e-15

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 87.0%

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

   if 2.19999999999999986e-15 < a < 8.2000000000000003e65

   1. Initial program 54.9%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. distribute-lft-out-- 66.9%

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

      3. div-sub 66.9%

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

      4. mul-1-neg 66.9%

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

      5. unsub-neg 66.9%

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

      6. distribute-rgt-out-- 66.9%

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

      7. associate-/l* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in t around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-lft-neg-out 66.9%

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

   8. Simplified 66.9%

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

   if 8.2000000000000003e65 < a

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. remove-double-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

      5. associate-*l/ 67.0%

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

      6. associate-/l* 97.3%

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

      7. fma-neg 97.3%

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

      8. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

      1. fma-undefine 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around 0 74.7%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 8 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-18}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-90}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.75e+226)
     x
     (if (<= a -1e+198)
       (/ (- y z) (/ a t))
       (if (<= a -1.35e+87)
         x
         (if (<= a -8.6e-144)
           t_2
           (if (<= a 1.85e-298)
             t_1
             (if (<= a 4.9e-235)
               t_2
               (if (<= a 1.25e-87)
                 t_1
                 (if (<= a 4.5e+153) (* t (/ (- y z) a)) x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.75e+226) {
		tmp = x;
	} else if (a <= -1e+198) {
		tmp = (y - z) / (a / t);
	} else if (a <= -1.35e+87) {
		tmp = x;
	} else if (a <= -8.6e-144) {
		tmp = t_2;
	} else if (a <= 1.85e-298) {
		tmp = t_1;
	} else if (a <= 4.9e-235) {
		tmp = t_2;
	} else if (a <= 1.25e-87) {
		tmp = t_1;
	} else if (a <= 4.5e+153) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-1.75d+226)) then
        tmp = x
    else if (a <= (-1d+198)) then
        tmp = (y - z) / (a / t)
    else if (a <= (-1.35d+87)) then
        tmp = x
    else if (a <= (-8.6d-144)) then
        tmp = t_2
    else if (a <= 1.85d-298) then
        tmp = t_1
    else if (a <= 4.9d-235) then
        tmp = t_2
    else if (a <= 1.25d-87) then
        tmp = t_1
    else if (a <= 4.5d+153) then
        tmp = t * ((y - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.75e+226) {
		tmp = x;
	} else if (a <= -1e+198) {
		tmp = (y - z) / (a / t);
	} else if (a <= -1.35e+87) {
		tmp = x;
	} else if (a <= -8.6e-144) {
		tmp = t_2;
	} else if (a <= 1.85e-298) {
		tmp = t_1;
	} else if (a <= 4.9e-235) {
		tmp = t_2;
	} else if (a <= 1.25e-87) {
		tmp = t_1;
	} else if (a <= 4.5e+153) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.75e+226:
		tmp = x
	elif a <= -1e+198:
		tmp = (y - z) / (a / t)
	elif a <= -1.35e+87:
		tmp = x
	elif a <= -8.6e-144:
		tmp = t_2
	elif a <= 1.85e-298:
		tmp = t_1
	elif a <= 4.9e-235:
		tmp = t_2
	elif a <= 1.25e-87:
		tmp = t_1
	elif a <= 4.5e+153:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.75e+226)
		tmp = x;
	elseif (a <= -1e+198)
		tmp = Float64(Float64(y - z) / Float64(a / t));
	elseif (a <= -1.35e+87)
		tmp = x;
	elseif (a <= -8.6e-144)
		tmp = t_2;
	elseif (a <= 1.85e-298)
		tmp = t_1;
	elseif (a <= 4.9e-235)
		tmp = t_2;
	elseif (a <= 1.25e-87)
		tmp = t_1;
	elseif (a <= 4.5e+153)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.75e+226)
		tmp = x;
	elseif (a <= -1e+198)
		tmp = (y - z) / (a / t);
	elseif (a <= -1.35e+87)
		tmp = x;
	elseif (a <= -8.6e-144)
		tmp = t_2;
	elseif (a <= 1.85e-298)
		tmp = t_1;
	elseif (a <= 4.9e-235)
		tmp = t_2;
	elseif (a <= 1.25e-87)
		tmp = t_1;
	elseif (a <= 4.5e+153)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+226], x, If[LessEqual[a, -1e+198], N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e+87], x, If[LessEqual[a, -8.6e-144], t$95$2, If[LessEqual[a, 1.85e-298], t$95$1, If[LessEqual[a, 4.9e-235], t$95$2, If[LessEqual[a, 1.25e-87], t$95$1, If[LessEqual[a, 4.5e+153], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.7499999999999999e226 or -1.00000000000000002e198 < a < -1.35000000000000003e87 or 4.5000000000000001e153 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 56.2%

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

   if -1.7499999999999999e226 < a < -1.00000000000000002e198

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in a around inf 75.6%

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

      1. clear-num 75.8%

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

      2. un-div-inv 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -1.35000000000000003e87 < a < -8.5999999999999998e-144 or 1.8499999999999999e-298 < a < 4.89999999999999965e-235

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-/l* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in a around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. associate-/l* 49.4%

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

      3. distribute-lft-neg-in 49.4%

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

      4. div-sub 49.4%

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

      5. *-inverses 49.4%

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

   8. Simplified 49.4%

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

   if -8.5999999999999998e-144 < a < 1.8499999999999999e-298 or 4.89999999999999965e-235 < a < 1.25000000000000011e-87

   1. Initial program 65.7%

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

   3. Taylor expanded in y around -inf 66.0%

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

   4. Taylor expanded in a around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-/l* 61.7%

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

      3. div-sub 61.7%

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

      4. distribute-rgt-neg-in 61.7%

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

      5. div-sub 61.7%

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

   6. Simplified 61.7%

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

   if 1.25000000000000011e-87 < a < 4.5000000000000001e153

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-256} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-256) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ x z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-256) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / z) * (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) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-256)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x / z) * (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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-256) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-256) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-256) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-256) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-256], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $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)))) < -1.99999999999999995e-256 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.1%

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

   if -1.99999999999999995e-256 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. distribute-lft-out-- 84.5%

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

      3. div-sub 84.5%

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

      4. mul-1-neg 84.5%

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

      5. unsub-neg 84.5%

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

      6. distribute-rgt-out-- 84.5%

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

      7. associate-/l* 89.9%

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

   5. Simplified 89.9%

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

      1. clear-num 87.2%

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

      2. un-div-inv 87.4%

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

   7. Applied egg-rr 87.4%

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

   8. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-*l/ 97.3%

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

      3. distribute-rgt-neg-in 97.3%

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

   10. Simplified 97.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-256} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-256)
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (if (<= t_1 0.0) (+ t (* (/ x z) (- y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-256) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - 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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-256)) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x / z) * (y - 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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-256) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-256:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	elif t_1 <= 0.0:
		tmp = t + ((x / z) * (y - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-256)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2e-256)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	elseif (t_1 <= 0.0)
		tmp = t + ((x / z) * (y - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-256], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999995e-256

   1. Initial program 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 93.7%

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

   4. Applied egg-rr 93.7%

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

   if -1.99999999999999995e-256 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. distribute-lft-out-- 84.5%

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

      3. div-sub 84.5%

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

      4. mul-1-neg 84.5%

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

      5. unsub-neg 84.5%

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

      6. distribute-rgt-out-- 84.5%

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

      7. associate-/l* 89.9%

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

   5. Simplified 89.9%

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

      1. clear-num 87.2%

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

      2. un-div-inv 87.4%

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

   7. Applied egg-rr 87.4%

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

   8. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-*l/ 97.3%

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

      3. distribute-rgt-neg-in 97.3%

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

   10. Simplified 97.3%

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

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

   1. Initial program 93.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-280}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-280)
     (- x (* (- t x) (/ (- y z) (- z a))))
     (if (<= t_1 0.0) (+ t (* (/ x z) (- y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-280) {
		tmp = x - ((t - x) * ((y - z) / (z - a)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - 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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-280)) then
        tmp = x - ((t - x) * ((y - z) / (z - a)))
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x / z) * (y - 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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-280) {
		tmp = x - ((t - x) * ((y - z) / (z - a)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-280:
		tmp = x - ((t - x) * ((y - z) / (z - a)))
	elif t_1 <= 0.0:
		tmp = t + ((x / z) * (y - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-280)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(z - a))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-280)
		tmp = x - ((t - x) * ((y - z) / (z - a)));
	elseif (t_1 <= 0.0)
		tmp = t + ((x / z) * (y - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-280], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000028e-280

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. remove-double-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

      5. associate-*l/ 79.5%

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

      6. associate-/l* 94.9%

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

      7. fma-neg 94.9%

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

      8. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

      1. fma-undefine 94.9%

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

   6. Applied egg-rr 94.9%

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

   if -5.00000000000000028e-280 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. associate--l+ 86.4%

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

      2. distribute-lft-out-- 86.4%

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

      3. div-sub 86.4%

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

      4. mul-1-neg 86.4%

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

      5. unsub-neg 86.4%

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

      6. distribute-rgt-out-- 86.4%

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

      7. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

      1. clear-num 89.2%

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

      2. un-div-inv 89.3%

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

   7. Applied egg-rr 89.3%

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

   8. Taylor expanded in t around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. associate-*l/ 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

