Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 91.0%

Time: 23.8s

Alternatives: 21

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: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-284}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -1e-296)
     t_2
     (if (<= t_2 1e-284)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -1e-296) {
		tmp = t_2;
	} else if (t_2 <= 1e-284) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -1e-296)
		tmp = t_2;
	elseif (t_2 <= 1e-284)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-296], t$95$2, If[LessEqual[t$95$2, 1e-284], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-296

   1. Initial program 89.5%

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

   if -1e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000004e-284

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. distribute-rgt-out-- 85.8%

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

      7. associate-/l* 97.2%

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

   5. Simplified 97.2%

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

   if 1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.4%

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

      1. +-commutative 91.4%

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

      2. fma-def 91.4%

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

   3. Simplified 91.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-296}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-284}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-301}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (* t (/ (- z) (- a z)))))
   (if (<= z -1.75e+114)
     t_2
     (if (<= z -1.6e+59)
       t_1
       (if (<= z -1.85e-44)
         (/ (* t (- z y)) z)
         (if (<= z -4.1e-143)
           t_1
           (if (<= z -4.1e-238)
             (+ x (* t (/ y a)))
             (if (<= z 3.6e-301)
               (- x (/ x (/ a y)))
               (if (<= z 2.05e-57)
                 (+ x (/ (* y t) a))
                 (if (<= z 5.5e+149) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -1.75e+114) {
		tmp = t_2;
	} else if (z <= -1.6e+59) {
		tmp = t_1;
	} else if (z <= -1.85e-44) {
		tmp = (t * (z - y)) / z;
	} else if (z <= -4.1e-143) {
		tmp = t_1;
	} else if (z <= -4.1e-238) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.6e-301) {
		tmp = x - (x / (a / y));
	} else if (z <= 2.05e-57) {
		tmp = x + ((y * t) / a);
	} else if (z <= 5.5e+149) {
		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 = (t - x) * (y / (a - z))
    t_2 = t * (-z / (a - z))
    if (z <= (-1.75d+114)) then
        tmp = t_2
    else if (z <= (-1.6d+59)) then
        tmp = t_1
    else if (z <= (-1.85d-44)) then
        tmp = (t * (z - y)) / z
    else if (z <= (-4.1d-143)) then
        tmp = t_1
    else if (z <= (-4.1d-238)) then
        tmp = x + (t * (y / a))
    else if (z <= 3.6d-301) then
        tmp = x - (x / (a / y))
    else if (z <= 2.05d-57) then
        tmp = x + ((y * t) / a)
    else if (z <= 5.5d+149) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -1.75e+114) {
		tmp = t_2;
	} else if (z <= -1.6e+59) {
		tmp = t_1;
	} else if (z <= -1.85e-44) {
		tmp = (t * (z - y)) / z;
	} else if (z <= -4.1e-143) {
		tmp = t_1;
	} else if (z <= -4.1e-238) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.6e-301) {
		tmp = x - (x / (a / y));
	} else if (z <= 2.05e-57) {
		tmp = x + ((y * t) / a);
	} else if (z <= 5.5e+149) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * (-z / (a - z))
	tmp = 0
	if z <= -1.75e+114:
		tmp = t_2
	elif z <= -1.6e+59:
		tmp = t_1
	elif z <= -1.85e-44:
		tmp = (t * (z - y)) / z
	elif z <= -4.1e-143:
		tmp = t_1
	elif z <= -4.1e-238:
		tmp = x + (t * (y / a))
	elif z <= 3.6e-301:
		tmp = x - (x / (a / y))
	elif z <= 2.05e-57:
		tmp = x + ((y * t) / a)
	elif z <= 5.5e+149:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.75e+114)
		tmp = t_2;
	elseif (z <= -1.6e+59)
		tmp = t_1;
	elseif (z <= -1.85e-44)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (z <= -4.1e-143)
		tmp = t_1;
	elseif (z <= -4.1e-238)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.6e-301)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 2.05e-57)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 5.5e+149)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -1.75e+114)
		tmp = t_2;
	elseif (z <= -1.6e+59)
		tmp = t_1;
	elseif (z <= -1.85e-44)
		tmp = (t * (z - y)) / z;
	elseif (z <= -4.1e-143)
		tmp = t_1;
	elseif (z <= -4.1e-238)
		tmp = x + (t * (y / a));
	elseif (z <= 3.6e-301)
		tmp = x - (x / (a / y));
	elseif (z <= 2.05e-57)
		tmp = x + ((y * t) / a);
	elseif (z <= 5.5e+149)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+114], t$95$2, If[LessEqual[z, -1.6e+59], t$95$1, If[LessEqual[z, -1.85e-44], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -4.1e-143], t$95$1, If[LessEqual[z, -4.1e-238], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-301], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-57], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+149], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.75e114 or 5.49999999999999999e149 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 39.6%