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

   1. Initial program 93.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-280}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-298}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z))))
        (t_2 (+ x (* y (/ (- t x) a))))
        (t_3 (* y (/ (- t x) (- a z)))))
   (if (<= a -2.1e+84)
     t_2
     (if (<= a -7.5e-19)
       t_1
       (if (<= a -5.2e-92)
         t_3
         (if (<= a -9.2e-144)
           t_1
           (if (<= a 3e-298)
             t_3
             (if (<= a 2.5e-280)
               (* t (- 1.0 (/ y z)))
               (if (<= a 7.5e-9) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double t_3 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.1e+84) {
		tmp = t_2;
	} else if (a <= -7.5e-19) {
		tmp = t_1;
	} else if (a <= -5.2e-92) {
		tmp = t_3;
	} else if (a <= -9.2e-144) {
		tmp = t_1;
	} else if (a <= 3e-298) {
		tmp = t_3;
	} else if (a <= 2.5e-280) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 7.5e-9) {
		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) * (t / (a - z))
    t_2 = x + (y * ((t - x) / a))
    t_3 = y * ((t - x) / (a - z))
    if (a <= (-2.1d+84)) then
        tmp = t_2
    else if (a <= (-7.5d-19)) then
        tmp = t_1
    else if (a <= (-5.2d-92)) then
        tmp = t_3
    else if (a <= (-9.2d-144)) then
        tmp = t_1
    else if (a <= 3d-298) then
        tmp = t_3
    else if (a <= 2.5d-280) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 7.5d-9) 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) * (t / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double t_3 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.1e+84) {
		tmp = t_2;
	} else if (a <= -7.5e-19) {
		tmp = t_1;
	} else if (a <= -5.2e-92) {
		tmp = t_3;
	} else if (a <= -9.2e-144) {
		tmp = t_1;
	} else if (a <= 3e-298) {
		tmp = t_3;
	} else if (a <= 2.5e-280) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 7.5e-9) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = x + (y * ((t - x) / a))
	t_3 = y * ((t - x) / (a - z))
	tmp = 0
	if a <= -2.1e+84:
		tmp = t_2
	elif a <= -7.5e-19:
		tmp = t_1
	elif a <= -5.2e-92:
		tmp = t_3
	elif a <= -9.2e-144:
		tmp = t_1
	elif a <= 3e-298:
		tmp = t_3
	elif a <= 2.5e-280:
		tmp = t * (1.0 - (y / z))
	elif a <= 7.5e-9:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	t_3 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.1e+84)
		tmp = t_2;
	elseif (a <= -7.5e-19)
		tmp = t_1;
	elseif (a <= -5.2e-92)
		tmp = t_3;
	elseif (a <= -9.2e-144)
		tmp = t_1;
	elseif (a <= 3e-298)
		tmp = t_3;
	elseif (a <= 2.5e-280)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 7.5e-9)
		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) * (t / (a - z));
	t_2 = x + (y * ((t - x) / a));
	t_3 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (a <= -2.1e+84)
		tmp = t_2;
	elseif (a <= -7.5e-19)
		tmp = t_1;
	elseif (a <= -5.2e-92)
		tmp = t_3;
	elseif (a <= -9.2e-144)
		tmp = t_1;
	elseif (a <= 3e-298)
		tmp = t_3;
	elseif (a <= 2.5e-280)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 7.5e-9)
		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[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+84], t$95$2, If[LessEqual[a, -7.5e-19], t$95$1, If[LessEqual[a, -5.2e-92], t$95$3, If[LessEqual[a, -9.2e-144], t$95$1, If[LessEqual[a, 3e-298], t$95$3, If[LessEqual[a, 2.5e-280], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-9], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.10000000000000019e84 or 7.49999999999999933e-9 < a

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 56.7%

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

      1. associate-/l* 67.5%

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

   5. Simplified 67.5%

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

   if -2.10000000000000019e84 < a < -7.49999999999999957e-19 or -5.2e-92 < a < -9.2e-144

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   if -7.49999999999999957e-19 < a < -5.2e-92 or -9.2e-144 < a < 2.9999999999999999e-298 or 2.50000000000000014e-280 < a < 7.49999999999999933e-9

   1. Initial program 71.9%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. div-sub 72.2%

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

   5. Simplified 72.2%

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

   if 2.9999999999999999e-298 < a < 2.50000000000000014e-280

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around 0 73.5%

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

      1. mul-1-neg 73.5%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. div-sub 100.0%

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

      5. *-inverses 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-295}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= a -2.1e+84)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -1.75e-18)
       t_1
       (if (<= a -3.4e-91)
         t_2
         (if (<= a -4.5e-142)
           t_1
           (if (<= a 3e-295)
             t_2
             (if (<= a 7e-280)
               (* t (- 1.0 (/ y z)))
               (if (<= a 5e-91) t_2 (- x (* (/ y a) (- x t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.1e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.75e-18) {
		tmp = t_1;
	} else if (a <= -3.4e-91) {
		tmp = t_2;
	} else if (a <= -4.5e-142) {
		tmp = t_1;
	} else if (a <= 3e-295) {
		tmp = t_2;
	} else if (a <= 7e-280) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5e-91) {
		tmp = t_2;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    t_2 = y * ((t - x) / (a - z))
    if (a <= (-2.1d+84)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-1.75d-18)) then
        tmp = t_1
    else if (a <= (-3.4d-91)) then
        tmp = t_2
    else if (a <= (-4.5d-142)) then
        tmp = t_1
    else if (a <= 3d-295) then
        tmp = t_2
    else if (a <= 7d-280) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 5d-91) then
        tmp = t_2
    else
        tmp = x - ((y / a) * (x - 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 = (y - z) * (t / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.1e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.75e-18) {
		tmp = t_1;
	} else if (a <= -3.4e-91) {
		tmp = t_2;
	} else if (a <= -4.5e-142) {
		tmp = t_1;
	} else if (a <= 3e-295) {
		tmp = t_2;
	} else if (a <= 7e-280) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5e-91) {
		tmp = t_2;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if a <= -2.1e+84:
		tmp = x + (y * ((t - x) / a))
	elif a <= -1.75e-18:
		tmp = t_1
	elif a <= -3.4e-91:
		tmp = t_2
	elif a <= -4.5e-142:
		tmp = t_1
	elif a <= 3e-295:
		tmp = t_2
	elif a <= 7e-280:
		tmp = t * (1.0 - (y / z))
	elif a <= 5e-91:
		tmp = t_2
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.1e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -1.75e-18)
		tmp = t_1;
	elseif (a <= -3.4e-91)
		tmp = t_2;
	elseif (a <= -4.5e-142)
		tmp = t_1;
	elseif (a <= 3e-295)
		tmp = t_2;
	elseif (a <= 7e-280)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 5e-91)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (a <= -2.1e+84)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -1.75e-18)
		tmp = t_1;
	elseif (a <= -3.4e-91)
		tmp = t_2;
	elseif (a <= -4.5e-142)
		tmp = t_1;
	elseif (a <= 3e-295)
		tmp = t_2;
	elseif (a <= 7e-280)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 5e-91)
		tmp = t_2;
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+84], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.75e-18], t$95$1, If[LessEqual[a, -3.4e-91], t$95$2, If[LessEqual[a, -4.5e-142], t$95$1, If[LessEqual[a, 3e-295], t$95$2, If[LessEqual[a, 7e-280], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-91], t$95$2, N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.10000000000000019e84

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -2.10000000000000019e84 < a < -1.7499999999999999e-18 or -3.40000000000000027e-91 < a < -4.50000000000000019e-142

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   if -1.7499999999999999e-18 < a < -3.40000000000000027e-91 or -4.50000000000000019e-142 < a < 2.99999999999999996e-295 or 7.0000000000000002e-280 < a < 4.99999999999999997e-91

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. div-sub 71.4%

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

   5. Simplified 71.4%

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

   if 2.99999999999999996e-295 < a < 7.0000000000000002e-280

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around 0 73.5%

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

      1. mul-1-neg 73.5%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. div-sub 100.0%

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

      5. *-inverses 100.0%

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

   8. Simplified 100.0%

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

   if 4.99999999999999997e-91 < a

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. remove-double-neg 84.7%

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

      3. unsub-neg 84.7%

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

      4. *-commutative 84.7%

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

      5. associate-*l/ 69.9%

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

      6. associate-/l* 89.1%

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

      7. fma-neg 89.1%

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

      8. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

      1. fma-undefine 89.1%

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

   6. Applied egg-rr 89.1%

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

   7. Taylor expanded in z around 0 68.0%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-18}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-19}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 0.105:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ a z)))))
   (if (<= a -2.3e+84)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -3e-19)
       (/ (- y z) (/ (- a z) t))
       (if (<= a -3.15e-99)
         (* y (/ (- t x) (- a z)))
         (if (<= a -1.65e-118)
           t_1
           (if (<= a 1.3e-87)
             (+ t (/ (- x t) (/ z y)))
             (if (<= a 0.105)
               (+ x (/ (* y (- t x)) a))
               (if (<= a 4e+56) t_1 (- x (* (/ y a) (- x t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (a <= -2.3e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3e-19) {
		tmp = (y - z) / ((a - z) / t);
	} else if (a <= -3.15e-99) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.65e-118) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 0.105) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 4e+56) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * (a / z))
    if (a <= (-2.3d+84)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-3d-19)) then
        tmp = (y - z) / ((a - z) / t)
    else if (a <= (-3.15d-99)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-1.65d-118)) then
        tmp = t_1
    else if (a <= 1.3d-87) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 0.105d0) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 4d+56) then
        tmp = t_1
    else
        tmp = x - ((y / a) * (x - 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 + ((t - x) * (a / z));
	double tmp;
	if (a <= -2.3e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3e-19) {
		tmp = (y - z) / ((a - z) / t);
	} else if (a <= -3.15e-99) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.65e-118) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 0.105) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 4e+56) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * (a / z))
	tmp = 0
	if a <= -2.3e+84:
		tmp = x + (y * ((t - x) / a))
	elif a <= -3e-19:
		tmp = (y - z) / ((a - z) / t)
	elif a <= -3.15e-99:
		tmp = y * ((t - x) / (a - z))
	elif a <= -1.65e-118:
		tmp = t_1
	elif a <= 1.3e-87:
		tmp = t + ((x - t) / (z / y))
	elif a <= 0.105:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 4e+56:
		tmp = t_1
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(a / z)))
	tmp = 0.0
	if (a <= -2.3e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -3e-19)
		tmp = Float64(Float64(y - z) / Float64(Float64(a - z) / t));
	elseif (a <= -3.15e-99)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -1.65e-118)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 0.105)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 4e+56)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * (a / z));
	tmp = 0.0;
	if (a <= -2.3e+84)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -3e-19)
		tmp = (y - z) / ((a - z) / t);
	elseif (a <= -3.15e-99)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -1.65e-118)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 0.105)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 4e+56)
		tmp = t_1;
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+84], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-19], N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.15e-99], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-118], t$95$1, If[LessEqual[a, 1.3e-87], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.105], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+56], t$95$1, N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.2999999999999999e84

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -2.2999999999999999e84 < a < -2.99999999999999993e-19

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. remove-double-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. *-commutative 69.7%