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

   4. Taylor expanded in y around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-*r/ 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. distribute-neg-frac 66.6%

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

   6. Simplified 66.6%

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

   if -1.75e114 < z < -1.59999999999999991e59 or -1.85e-44 < z < -4.1e-143 or 2.0500000000000001e-57 < z < 5.49999999999999999e149

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. div-sub 56.7%

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

      2. associate-*r/ 59.5%

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

      3. associate-/l* 56.6%

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

      4. associate-/r/ 60.9%

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

   5. Simplified 60.9%

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

   if -1.59999999999999991e59 < z < -1.85e-44

   1. Initial program 73.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. Taylor expanded in a around 0 52.1%

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

      1. associate-*r/ 52.1%

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

      2. neg-mul-1 52.1%

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

      3. *-commutative 52.1%

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

      4. distribute-rgt-neg-out 52.1%

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

   6. Simplified 52.1%

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

   if -4.1e-143 < z < -4.1000000000000001e-238

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in t around inf 79.2%

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

      1. associate-*r/ 89.2%

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

   8. Simplified 89.2%

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

   if -4.1000000000000001e-238 < z < 3.60000000000000007e-301

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in t around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. associate-/l* 93.1%

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

   8. Simplified 93.1%

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

   if 3.60000000000000007e-301 < z < 2.0500000000000001e-57

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 81.1%

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

      1. associate-/l* 78.3%

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

      2. associate-/r/ 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in t around inf 73.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+59}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-143}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-301}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-296} \lor \neg \left(t\_1 \leq 10^{-284}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-296) (not (<= t_1 1e-284)))
     t_1
     (+ t (/ (- x t) (/ 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 <= -1e-296) || !(t_1 <= 1e-284)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (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 <= (-1d-296)) .or. (.not. (t_1 <= 1d-284))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (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 <= -1e-296) || !(t_1 <= 1e-284)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (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 <= -1e-296) or not (t_1 <= 1e-284):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (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 <= -1e-296) || !(t_1 <= 1e-284))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(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 <= -1e-296) || ~((t_1 <= 1e-284)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (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, -1e-296], N[Not[LessEqual[t$95$1, 1e-284]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $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)))) < -1e-296 or 1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.4%

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

   if -1e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000004e-284

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. distribute-rgt-out-- 85.8%

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

      7. associate-/l* 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-284}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{z}{t - x}}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ z (- t x)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= z -2.7e+14)
     t
     (if (<= z -6.5e-238)
       t_2
       (if (<= z 4.4e-306)
         (* x (- 1.0 (/ y a)))
         (if (<= z 2.05e-79)
           (+ x (/ (* y t) a))
           (if (<= z 1.15e-31)
             t_1
             (if (<= z 4.7e+58) t_2 (if (<= z 1.15e+138) t_1 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (z / (t - x));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (z <= -2.7e+14) {
		tmp = t;
	} else if (z <= -6.5e-238) {
		tmp = t_2;
	} else if (z <= 4.4e-306) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.05e-79) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.15e-31) {
		tmp = t_1;
	} else if (z <= 4.7e+58) {
		tmp = t_2;
	} else if (z <= 1.15e+138) {
		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) :: t_2
    real(8) :: tmp
    t_1 = -y / (z / (t - x))
    t_2 = x + (t * (y / a))
    if (z <= (-2.7d+14)) then
        tmp = t
    else if (z <= (-6.5d-238)) then
        tmp = t_2
    else if (z <= 4.4d-306) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.05d-79) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.15d-31) then
        tmp = t_1
    else if (z <= 4.7d+58) then
        tmp = t_2
    else if (z <= 1.15d+138) 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 = -y / (z / (t - x));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (z <= -2.7e+14) {
		tmp = t;
	} else if (z <= -6.5e-238) {
		tmp = t_2;
	} else if (z <= 4.4e-306) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.05e-79) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.15e-31) {
		tmp = t_1;
	} else if (z <= 4.7e+58) {
		tmp = t_2;
	} else if (z <= 1.15e+138) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / (z / (t - x))
	t_2 = x + (t * (y / a))
	tmp = 0
	if z <= -2.7e+14:
		tmp = t
	elif z <= -6.5e-238:
		tmp = t_2
	elif z <= 4.4e-306:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.05e-79:
		tmp = x + ((y * t) / a)
	elif z <= 1.15e-31:
		tmp = t_1
	elif z <= 4.7e+58:
		tmp = t_2
	elif z <= 1.15e+138:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(z / Float64(t - x)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= -6.5e-238)
		tmp = t_2;
	elseif (z <= 4.4e-306)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.05e-79)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.15e-31)
		tmp = t_1;
	elseif (z <= 4.7e+58)
		tmp = t_2;
	elseif (z <= 1.15e+138)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / (z / (t - x));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= -6.5e-238)
		tmp = t_2;
	elseif (z <= 4.4e-306)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.05e-79)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.15e-31)
		tmp = t_1;
	elseif (z <= 4.7e+58)
		tmp = t_2;
	elseif (z <= 1.15e+138)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+14], t, If[LessEqual[z, -6.5e-238], t$95$2, If[LessEqual[z, 4.4e-306], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-79], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-31], t$95$1, If[LessEqual[z, 4.7e+58], t$95$2, If[LessEqual[z, 1.15e+138], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7e14 or 1.15000000000000004e138 < z