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

      5. associate-*l/ 50.7%

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

      6. associate-/l* 69.9%

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

      7. fma-neg 69.8%

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

      8. remove-double-neg 69.8%

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

   3. Simplified 69.8%

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

      1. fma-undefine 69.9%

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

   6. Applied egg-rr 69.9%

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

   7. Taylor expanded in t around inf 59.2%

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

      1. div-sub 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-/r/ 55.7%

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

   9. Simplified 55.7%

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

   if -2.99999999999999993e-19 < a < -3.14999999999999996e-99

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. div-sub 93.8%

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

   5. Simplified 93.8%

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

   if -3.14999999999999996e-99 < a < -1.65e-118 or 0.104999999999999996 < a < 4.00000000000000037e56

   1. Initial program 61.3%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. distribute-lft-out-- 66.9%

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

      3. div-sub 66.9%

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

      4. mul-1-neg 66.9%

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

      5. unsub-neg 66.9%

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

      6. distribute-rgt-out-- 66.9%

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

      7. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 74.4%

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

      1. neg-mul-1 74.4%

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

      2. distribute-neg-frac 74.4%

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

   8. Simplified 74.4%

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

   if -1.65e-118 < a < 1.30000000000000001e-87

   1. Initial program 67.6%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. associate--l+ 84.3%

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

      2. distribute-lft-out-- 84.3%

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

      3. div-sub 84.3%

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

      4. mul-1-neg 84.3%

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

      5. unsub-neg 84.3%

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

      6. distribute-rgt-out-- 84.3%

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

      7. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

      1. clear-num 85.7%

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

      2. un-div-inv 86.8%

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

   7. Applied egg-rr 86.8%

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

   8. Taylor expanded in y around inf 83.5%

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

   if 1.30000000000000001e-87 < a < 0.104999999999999996

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 82.7%

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

   if 4.00000000000000037e56 < a

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. remove-double-neg 92.8%

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

      3. unsub-neg 92.8%

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

      4. *-commutative 92.8%

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

      5. associate-*l/ 66.4%

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

      6. associate-/l* 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

      1. fma-undefine 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in z around 0 71.4%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-19}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 0.105:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ t_2 := x - x \cdot \frac{y}{a}\\ t_3 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+195}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z)))
        (t_2 (- x (* x (/ y a))))
        (t_3 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.35e+226)
     x
     (if (<= a -6e+195)
       (/ (- y z) (/ a t))
       (if (<= a -1.95e+84)
         t_2
         (if (<= a -6.8e-144)
           t_3
           (if (<= a 2.2e-297)
             t_1
             (if (<= a 2.4e-249) t_3 (if (<= a 1.32e-69) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = x - (x * (y / a));
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.35e+226) {
		tmp = x;
	} else if (a <= -6e+195) {
		tmp = (y - z) / (a / t);
	} else if (a <= -1.95e+84) {
		tmp = t_2;
	} else if (a <= -6.8e-144) {
		tmp = t_3;
	} else if (a <= 2.2e-297) {
		tmp = t_1;
	} else if (a <= 2.4e-249) {
		tmp = t_3;
	} else if (a <= 1.32e-69) {
		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 = y * ((x - t) / z)
    t_2 = x - (x * (y / a))
    t_3 = t * (1.0d0 - (y / z))
    if (a <= (-2.35d+226)) then
        tmp = x
    else if (a <= (-6d+195)) then
        tmp = (y - z) / (a / t)
    else if (a <= (-1.95d+84)) then
        tmp = t_2
    else if (a <= (-6.8d-144)) then
        tmp = t_3
    else if (a <= 2.2d-297) then
        tmp = t_1
    else if (a <= 2.4d-249) then
        tmp = t_3
    else if (a <= 1.32d-69) 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 = y * ((x - t) / z);
	double t_2 = x - (x * (y / a));
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.35e+226) {
		tmp = x;
	} else if (a <= -6e+195) {
		tmp = (y - z) / (a / t);
	} else if (a <= -1.95e+84) {
		tmp = t_2;
	} else if (a <= -6.8e-144) {
		tmp = t_3;
	} else if (a <= 2.2e-297) {
		tmp = t_1;
	} else if (a <= 2.4e-249) {
		tmp = t_3;
	} else if (a <= 1.32e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	t_2 = x - (x * (y / a))
	t_3 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.35e+226:
		tmp = x
	elif a <= -6e+195:
		tmp = (y - z) / (a / t)
	elif a <= -1.95e+84:
		tmp = t_2
	elif a <= -6.8e-144:
		tmp = t_3
	elif a <= 2.2e-297:
		tmp = t_1
	elif a <= 2.4e-249:
		tmp = t_3
	elif a <= 1.32e-69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	t_3 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -2.35e+226)
		tmp = x;
	elseif (a <= -6e+195)
		tmp = Float64(Float64(y - z) / Float64(a / t));
	elseif (a <= -1.95e+84)
		tmp = t_2;
	elseif (a <= -6.8e-144)
		tmp = t_3;
	elseif (a <= 2.2e-297)
		tmp = t_1;
	elseif (a <= 2.4e-249)
		tmp = t_3;
	elseif (a <= 1.32e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	t_2 = x - (x * (y / a));
	t_3 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.35e+226)
		tmp = x;
	elseif (a <= -6e+195)
		tmp = (y - z) / (a / t);
	elseif (a <= -1.95e+84)
		tmp = t_2;
	elseif (a <= -6.8e-144)
		tmp = t_3;
	elseif (a <= 2.2e-297)
		tmp = t_1;
	elseif (a <= 2.4e-249)
		tmp = t_3;
	elseif (a <= 1.32e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.35e+226], x, If[LessEqual[a, -6e+195], N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e+84], t$95$2, If[LessEqual[a, -6.8e-144], t$95$3, If[LessEqual[a, 2.2e-297], t$95$1, If[LessEqual[a, 2.4e-249], t$95$3, If[LessEqual[a, 1.32e-69], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.34999999999999996e226

   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 73.1%

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

   if -2.34999999999999996e226 < a < -6.0000000000000001e195

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in a around inf 75.6%

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

      1. clear-num 75.8%

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

      2. un-div-inv 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -6.0000000000000001e195 < a < -1.95000000000000008e84 or 1.32000000000000007e-69 < a

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. remove-double-neg 85.6%

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

      3. unsub-neg 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-*l/ 69.8%

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

      6. associate-/l* 88.7%

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

      7. fma-neg 88.7%

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

      8. remove-double-neg 88.7%

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

   3. Simplified 88.7%

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

      1. fma-undefine 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in z around 0 67.2%

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

   8. Taylor expanded in t around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. associate-/l* 49.6%

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

      3. distribute-lft-neg-out 49.6%

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

      4. *-commutative 49.6%

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

   10. Simplified 49.6%

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

   if -1.95000000000000008e84 < a < -6.80000000000000035e-144 or 2.1999999999999998e-297 < a < 2.40000000000000013e-249

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in a around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. associate-/l* 50.1%

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

      3. distribute-lft-neg-in 50.1%

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

      4. div-sub 50.1%

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

      5. *-inverses 50.1%

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

   8. Simplified 50.1%

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

   if -6.80000000000000035e-144 < a < 2.1999999999999998e-297 or 2.40000000000000013e-249 < a < 1.32000000000000007e-69

   1. Initial program 67.2%

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

   3. Taylor expanded in y around -inf 67.5%

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

   4. Taylor expanded in a around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. associate-/l* 60.6%

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

      3. div-sub 60.6%

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

      4. distribute-rgt-neg-in 60.6%

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

      5. div-sub 60.6%

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

   6. Simplified 60.6%

      \[\leadsto \color{blue}{y \cdot \left(-\frac{t - x}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+195}:\\ \;\;\;\;\frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+84}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.04e+37)
   x
   (if (<= a -1.65e-142)
     t
     (if (<= a 2.7e-297)
       (/ (* x y) z)
       (if (<= a 5.2e-242)
         t
         (if (<= a 4.2e-102)
           (* x (/ y z))
           (if (<= a 2e+153) (* t (/ (- y z) a)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.04e+37) {
		tmp = x;
	} else if (a <= -1.65e-142) {
		tmp = t;
	} else if (a <= 2.7e-297) {
		tmp = (x * y) / z;
	} else if (a <= 5.2e-242) {
		tmp = t;
	} else if (a <= 4.2e-102) {
		tmp = x * (y / z);
	} else if (a <= 2e+153) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.04d+37)) then
        tmp = x
    else if (a <= (-1.65d-142)) then
        tmp = t
    else if (a <= 2.7d-297) then
        tmp = (x * y) / z
    else if (a <= 5.2d-242) then
        tmp = t
    else if (a <= 4.2d-102) then
        tmp = x * (y / z)
    else if (a <= 2d+153) then
        tmp = t * ((y - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.04e+37) {
		tmp = x;
	} else if (a <= -1.65e-142) {
		tmp = t;
	} else if (a <= 2.7e-297) {
		tmp = (x * y) / z;
	} else if (a <= 5.2e-242) {
		tmp = t;
	} else if (a <= 4.2e-102) {
		tmp = x * (y / z);
	} else if (a <= 2e+153) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.04e+37:
		tmp = x
	elif a <= -1.65e-142:
		tmp = t
	elif a <= 2.7e-297:
		tmp = (x * y) / z
	elif a <= 5.2e-242:
		tmp = t
	elif a <= 4.2e-102:
		tmp = x * (y / z)
	elif a <= 2e+153:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.04e+37)
		tmp = x;
	elseif (a <= -1.65e-142)
		tmp = t;
	elseif (a <= 2.7e-297)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 5.2e-242)
		tmp = t;
	elseif (a <= 4.2e-102)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2e+153)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.04e+37)
		tmp = x;
	elseif (a <= -1.65e-142)
		tmp = t;
	elseif (a <= 2.7e-297)
		tmp = (x * y) / z;
	elseif (a <= 5.2e-242)
		tmp = t;
	elseif (a <= 4.2e-102)
		tmp = x * (y / z);
	elseif (a <= 2e+153)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.04e+37], x, If[LessEqual[a, -1.65e-142], t, If[LessEqual[a, 2.7e-297], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5.2e-242], t, If[LessEqual[a, 4.2e-102], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+153], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.0400000000000001e37 or 2e153 < a

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 47.2%

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

   if -1.0400000000000001e37 < a < -1.6499999999999998e-142 or 2.7000000000000001e-297 < a < 5.20000000000000034e-242

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 40.8%

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

   if -1.6499999999999998e-142 < a < 2.7000000000000001e-297

   1. Initial program 55.2%

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

   3. Taylor expanded in y around -inf 68.3%

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

   4. Taylor expanded in t around 0 57.6%

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

      1. associate-*r/ 57.6%

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

      2. mul-1-neg 57.6%

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

      3. distribute-rgt-neg-in 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in a around 0 54.1%

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

   if 5.20000000000000034e-242 < a < 4.2e-102

   1. Initial program 73.4%

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

   3. Taylor expanded in y around -inf 64.3%

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

   4. Taylor expanded in t around 0 41.1%

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

      1. associate-*r/ 41.1%

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

      2. mul-1-neg 41.1%

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

      3. distribute-rgt-neg-in 41.1%

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

   6. Simplified 41.1%

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

   7. Taylor expanded in a around 0 39.1%

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

      1. associate-/l* 41.5%

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

   9. Simplified 41.5%

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

   if 4.2e-102 < a < 2e153

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= t -2.6e+97)
     (* (- y z) (/ t a))
     (if (<= t -5.8e+49)
       x
       (if (<= t -1.65e-21)
         t_1
         (if (<= t 1.75e-141)
           (* x (/ y (- z a)))
           (if (<= t 2.5e+51)
             (* y (/ (- x t) z))
             (if (<= t 1.3e+156) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (t <= -2.6e+97) {
		tmp = (y - z) * (t / a);
	} else if (t <= -5.8e+49) {
		tmp = x;
	} else if (t <= -1.65e-21) {
		tmp = t_1;
	} else if (t <= 1.75e-141) {
		tmp = x * (y / (z - a));
	} else if (t <= 2.5e+51) {
		tmp = y * ((x - t) / z);
	} else if (t <= 1.3e+156) {
		tmp = t_1;
	} 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 - z) / a)
    if (t <= (-2.6d+97)) then
        tmp = (y - z) * (t / a)
    else if (t <= (-5.8d+49)) then
        tmp = x
    else if (t <= (-1.65d-21)) then
        tmp = t_1
    else if (t <= 1.75d-141) then
        tmp = x * (y / (z - a))
    else if (t <= 2.5d+51) then
        tmp = y * ((x - t) / z)
    else if (t <= 1.3d+156) then
        tmp = t_1
    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 - z) / a);
	double tmp;
	if (t <= -2.6e+97) {
		tmp = (y - z) * (t / a);
	} else if (t <= -5.8e+49) {
		tmp = x;
	} else if (t <= -1.65e-21) {
		tmp = t_1;
	} else if (t <= 1.75e-141) {
		tmp = x * (y / (z - a));
	} else if (t <= 2.5e+51) {
		tmp = y * ((x - t) / z);
	} else if (t <= 1.3e+156) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if t <= -2.6e+97:
		tmp = (y - z) * (t / a)
	elif t <= -5.8e+49:
		tmp = x
	elif t <= -1.65e-21:
		tmp = t_1
	elif t <= 1.75e-141:
		tmp = x * (y / (z - a))
	elif t <= 2.5e+51:
		tmp = y * ((x - t) / z)
	elif t <= 1.3e+156:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (t <= -2.6e+97)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (t <= -5.8e+49)
		tmp = x;
	elseif (t <= -1.65e-21)
		tmp = t_1;
	elseif (t <= 1.75e-141)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (t <= 2.5e+51)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (t <= 1.3e+156)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (t <= -2.6e+97)
		tmp = (y - z) * (t / a);
	elseif (t <= -5.8e+49)
		tmp = x;
	elseif (t <= -1.65e-21)
		tmp = t_1;
	elseif (t <= 1.75e-141)
		tmp = x * (y / (z - a));
	elseif (t <= 2.5e+51)
		tmp = y * ((x - t) / z);
	elseif (t <= 1.3e+156)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+97], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e+49], x, If[LessEqual[t, -1.65e-21], t$95$1, If[LessEqual[t, 1.75e-141], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+51], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+156], t$95$1, t]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.6e97

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/l* 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in a around inf 54.4%

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

   if -2.6e97 < t < -5.8e49

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 46.8%

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

   if -5.8e49 < t < -1.65000000000000004e-21 or 2.5e51 < t < 1.30000000000000009e156

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/l* 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 45.2%

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

   8. Simplified 45.2%

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

   if -1.65000000000000004e-21 < t < 1.7500000000000001e-141

   1. Initial program 65.7%

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

   3. Taylor expanded in y around -inf 44.5%

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

   4. Taylor expanded in t around 0 37.5%

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

      1. associate-*r/ 37.5%

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

      2. mul-1-neg 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

   6. Simplified 37.5%

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

   7. Taylor expanded in x around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. associate-*r/ 38.6%

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

      3. distribute-rgt-neg-in 38.6%

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

      4. distribute-neg-frac2 38.6%

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

      5. sub-neg 38.6%

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

      6. distribute-neg-in 38.6%

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

      7. remove-double-neg 38.6%

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

   9. Simplified 38.6%

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

   if 1.7500000000000001e-141 < t < 2.5e51

   1. Initial program 82.8%

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

   3. Taylor expanded in y around -inf 57.0%

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

   4. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/l* 59.4%

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

      3. div-sub 59.4%

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

      4. distribute-rgt-neg-in 59.4%

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

      5. div-sub 59.4%

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

   6. Simplified 59.4%

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

   if 1.30000000000000009e156 < t

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 55.9%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -3.8e+108)
     t
     (if (<= z -2.4e+41)
       x
       (if (<= z -6.5e+22)
         t
         (if (<= z -4e-135)
           t_1
           (if (<= z -2.6e-238)
             x
             (if (<= z 2.2e-66) t_1 (if (<= z 4.4e+110) 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 <= -3.8e+108) {
		tmp = t;
	} else if (z <= -2.4e+41) {
		tmp = x;
	} else if (z <= -6.5e+22) {
		tmp = t;
	} else if (z <= -4e-135) {
		tmp = t_1;
	} else if (z <= -2.6e-238) {
		tmp = x;
	} else if (z <= 2.2e-66) {
		tmp = t_1;
	} else if (z <= 4.4e+110) {
		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 <= (-3.8d+108)) then
        tmp = t
    else if (z <= (-2.4d+41)) then
        tmp = x
    else if (z <= (-6.5d+22)) then
        tmp = t
    else if (z <= (-4d-135)) then
        tmp = t_1
    else if (z <= (-2.6d-238)) then
        tmp = x
    else if (z <= 2.2d-66) then
        tmp = t_1
    else if (z <= 4.4d+110) 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 <= -3.8e+108) {
		tmp = t;
	} else if (z <= -2.4e+41) {
		tmp = x;
	} else if (z <= -6.5e+22) {
		tmp = t;
	} else if (z <= -4e-135) {
		tmp = t_1;
	} else if (z <= -2.6e-238) {
		tmp = x;
	} else if (z <= 2.2e-66) {
		tmp = t_1;
	} else if (z <= 4.4e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -3.8e+108:
		tmp = t
	elif z <= -2.4e+41:
		tmp = x
	elif z <= -6.5e+22:
		tmp = t
	elif z <= -4e-135:
		tmp = t_1
	elif z <= -2.6e-238:
		tmp = x
	elif z <= 2.2e-66:
		tmp = t_1
	elif z <= 4.4e+110:
		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 <= -3.8e+108)
		tmp = t;
	elseif (z <= -2.4e+41)
		tmp = x;
	elseif (z <= -6.5e+22)
		tmp = t;
	elseif (z <= -4e-135)
		tmp = t_1;
	elseif (z <= -2.6e-238)
		tmp = x;
	elseif (z <= 2.2e-66)
		tmp = t_1;
	elseif (z <= 4.4e+110)
		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 <= -3.8e+108)
		tmp = t;
	elseif (z <= -2.4e+41)
		tmp = x;
	elseif (z <= -6.5e+22)
		tmp = t;
	elseif (z <= -4e-135)
		tmp = t_1;
	elseif (z <= -2.6e-238)
		tmp = x;
	elseif (z <= 2.2e-66)
		tmp = t_1;
	elseif (z <= 4.4e+110)
		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, -3.8e+108], t, If[LessEqual[z, -2.4e+41], x, If[LessEqual[z, -6.5e+22], t, If[LessEqual[z, -4e-135], t$95$1, If[LessEqual[z, -2.6e-238], x, If[LessEqual[z, 2.2e-66], t$95$1, If[LessEqual[z, 4.4e+110], x, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000008e108 or -2.4000000000000002e41 < z < -6.49999999999999979e22 or 4.39999999999999984e110 < z

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -3.80000000000000008e108 < z < -2.4000000000000002e41 or -4.0000000000000002e-135 < z < -2.6000000000000001e-238 or 2.2000000000000001e-66 < z < 4.39999999999999984e110

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf 43.6%

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

   if -6.49999999999999979e22 < z < -4.0000000000000002e-135 or -2.6000000000000001e-238 < z < 2.2000000000000001e-66