   1. Initial program 61.7%

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

   3. Taylor expanded in z around inf 55.2%

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

   if -2.7e14 < z < -6.5000000000000006e-238 or 1.1499999999999999e-31 < z < 4.69999999999999972e58

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r/ 63.7%

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

   8. Simplified 63.7%

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

   if -6.5000000000000006e-238 < z < 4.40000000000000031e-306

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

   if 4.40000000000000031e-306 < z < 2.04999999999999997e-79

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in t around inf 73.5%

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

   if 2.04999999999999997e-79 < z < 1.1499999999999999e-31 or 4.69999999999999972e58 < z < 1.15000000000000004e138

   1. Initial program 78.8%

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

   3. Taylor expanded in y around -inf 61.0%

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

   4. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+138}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := \frac{-y}{\frac{z}{t - x}}\\ t_3 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a))))
        (t_2 (/ (- y) (/ z (- t x))))
        (t_3 (* t (/ (- z) (- a z)))))
   (if (<= z -2.75e+14)
     t_3
     (if (<= z -2.55e-238)
       t_1
       (if (<= z 1.3e-306)
         (* x (- 1.0 (/ y a)))
         (if (<= z 2.1e-76)
           (+ x (/ (* y t) a))
           (if (<= z 6e-30)
             t_2
             (if (<= z 2.2e+58) t_1 (if (<= z 4.5e+135) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = -y / (z / (t - x));
	double t_3 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.75e+14) {
		tmp = t_3;
	} else if (z <= -2.55e-238) {
		tmp = t_1;
	} else if (z <= 1.3e-306) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6e-30) {
		tmp = t_2;
	} else if (z <= 2.2e+58) {
		tmp = t_1;
	} else if (z <= 4.5e+135) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = x + (t * (y / a))
    t_2 = -y / (z / (t - x))
    t_3 = t * (-z / (a - z))
    if (z <= (-2.75d+14)) then
        tmp = t_3
    else if (z <= (-2.55d-238)) then
        tmp = t_1
    else if (z <= 1.3d-306) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.1d-76) then
        tmp = x + ((y * t) / a)
    else if (z <= 6d-30) then
        tmp = t_2
    else if (z <= 2.2d+58) then
        tmp = t_1
    else if (z <= 4.5d+135) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = -y / (z / (t - x));
	double t_3 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.75e+14) {
		tmp = t_3;
	} else if (z <= -2.55e-238) {
		tmp = t_1;
	} else if (z <= 1.3e-306) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6e-30) {
		tmp = t_2;
	} else if (z <= 2.2e+58) {
		tmp = t_1;
	} else if (z <= 4.5e+135) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = -y / (z / (t - x))
	t_3 = t * (-z / (a - z))
	tmp = 0
	if z <= -2.75e+14:
		tmp = t_3
	elif z <= -2.55e-238:
		tmp = t_1
	elif z <= 1.3e-306:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.1e-76:
		tmp = x + ((y * t) / a)
	elif z <= 6e-30:
		tmp = t_2
	elif z <= 2.2e+58:
		tmp = t_1
	elif z <= 4.5e+135:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(Float64(-y) / Float64(z / Float64(t - x)))
	t_3 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.75e+14)
		tmp = t_3;
	elseif (z <= -2.55e-238)
		tmp = t_1;
	elseif (z <= 1.3e-306)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.1e-76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 6e-30)
		tmp = t_2;
	elseif (z <= 2.2e+58)
		tmp = t_1;
	elseif (z <= 4.5e+135)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = -y / (z / (t - x));
	t_3 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -2.75e+14)
		tmp = t_3;
	elseif (z <= -2.55e-238)
		tmp = t_1;
	elseif (z <= 1.3e-306)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.1e-76)
		tmp = x + ((y * t) / a);
	elseif (z <= 6e-30)
		tmp = t_2;
	elseif (z <= 2.2e+58)
		tmp = t_1;
	elseif (z <= 4.5e+135)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+14], t$95$3, If[LessEqual[z, -2.55e-238], t$95$1, If[LessEqual[z, 1.3e-306], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-30], t$95$2, If[LessEqual[z, 2.2e+58], t$95$1, If[LessEqual[z, 4.5e+135], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.75e14 or 4.50000000000000007e135 < z