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 38.4%

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

   8. Simplified 38.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -6e+106)
     t
     (if (<= z -1.5e+41)
       x
       (if (<= z -3e+33)
         (* x (/ y z))
         (if (<= z -2.4e-129)
           t_1
           (if (<= z -6.2e-237)
             x
             (if (<= z 3.7e-66) t_1 (if (<= z 5e+110) 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 <= -6e+106) {
		tmp = t;
	} else if (z <= -1.5e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-129) {
		tmp = t_1;
	} else if (z <= -6.2e-237) {
		tmp = x;
	} else if (z <= 3.7e-66) {
		tmp = t_1;
	} else if (z <= 5e+110) {
		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 <= (-6d+106)) then
        tmp = t
    else if (z <= (-1.5d+41)) then
        tmp = x
    else if (z <= (-3d+33)) then
        tmp = x * (y / z)
    else if (z <= (-2.4d-129)) then
        tmp = t_1
    else if (z <= (-6.2d-237)) then
        tmp = x
    else if (z <= 3.7d-66) then
        tmp = t_1
    else if (z <= 5d+110) 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 <= -6e+106) {
		tmp = t;
	} else if (z <= -1.5e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-129) {
		tmp = t_1;
	} else if (z <= -6.2e-237) {
		tmp = x;
	} else if (z <= 3.7e-66) {
		tmp = t_1;
	} else if (z <= 5e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -6e+106:
		tmp = t
	elif z <= -1.5e+41:
		tmp = x
	elif z <= -3e+33:
		tmp = x * (y / z)
	elif z <= -2.4e-129:
		tmp = t_1
	elif z <= -6.2e-237:
		tmp = x
	elif z <= 3.7e-66:
		tmp = t_1
	elif z <= 5e+110:
		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 <= -6e+106)
		tmp = t;
	elseif (z <= -1.5e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.4e-129)
		tmp = t_1;
	elseif (z <= -6.2e-237)
		tmp = x;
	elseif (z <= 3.7e-66)
		tmp = t_1;
	elseif (z <= 5e+110)
		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 <= -6e+106)
		tmp = t;
	elseif (z <= -1.5e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = x * (y / z);
	elseif (z <= -2.4e-129)
		tmp = t_1;
	elseif (z <= -6.2e-237)
		tmp = x;
	elseif (z <= 3.7e-66)
		tmp = t_1;
	elseif (z <= 5e+110)
		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, -6e+106], t, If[LessEqual[z, -1.5e+41], x, If[LessEqual[z, -3e+33], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-129], t$95$1, If[LessEqual[z, -6.2e-237], x, If[LessEqual[z, 3.7e-66], t$95$1, If[LessEqual[z, 5e+110], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e106 or 4.99999999999999978e110 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in z around inf 52.8%

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

   if -6.0000000000000001e106 < z < -1.4999999999999999e41 or -2.39999999999999989e-129 < z < -6.1999999999999997e-237 or 3.7000000000000002e-66 < z < 4.99999999999999978e110

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf 43.6%

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

   if -1.4999999999999999e41 < z < -2.99999999999999984e33

   1. Initial program 74.7%

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

   3. Taylor expanded in y around -inf 76.0%

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

   4. Taylor expanded in t around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

   if -2.99999999999999984e33 < z < -2.39999999999999989e-129 or -6.1999999999999997e-237 < z < 3.7000000000000002e-66

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 47.4%

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

      1. *-commutative 47.4%

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

      2. associate-/l* 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. associate-/l* 37.7%

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

   8. Simplified 37.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -2.5e+106)
     t
     (if (<= z -2.6e+41)
       x
       (if (<= z -2.8e+33)
         (* x (/ y z))
         (if (<= z -4.4e-130)
           t_1
           (if (<= z -1.95e-240)
             x
             (if (<= z 1.9e-61) t_1 (if (<= z 1.15e+117) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= -2.6e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x * (y / z);
	} else if (z <= -4.4e-130) {
		tmp = t_1;
	} else if (z <= -1.95e-240) {
		tmp = x;
	} else if (z <= 1.9e-61) {
		tmp = t_1;
	} else if (z <= 1.15e+117) {
		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 = y * (t / a)
    if (z <= (-2.5d+106)) then
        tmp = t
    else if (z <= (-2.6d+41)) then
        tmp = x
    else if (z <= (-2.8d+33)) then
        tmp = x * (y / z)
    else if (z <= (-4.4d-130)) then
        tmp = t_1
    else if (z <= (-1.95d-240)) then
        tmp = x
    else if (z <= 1.9d-61) then
        tmp = t_1
    else if (z <= 1.15d+117) 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 = y * (t / a);
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= -2.6e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x * (y / z);
	} else if (z <= -4.4e-130) {
		tmp = t_1;
	} else if (z <= -1.95e-240) {
		tmp = x;
	} else if (z <= 1.9e-61) {
		tmp = t_1;
	} else if (z <= 1.15e+117) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -2.5e+106:
		tmp = t
	elif z <= -2.6e+41:
		tmp = x
	elif z <= -2.8e+33:
		tmp = x * (y / z)
	elif z <= -4.4e-130:
		tmp = t_1
	elif z <= -1.95e-240:
		tmp = x
	elif z <= 1.9e-61:
		tmp = t_1
	elif z <= 1.15e+117:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= -2.6e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -4.4e-130)
		tmp = t_1;
	elseif (z <= -1.95e-240)
		tmp = x;
	elseif (z <= 1.9e-61)
		tmp = t_1;
	elseif (z <= 1.15e+117)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= -2.6e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = x * (y / z);
	elseif (z <= -4.4e-130)
		tmp = t_1;
	elseif (z <= -1.95e-240)
		tmp = x;
	elseif (z <= 1.9e-61)
		tmp = t_1;
	elseif (z <= 1.15e+117)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+106], t, If[LessEqual[z, -2.6e+41], x, If[LessEqual[z, -2.8e+33], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-130], t$95$1, If[LessEqual[z, -1.95e-240], x, If[LessEqual[z, 1.9e-61], t$95$1, If[LessEqual[z, 1.15e+117], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4999999999999999e106 or 1.14999999999999994e117 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in z around inf 52.8%

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

   if -2.4999999999999999e106 < z < -2.6000000000000001e41 or -4.3999999999999997e-130 < z < -1.95000000000000007e-240 or 1.8999999999999999e-61 < z < 1.14999999999999994e117

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf 43.6%

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

   if -2.6000000000000001e41 < z < -2.8000000000000001e33

   1. Initial program 74.7%

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

   3. Taylor expanded in y around -inf 76.0%

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

   4. Taylor expanded in t around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

   if -2.8000000000000001e33 < z < -4.3999999999999997e-130 or -1.95000000000000007e-240 < z < 1.8999999999999999e-61

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 47.4%

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

      1. *-commutative 47.4%

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

      2. associate-/l* 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. associate-/l* 37.7%

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

   8. Simplified 37.7%

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

   9. Taylor expanded in t around 0 32.8%

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

       1. *-commutative 32.8%

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

       2. associate-/l* 38.7%

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

   11. Simplified 38.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a t))))
   (if (<= z -2.9e+112)
     t
     (if (<= z -1.7e+41)
       x
       (if (<= z -3e+33)
         (* x (/ y z))
         (if (<= z -6.5e-132)
           t_1
           (if (<= z -2.6e-241)
             x
             (if (<= z 1.3e-65) t_1 (if (<= z 3.1e+110) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / t);
	double tmp;
	if (z <= -2.9e+112) {
		tmp = t;
	} else if (z <= -1.7e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -6.5e-132) {
		tmp = t_1;
	} else if (z <= -2.6e-241) {
		tmp = x;
	} else if (z <= 1.3e-65) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		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 = y / (a / t)
    if (z <= (-2.9d+112)) then
        tmp = t
    else if (z <= (-1.7d+41)) then
        tmp = x
    else if (z <= (-3d+33)) then
        tmp = x * (y / z)
    else if (z <= (-6.5d-132)) then
        tmp = t_1
    else if (z <= (-2.6d-241)) then
        tmp = x
    else if (z <= 1.3d-65) then
        tmp = t_1
    else if (z <= 3.1d+110) 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 = y / (a / t);
	double tmp;
	if (z <= -2.9e+112) {
		tmp = t;
	} else if (z <= -1.7e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -6.5e-132) {
		tmp = t_1;
	} else if (z <= -2.6e-241) {
		tmp = x;
	} else if (z <= 1.3e-65) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / t)
	tmp = 0
	if z <= -2.9e+112:
		tmp = t
	elif z <= -1.7e+41:
		tmp = x
	elif z <= -3e+33:
		tmp = x * (y / z)
	elif z <= -6.5e-132:
		tmp = t_1
	elif z <= -2.6e-241:
		tmp = x
	elif z <= 1.3e-65:
		tmp = t_1
	elif z <= 3.1e+110:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / t))
	tmp = 0.0
	if (z <= -2.9e+112)
		tmp = t;
	elseif (z <= -1.7e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -6.5e-132)
		tmp = t_1;
	elseif (z <= -2.6e-241)
		tmp = x;
	elseif (z <= 1.3e-65)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / t);
	tmp = 0.0;
	if (z <= -2.9e+112)
		tmp = t;
	elseif (z <= -1.7e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = x * (y / z);
	elseif (z <= -6.5e-132)
		tmp = t_1;
	elseif (z <= -2.6e-241)
		tmp = x;
	elseif (z <= 1.3e-65)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+112], t, If[LessEqual[z, -1.7e+41], x, If[LessEqual[z, -3e+33], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-132], t$95$1, If[LessEqual[z, -2.6e-241], x, If[LessEqual[z, 1.3e-65], t$95$1, If[LessEqual[z, 3.1e+110], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9000000000000002e112 or 3.10000000000000017e110 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in z around inf 52.8%

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

   if -2.9000000000000002e112 < z < -1.69999999999999999e41 or -6.49999999999999991e-132 < z < -2.5999999999999999e-241 or 1.30000000000000005e-65 < z < 3.10000000000000017e110

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf 43.6%

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

   if -1.69999999999999999e41 < z < -2.99999999999999984e33

   1. Initial program 74.7%

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

   3. Taylor expanded in y around -inf 76.0%

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

   4. Taylor expanded in t around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

   if -2.99999999999999984e33 < z < -6.49999999999999991e-132 or -2.5999999999999999e-241 < z < 1.30000000000000005e-65

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 47.4%

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

      1. *-commutative 47.4%

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

      2. associate-/l* 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. associate-/l* 37.7%

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

   8. Simplified 37.7%

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

      1. *-commutative 37.7%

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

      2. associate-/r/ 38.7%

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

   10. Applied egg-rr 38.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-132}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= x -4.1e+226)
     x
     (if (<= x -2.3e+92)
       t_1
       (if (<= x -8e-30)
         t
         (if (<= x 3.2e-81)
           (* y (/ t (- a z)))
           (if (<= x 5.8e+68) x (if (<= x 1.08e+178) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (x <= -4.1e+226) {
		tmp = x;
	} else if (x <= -2.3e+92) {
		tmp = t_1;
	} else if (x <= -8e-30) {
		tmp = t;
	} else if (x <= 3.2e-81) {
		tmp = y * (t / (a - z));
	} else if (x <= 5.8e+68) {
		tmp = x;
	} else if (x <= 1.08e+178) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (x <= (-4.1d+226)) then
        tmp = x
    else if (x <= (-2.3d+92)) then
        tmp = t_1
    else if (x <= (-8d-30)) then
        tmp = t
    else if (x <= 3.2d-81) then
        tmp = y * (t / (a - z))
    else if (x <= 5.8d+68) then
        tmp = x
    else if (x <= 1.08d+178) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (x <= -4.1e+226) {
		tmp = x;
	} else if (x <= -2.3e+92) {
		tmp = t_1;
	} else if (x <= -8e-30) {
		tmp = t;
	} else if (x <= 3.2e-81) {
		tmp = y * (t / (a - z));
	} else if (x <= 5.8e+68) {
		tmp = x;
	} else if (x <= 1.08e+178) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if x <= -4.1e+226:
		tmp = x
	elif x <= -2.3e+92:
		tmp = t_1
	elif x <= -8e-30:
		tmp = t
	elif x <= 3.2e-81:
		tmp = y * (t / (a - z))
	elif x <= 5.8e+68:
		tmp = x
	elif x <= 1.08e+178:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (x <= -4.1e+226)
		tmp = x;
	elseif (x <= -2.3e+92)
		tmp = t_1;
	elseif (x <= -8e-30)
		tmp = t;
	elseif (x <= 3.2e-81)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (x <= 5.8e+68)
		tmp = x;
	elseif (x <= 1.08e+178)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (x <= -4.1e+226)
		tmp = x;
	elseif (x <= -2.3e+92)
		tmp = t_1;
	elseif (x <= -8e-30)
		tmp = t;
	elseif (x <= 3.2e-81)
		tmp = y * (t / (a - z));
	elseif (x <= 5.8e+68)
		tmp = x;
	elseif (x <= 1.08e+178)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+226], x, If[LessEqual[x, -2.3e+92], t$95$1, If[LessEqual[x, -8e-30], t, If[LessEqual[x, 3.2e-81], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+68], x, If[LessEqual[x, 1.08e+178], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.09999999999999985e226 or 3.2e-81 < x < 5.80000000000000023e68 or 1.07999999999999996e178 < x

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 40.1%

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

   if -4.09999999999999985e226 < x < -2.29999999999999998e92 or 5.80000000000000023e68 < x < 1.07999999999999996e178

   1. Initial program 79.3%

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

   3. Taylor expanded in y around -inf 49.2%

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

   4. Taylor expanded in t around 0 44.8%

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

      1. associate-*r/ 44.8%

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

      2. mul-1-neg 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   6. Simplified 44.8%

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

   7. Taylor expanded in a around 0 42.4%

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

      1. associate-/l* 49.8%

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

   9. Simplified 49.8%

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

   if -2.29999999999999998e92 < x < -8.000000000000001e-30

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf 40.4%

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

   if -8.000000000000001e-30 < x < 3.2e-81

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. associate-*l/ 46.4%

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

      2. *-commutative 46.4%

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

   8. Simplified 46.4%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= a -2.3e+84)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -4.8e-21)
       t_1
       (if (<= a -2.3e-91)
         (* y (/ (- t x) (- a z)))
         (if (<= a -2.2e-142)
           t_1
           (if (<= a 1.3e-87)
             (- t (/ (* y (- t x)) z))
             (- x (* (/ y a) (- x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -2.3e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -4.8e-21) {
		tmp = t_1;
	} else if (a <= -2.3e-91) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -2.2e-142) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (a <= (-2.3d+84)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-4.8d-21)) then
        tmp = t_1
    else if (a <= (-2.3d-91)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-2.2d-142)) then
        tmp = t_1
    else if (a <= 1.3d-87) then
        tmp = t - ((y * (t - x)) / z)
    else
        tmp = x - ((y / a) * (x - 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 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -2.3e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -4.8e-21) {
		tmp = t_1;
	} else if (a <= -2.3e-91) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -2.2e-142) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -2.3e+84:
		tmp = x + (y * ((t - x) / a))
	elif a <= -4.8e-21:
		tmp = t_1
	elif a <= -2.3e-91:
		tmp = y * ((t - x) / (a - z))
	elif a <= -2.2e-142:
		tmp = t_1
	elif a <= 1.3e-87:
		tmp = t - ((y * (t - x)) / z)
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.3e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -4.8e-21)
		tmp = t_1;
	elseif (a <= -2.3e-91)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -2.2e-142)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -2.3e+84)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -4.8e-21)
		tmp = t_1;
	elseif (a <= -2.3e-91)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -2.2e-142)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = t - ((y * (t - x)) / z);
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+84], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-21], t$95$1, If[LessEqual[a, -2.3e-91], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-142], t$95$1, If[LessEqual[a, 1.3e-87], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.2999999999999999e84

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -2.2999999999999999e84 < a < -4.7999999999999999e-21 or -2.29999999999999996e-91 < a < -2.20000000000000016e-142

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 46.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 64.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 64.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   if -4.7999999999999999e-21 < a < -2.29999999999999996e-91

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 92.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 92.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -2.20000000000000016e-142 < a < 1.30000000000000001e-87

   1. Initial program 66.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 84.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.4%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.4%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 84.4%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 85.9%

         \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y - a}{z}} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]

   6. Taylor expanded in y around inf 78.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   if 1.30000000000000001e-87 < a

   1. Initial program 84.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 84.7%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 84.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 89.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 89.1%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 68.0%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-142}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= a -2.2e+84)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -1.3e-18)
       t_1
       (if (<= a -1.6e-92)
         (* y (/ (- t x) (- a z)))
         (if (<= a -1.5e-118)
           t_1
           (if (<= a 1.3e-87)
             (+ t (/ (- x t) (/ z y)))
             (- x (* (/ y a) (- x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -2.2e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.3e-18) {
		tmp = t_1;
	} else if (a <= -1.6e-92) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.5e-118) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (a <= (-2.2d+84)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-1.3d-18)) then
        tmp = t_1
    else if (a <= (-1.6d-92)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-1.5d-118)) then
        tmp = t_1
    else if (a <= 1.3d-87) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x - ((y / a) * (x - 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 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -2.2e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.3e-18) {
		tmp = t_1;
	} else if (a <= -1.6e-92) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.5e-118) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -2.2e+84:
		tmp = x + (y * ((t - x) / a))
	elif a <= -1.3e-18:
		tmp = t_1
	elif a <= -1.6e-92:
		tmp = y * ((t - x) / (a - z))
	elif a <= -1.5e-118:
		tmp = t_1
	elif a <= 1.3e-87:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.2e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -1.3e-18)
		tmp = t_1;
	elseif (a <= -1.6e-92)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -1.5e-118)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -2.2e+84)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -1.3e-18)
		tmp = t_1;
	elseif (a <= -1.6e-92)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -1.5e-118)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+84], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-18], t$95$1, If[LessEqual[a, -1.6e-92], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-118], t$95$1, If[LessEqual[a, 1.3e-87], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.1999999999999998e84

   1. Initial program 91.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if -2.1999999999999998e84 < a < -1.3e-18 or -1.5999999999999998e-92 < a < -1.50000000000000009e-118

   1. Initial program 74.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.8%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 61.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   if -1.3e-18 < a < -1.5999999999999998e-92

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 92.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 92.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -1.50000000000000009e-118 < a < 1.30000000000000001e-87

   1. Initial program 67.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 84.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 84.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 86.9%

         \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y - a}{z}} \]

   5. Simplified 86.9%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]
   6. Step-by-step derivation

      1. clear-num 85.7%

         \[\leadsto t - \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{z}{y - a}}} \]

      2. un-div-inv 86.8%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Applied egg-rr 86.8%

      \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 83.5%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   if 1.30000000000000001e-87 < a

   1. Initial program 84.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 84.7%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 84.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 89.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 89.1%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 68.0%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-118}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (/ (- a z) t))))
   (if (<= a -2.1e+84)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -1.42e-21)
       t_1
       (if (<= a -1.58e-99)
         (* y (/ (- t x) (- a z)))
         (if (<= a -4.6e-119)
           t_1
           (if (<= a 1.3e-87)
             (+ t (/ (- x t) (/ z y)))
             (- x (* (/ y a) (- x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / ((a - z) / t);
	double tmp;
	if (a <= -2.1e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.42e-21) {
		tmp = t_1;
	} else if (a <= -1.58e-99) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -4.6e-119) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) / ((a - z) / t)
    if (a <= (-2.1d+84)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-1.42d-21)) then
        tmp = t_1
    else if (a <= (-1.58d-99)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-4.6d-119)) then
        tmp = t_1
    else if (a <= 1.3d-87) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x - ((y / a) * (x - 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 = (y - z) / ((a - z) / t);
	double tmp;
	if (a <= -2.1e+84) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.42e-21) {
		tmp = t_1;
	} else if (a <= -1.58e-99) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -4.6e-119) {
		tmp = t_1;
	} else if (a <= 1.3e-87) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / ((a - z) / t)
	tmp = 0
	if a <= -2.1e+84:
		tmp = x + (y * ((t - x) / a))
	elif a <= -1.42e-21:
		tmp = t_1
	elif a <= -1.58e-99:
		tmp = y * ((t - x) / (a - z))
	elif a <= -4.6e-119:
		tmp = t_1
	elif a <= 1.3e-87:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(Float64(a - z) / t))
	tmp = 0.0
	if (a <= -2.1e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -1.42e-21)
		tmp = t_1;
	elseif (a <= -1.58e-99)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -4.6e-119)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / ((a - z) / t);
	tmp = 0.0;
	if (a <= -2.1e+84)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -1.42e-21)
		tmp = t_1;
	elseif (a <= -1.58e-99)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -4.6e-119)
		tmp = t_1;
	elseif (a <= 1.3e-87)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+84], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-21], t$95$1, If[LessEqual[a, -1.58e-99], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-119], t$95$1, If[LessEqual[a, 1.3e-87], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.10000000000000019e84

   1. Initial program 91.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if -2.10000000000000019e84 < a < -1.42e-21 or -1.5800000000000001e-99 < a < -4.59999999999999987e-119

   1. Initial program 72.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 72.8%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 72.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 72.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 52.3%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 73.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 73.0%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 73.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 73.1%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in t around inf 61.9%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   8. Step-by-step derivation

      1. div-sub 61.9%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

      2. *-commutative 61.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

      3. associate-/r/ 59.1%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

   9. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

   if -1.42e-21 < a < -1.5800000000000001e-99

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 93.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 93.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -4.59999999999999987e-119 < a < 1.30000000000000001e-87

   1. Initial program 67.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 84.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 84.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 86.9%

         \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y - a}{z}} \]

   5. Simplified 86.9%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]
   6. Step-by-step derivation

      1. clear-num 85.7%

         \[\leadsto t - \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{z}{y - a}}} \]

      2. un-div-inv 86.8%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Applied egg-rr 86.8%

      \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 83.5%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   if 1.30000000000000001e-87 < a

   1. Initial program 84.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 84.7%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 84.7%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 84.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 89.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 89.1%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 89.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 68.0%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-21}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 33.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z - a}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y (- z a)))))
   (if (<= x -3.6e+225)
     x
     (if (<= x -2.7e-47)
       t_1
       (if (<= x 6.3e-80)
         (* y (/ t (- a z)))
         (if (<= x 1.6e+69) x (if (<= x 1.45e+189) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / (z - a));
	double tmp;
	if (x <= -3.6e+225) {
		tmp = x;
	} else if (x <= -2.7e-47) {
		tmp = t_1;
	} else if (x <= 6.3e-80) {
		tmp = y * (t / (a - z));
	} else if (x <= 1.6e+69) {
		tmp = x;
	} else if (x <= 1.45e+189) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (z - a))
    if (x <= (-3.6d+225)) then
        tmp = x
    else if (x <= (-2.7d-47)) then
        tmp = t_1
    else if (x <= 6.3d-80) then
        tmp = y * (t / (a - z))
    else if (x <= 1.6d+69) then
        tmp = x
    else if (x <= 1.45d+189) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / (z - a));
	double tmp;
	if (x <= -3.6e+225) {
		tmp = x;
	} else if (x <= -2.7e-47) {
		tmp = t_1;
	} else if (x <= 6.3e-80) {
		tmp = y * (t / (a - z));
	} else if (x <= 1.6e+69) {
		tmp = x;
	} else if (x <= 1.45e+189) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / (z - a))
	tmp = 0
	if x <= -3.6e+225:
		tmp = x
	elif x <= -2.7e-47:
		tmp = t_1
	elif x <= 6.3e-80:
		tmp = y * (t / (a - z))
	elif x <= 1.6e+69:
		tmp = x
	elif x <= 1.45e+189:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (x <= -3.6e+225)
		tmp = x;
	elseif (x <= -2.7e-47)
		tmp = t_1;
	elseif (x <= 6.3e-80)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (x <= 1.6e+69)
		tmp = x;
	elseif (x <= 1.45e+189)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / (z - a));
	tmp = 0.0;
	if (x <= -3.6e+225)
		tmp = x;
	elseif (x <= -2.7e-47)
		tmp = t_1;
	elseif (x <= 6.3e-80)
		tmp = y * (t / (a - z));
	elseif (x <= 1.6e+69)
		tmp = x;
	elseif (x <= 1.45e+189)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+225], x, If[LessEqual[x, -2.7e-47], t$95$1, If[LessEqual[x, 6.3e-80], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+69], x, If[LessEqual[x, 1.45e+189], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999998e225 or 6.29999999999999966e-80 < x < 1.59999999999999992e69 or 1.4500000000000001e189 < x

   1. Initial program 65.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{x} \]

   if -3.5999999999999998e225 < x < -2.6999999999999998e-47 or 1.59999999999999992e69 < x < 1.4500000000000001e189

   1. Initial program 79.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 45.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   4. Taylor expanded in t around 0 40.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 40.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{a - z}} \]

      2. mul-1-neg 40.9%

         \[\leadsto \frac{\color{blue}{-x \cdot y}}{a - z} \]

      3. distribute-rgt-neg-in 40.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{a - z} \]

   6. Simplified 40.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{a - z}} \]

   7. Taylor expanded in x around 0 40.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-*r/ 47.3%

         \[\leadsto -\color{blue}{x \cdot \frac{y}{a - z}} \]

      3. distribute-rgt-neg-in 47.3%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y}{a - z}\right)} \]

      4. distribute-neg-frac2 47.3%

         \[\leadsto x \cdot \color{blue}{\frac{y}{-\left(a - z\right)}} \]

      5. sub-neg 47.3%

         \[\leadsto x \cdot \frac{y}{-\color{blue}{\left(a + \left(-z\right)\right)}} \]

      6. distribute-neg-in 47.3%

         \[\leadsto x \cdot \frac{y}{\color{blue}{\left(-a\right) + \left(-\left(-z\right)\right)}} \]

      7. remove-double-neg 47.3%

         \[\leadsto x \cdot \frac{y}{\left(-a\right) + \color{blue}{z}} \]

   9. Simplified 47.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{\left(-a\right) + z}} \]

   if -2.6999999999999998e-47 < x < 6.29999999999999966e-80

   1. Initial program 91.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 66.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 74.1%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   6. Taylor expanded in y around inf 44.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-*l/ 46.7%

         \[\leadsto \color{blue}{\frac{t}{a - z} \cdot y} \]

      2. *-commutative 46.7%

         \[\leadsto \color{blue}{y \cdot \frac{t}{a - z}} \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{y \cdot \frac{t}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -1.65e-59)
     t_1
     (if (<= z 2.95e-128)
       (+ x (/ (* (- y z) (- t x)) a))
       (if (<= z 1.08e-88)
         (* y (/ (- t x) (- a z)))
         (if (<= z 8.6e+49) (- x (* (/ y a) (- x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -1.65e-59) {
		tmp = t_1;
	} else if (z <= 2.95e-128) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 1.08e-88) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.6e+49) {
		tmp = x - ((y / a) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-1.65d-59)) then
        tmp = t_1
    else if (z <= 2.95d-128) then
        tmp = x + (((y - z) * (t - x)) / a)
    else if (z <= 1.08d-88) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 8.6d+49) then
        tmp = x - ((y / a) * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -1.65e-59) {
		tmp = t_1;
	} else if (z <= 2.95e-128) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 1.08e-88) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.6e+49) {
		tmp = x - ((y / a) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -1.65e-59:
		tmp = t_1
	elif z <= 2.95e-128:
		tmp = x + (((y - z) * (t - x)) / a)
	elif z <= 1.08e-88:
		tmp = y * ((t - x) / (a - z))
	elif z <= 8.6e+49:
		tmp = x - ((y / a) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -1.65e-59)
		tmp = t_1;
	elseif (z <= 2.95e-128)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / a));
	elseif (z <= 1.08e-88)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 8.6e+49)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -1.65e-59)
		tmp = t_1;
	elseif (z <= 2.95e-128)
		tmp = x + (((y - z) * (t - x)) / a);
	elseif (z <= 1.08e-88)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 8.6e+49)
		tmp = x - ((y / a) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-59], t$95$1, If[LessEqual[z, 2.95e-128], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-88], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+49], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.64999999999999991e-59 or 8.5999999999999998e49 < z

   1. Initial program 66.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 63.0%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 63.0%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 63.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 63.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 63.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 76.6%

         \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y - a}{z}} \]

   5. Simplified 76.6%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]

   if -1.64999999999999991e-59 < z < 2.95000000000000017e-128

   1. Initial program 94.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 80.4%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right)}}{a} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}} \]

   if 2.95000000000000017e-128 < z < 1.07999999999999995e-88

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 99.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if 1.07999999999999995e-88 < z < 8.5999999999999998e49

   1. Initial program 92.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 92.4%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 92.4%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 92.4%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 92.4%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 78.6%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 90.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 90.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 90.6%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 90.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 59.6%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -2e-59)
     t_1
     (if (<= z 2.2e-127)
       (+ x (/ (* (- y z) (- t x)) a))
       (if (<= z 9.8e-48)
         (* y (/ (- t x) (- a z)))
         (if (<= z 1.5e+50) (+ x (* (/ z (- a z)) (- x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -2e-59) {
		tmp = t_1;
	} else if (z <= 2.2e-127) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 9.8e-48) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.5e+50) {
		tmp = x + ((z / (a - z)) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-2d-59)) then
        tmp = t_1
    else if (z <= 2.2d-127) then
        tmp = x + (((y - z) * (t - x)) / a)
    else if (z <= 9.8d-48) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.5d+50) then
        tmp = x + ((z / (a - z)) * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -2e-59) {
		tmp = t_1;
	} else if (z <= 2.2e-127) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 9.8e-48) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.5e+50) {
		tmp = x + ((z / (a - z)) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -2e-59:
		tmp = t_1
	elif z <= 2.2e-127:
		tmp = x + (((y - z) * (t - x)) / a)
	elif z <= 9.8e-48:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.5e+50:
		tmp = x + ((z / (a - z)) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -2e-59)
		tmp = t_1;
	elseif (z <= 2.2e-127)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / a));
	elseif (z <= 9.8e-48)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.5e+50)
		tmp = Float64(x + Float64(Float64(z / Float64(a - z)) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -2e-59)
		tmp = t_1;
	elseif (z <= 2.2e-127)
		tmp = x + (((y - z) * (t - x)) / a);
	elseif (z <= 9.8e-48)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.5e+50)
		tmp = x + ((z / (a - z)) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-59], t$95$1, If[LessEqual[z, 2.2e-127], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-48], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+50], N[(x + N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0000000000000001e-59 or 1.4999999999999999e50 < z

   1. Initial program 66.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 63.0%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 63.0%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 63.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 63.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 63.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 76.6%

         \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y - a}{z}} \]

   5. Simplified 76.6%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]

   if -2.0000000000000001e-59 < z < 2.2000000000000001e-127

   1. Initial program 94.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 80.4%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right)}}{a} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}} \]

   if 2.2000000000000001e-127 < z < 9.8000000000000005e-48

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 87.5%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 87.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if 9.8000000000000005e-48 < z < 1.4999999999999999e50

   1. Initial program 90.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 56.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 56.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. unsub-neg 56.4%

         \[\leadsto \color{blue}{x - \frac{z \cdot \left(t - x\right)}{a - z}} \]

      3. *-commutative 56.4%

         \[\leadsto x - \frac{\color{blue}{\left(t - x\right) \cdot z}}{a - z} \]

      4. associate-/l* 64.2%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{z}{a - z}} \]

   5. Simplified 64.2%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \frac{z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-59}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-238}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -6.8e+178)
     t_2
     (if (<= z -2.65e-154)
       t_1
       (if (<= z -1.1e-238)
         (- x (* x (/ y a)))
         (if (<= z 2.45e+91) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -6.8e+178) {
		tmp = t_2;
	} else if (z <= -2.65e-154) {
		tmp = t_1;
	} else if (z <= -1.1e-238) {
		tmp = x - (x * (y / a));
	} else if (z <= 2.45e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-6.8d+178)) then
        tmp = t_2
    else if (z <= (-2.65d-154)) then
        tmp = t_1
    else if (z <= (-1.1d-238)) then
        tmp = x - (x * (y / a))
    else if (z <= 2.45d+91) 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 = y * ((t - x) / (a - z));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -6.8e+178) {
		tmp = t_2;
	} else if (z <= -2.65e-154) {
		tmp = t_1;
	} else if (z <= -1.1e-238) {
		tmp = x - (x * (y / a));
	} else if (z <= 2.45e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -6.8e+178:
		tmp = t_2
	elif z <= -2.65e-154:
		tmp = t_1
	elif z <= -1.1e-238:
		tmp = x - (x * (y / a))
	elif z <= 2.45e+91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6.8e+178)
		tmp = t_2;
	elseif (z <= -2.65e-154)
		tmp = t_1;
	elseif (z <= -1.1e-238)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 2.45e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6.8e+178)
		tmp = t_2;
	elseif (z <= -2.65e-154)
		tmp = t_1;
	elseif (z <= -1.1e-238)
		tmp = x - (x * (y / a));
	elseif (z <= 2.45e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+178], t$95$2, If[LessEqual[z, -2.65e-154], t$95$1, If[LessEqual[z, -1.1e-238], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+91], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000005e178 or 2.45000000000000015e91 < z

   1. Initial program 55.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 27.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 27.9%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 53.1%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 53.1%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   6. Taylor expanded in a around 0 25.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.2%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 57.8%

         \[\leadsto -\color{blue}{t \cdot \frac{y - z}{z}} \]

      3. distribute-lft-neg-in 57.8%

         \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 57.8%

         \[\leadsto \left(-t\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. *-inverses 57.8%

         \[\leadsto \left(-t\right) \cdot \left(\frac{y}{z} - \color{blue}{1}\right) \]

   8. Simplified 57.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\frac{y}{z} - 1\right)} \]

   if -6.8000000000000005e178 < z < -2.6500000000000001e-154 or -1.09999999999999996e-238 < z < 2.45000000000000015e91

   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 58.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 58.7%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 58.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -2.6500000000000001e-154 < z < -1.09999999999999996e-238

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 100.0%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 89.1%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.8%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 89.1%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]

   8. Taylor expanded in t around 0 72.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} + x \]
   9. Step-by-step derivation

      1. mul-1-neg 72.5%

         \[\leadsto \color{blue}{\left(-\frac{x \cdot y}{a}\right)} + x \]

      2. associate-/l* 83.3%

         \[\leadsto \left(-\color{blue}{x \cdot \frac{y}{a}}\right) + x \]

      3. distribute-lft-neg-out 83.3%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{y}{a}} + x \]

      4. *-commutative 83.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]

   10. Simplified 83.3%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-238}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -2.46 \cdot 10^{+185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= x -2.46e+185)
     t_2
     (if (<= x -3.5e+89)
       t_1
       (if (<= x 3.6e-68)
         (* (- y z) (/ t (- a z)))
         (if (<= x 1.6e+118) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (x <= -2.46e+185) {
		tmp = t_2;
	} else if (x <= -3.5e+89) {
		tmp = t_1;
	} else if (x <= 3.6e-68) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 1.6e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x - (x * (y / a))
    if (x <= (-2.46d+185)) then
        tmp = t_2
    else if (x <= (-3.5d+89)) then
        tmp = t_1
    else if (x <= 3.6d-68) then
        tmp = (y - z) * (t / (a - z))
    else if (x <= 1.6d+118) 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 = y * ((t - x) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (x <= -2.46e+185) {
		tmp = t_2;
	} else if (x <= -3.5e+89) {
		tmp = t_1;
	} else if (x <= 3.6e-68) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 1.6e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if x <= -2.46e+185:
		tmp = t_2
	elif x <= -3.5e+89:
		tmp = t_1
	elif x <= 3.6e-68:
		tmp = (y - z) * (t / (a - z))
	elif x <= 1.6e+118:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -2.46e+185)
		tmp = t_2;
	elseif (x <= -3.5e+89)
		tmp = t_1;
	elseif (x <= 3.6e-68)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (x <= 1.6e+118)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (x <= -2.46e+185)
		tmp = t_2;
	elseif (x <= -3.5e+89)
		tmp = t_1;
	elseif (x <= 3.6e-68)
		tmp = (y - z) * (t / (a - z));
	elseif (x <= 1.6e+118)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.46e+185], t$95$2, If[LessEqual[x, -3.5e+89], t$95$1, If[LessEqual[x, 3.6e-68], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+118], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4600000000000001e185 or 1.60000000000000008e118 < x

   1. Initial program 60.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 60.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 60.8%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 60.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 60.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 48.0%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 63.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 63.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 63.7%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 63.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 63.7%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 54.9%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]

   8. Taylor expanded in t around 0 45.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} + x \]
   9. Step-by-step derivation

      1. mul-1-neg 45.0%

         \[\leadsto \color{blue}{\left(-\frac{x \cdot y}{a}\right)} + x \]

      2. associate-/l* 53.7%

         \[\leadsto \left(-\color{blue}{x \cdot \frac{y}{a}}\right) + x \]

      3. distribute-lft-neg-out 53.7%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{y}{a}} + x \]

      4. *-commutative 53.7%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]

   10. Simplified 53.7%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]

   if -2.4600000000000001e185 < x < -3.5000000000000001e89 or 3.60000000000000007e-68 < x < 1.60000000000000008e118

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 55.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 55.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -3.5000000000000001e89 < x < 3.60000000000000007e-68

   1. Initial program 89.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 58.4%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 68.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.46 \cdot 10^{+185}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+124}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= x -1.95e+177)
     t_1
     (if (<= x -6.6e+91)
       (* y (/ (- t x) (- a z)))
       (if (<= x 5.1e-67)
         (* (- y z) (/ t (- a z)))
         (if (<= x 6.6e+124) (* (- 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 <= -1.95e+177) {
		tmp = t_1;
	} else if (x <= -6.6e+91) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 5.1e-67) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 6.6e+124) {
		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 <= (-1.95d+177)) then
        tmp = t_1
    else if (x <= (-6.6d+91)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 5.1d-67) then
        tmp = (y - z) * (t / (a - z))
    else if (x <= 6.6d+124) 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 <= -1.95e+177) {
		tmp = t_1;
	} else if (x <= -6.6e+91) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 5.1e-67) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 6.6e+124) {
		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 <= -1.95e+177:
		tmp = t_1
	elif x <= -6.6e+91:
		tmp = y * ((t - x) / (a - z))
	elif x <= 5.1e-67:
		tmp = (y - z) * (t / (a - z))
	elif x <= 6.6e+124:
		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 <= -1.95e+177)
		tmp = t_1;
	elseif (x <= -6.6e+91)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 5.1e-67)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (x <= 6.6e+124)
		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 <= -1.95e+177)
		tmp = t_1;
	elseif (x <= -6.6e+91)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 5.1e-67)
		tmp = (y - z) * (t / (a - z));
	elseif (x <= 6.6e+124)
		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, -1.95e+177], t$95$1, If[LessEqual[x, -6.6e+91], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-67], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.6e+124], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.95e177 or 6.60000000000000029e124 < x

   1. Initial program 60.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 60.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 60.8%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 60.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 60.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 48.0%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 63.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 63.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 63.7%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 63.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 63.7%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in z around 0 54.9%

      \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} + x \]

   8. Taylor expanded in t around 0 45.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} + x \]
   9. Step-by-step derivation

      1. mul-1-neg 45.0%

         \[\leadsto \color{blue}{\left(-\frac{x \cdot y}{a}\right)} + x \]

      2. associate-/l* 53.7%

         \[\leadsto \left(-\color{blue}{x \cdot \frac{y}{a}}\right) + x \]

      3. distribute-lft-neg-out 53.7%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{y}{a}} + x \]

      4. *-commutative 53.7%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]

   10. Simplified 53.7%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-x\right)} + x \]

   if -1.95e177 < x < -6.60000000000000034e91

   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 71.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 71.7%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -6.60000000000000034e91 < x < 5.09999999999999982e-67

   1. Initial program 89.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. *-commutative 58.4%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 68.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   if 5.09999999999999982e-67 < x < 6.60000000000000029e124

   1. Initial program 81.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 81.3%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 81.3%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 81.3%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 81.3%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 65.8%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 82.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 82.6%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 82.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   6. Applied egg-rr 82.6%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z} + x} \]

   7. Taylor expanded in y around inf 48.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   8. Step-by-step derivation

      1. div-sub 48.7%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 44.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. *-commutative 44.3%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot y}}{a - z} \]

      4. associate-*r/ 49.1%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

      5. *-commutative 49.1%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   9. Simplified 49.1%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+177}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+124}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+106) t (if (<= z 3.6e+110) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+106) {
		tmp = t;
	} else if (z <= 3.6e+110) {
		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 <= (-3.4d+106)) then
        tmp = t
    else if (z <= 3.6d+110) 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 <= -3.4e+106) {
		tmp = t;
	} else if (z <= 3.6e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+106:
		tmp = t
	elif z <= 3.6e+110:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+106)
		tmp = t;
	elseif (z <= 3.6e+110)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+106)
		tmp = t;
	elseif (z <= 3.6e+110)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+106], t, If[LessEqual[z, 3.6e+110], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999994e106 or 3.5999999999999997e110 < z

   1. Initial program 58.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 52.8%

      \[\leadsto \color{blue}{t} \]

   if -3.39999999999999994e106 < z < 3.5999999999999997e110

   1. Initial program 88.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 31.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 24.2% 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 79.8%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 22.1%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 22.1%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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)))))