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0 41.6%

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

   4. Taylor expanded in y around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. associate-*r/ 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

      4. distribute-neg-frac 60.7%

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

   6. Simplified 60.7%

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

   if -2.75e14 < z < -2.55e-238 or 5.9999999999999998e-30 < z < 2.2000000000000001e58

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r/ 63.7%

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

   8. Simplified 63.7%

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

   if -2.55e-238 < z < 1.3e-306

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

   if 1.3e-306 < z < 2.09999999999999992e-76

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in t around inf 73.5%

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

   if 2.09999999999999992e-76 < z < 5.9999999999999998e-30 or 2.2000000000000001e58 < z < 4.50000000000000007e135

   1. Initial program 78.8%

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

   3. Taylor expanded in y around -inf 61.0%

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

   4. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-30}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := \frac{-y}{\frac{z}{t - x}}\\ t_3 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-294}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a))))
        (t_2 (/ (- y) (/ z (- t x))))
        (t_3 (* t (/ (- z) (- a z)))))
   (if (<= z -2.8e+14)
     t_3
     (if (<= z -6.5e-238)
       t_1
       (if (<= z 7e-294)
         (- x (/ x (/ a y)))
         (if (<= z 1.25e-75)
           (+ x (/ (* y t) a))
           (if (<= z 1.3e-31)
             t_2
             (if (<= z 1.26e+57) t_1 (if (<= z 1.45e+141) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = -y / (z / (t - x));
	double t_3 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.8e+14) {
		tmp = t_3;
	} else if (z <= -6.5e-238) {
		tmp = t_1;
	} else if (z <= 7e-294) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.25e-75) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.3e-31) {
		tmp = t_2;
	} else if (z <= 1.26e+57) {
		tmp = t_1;
	} else if (z <= 1.45e+141) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = x + (t * (y / a))
    t_2 = -y / (z / (t - x))
    t_3 = t * (-z / (a - z))
    if (z <= (-2.8d+14)) then
        tmp = t_3
    else if (z <= (-6.5d-238)) then
        tmp = t_1
    else if (z <= 7d-294) then
        tmp = x - (x / (a / y))
    else if (z <= 1.25d-75) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.3d-31) then
        tmp = t_2
    else if (z <= 1.26d+57) then
        tmp = t_1
    else if (z <= 1.45d+141) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = -y / (z / (t - x));
	double t_3 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.8e+14) {
		tmp = t_3;
	} else if (z <= -6.5e-238) {
		tmp = t_1;
	} else if (z <= 7e-294) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.25e-75) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.3e-31) {
		tmp = t_2;
	} else if (z <= 1.26e+57) {
		tmp = t_1;
	} else if (z <= 1.45e+141) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = -y / (z / (t - x))
	t_3 = t * (-z / (a - z))
	tmp = 0
	if z <= -2.8e+14:
		tmp = t_3
	elif z <= -6.5e-238:
		tmp = t_1
	elif z <= 7e-294:
		tmp = x - (x / (a / y))
	elif z <= 1.25e-75:
		tmp = x + ((y * t) / a)
	elif z <= 1.3e-31:
		tmp = t_2
	elif z <= 1.26e+57:
		tmp = t_1
	elif z <= 1.45e+141:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(Float64(-y) / Float64(z / Float64(t - x)))
	t_3 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.8e+14)
		tmp = t_3;
	elseif (z <= -6.5e-238)
		tmp = t_1;
	elseif (z <= 7e-294)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 1.25e-75)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.3e-31)
		tmp = t_2;
	elseif (z <= 1.26e+57)
		tmp = t_1;
	elseif (z <= 1.45e+141)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = -y / (z / (t - x));
	t_3 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -2.8e+14)
		tmp = t_3;
	elseif (z <= -6.5e-238)
		tmp = t_1;
	elseif (z <= 7e-294)
		tmp = x - (x / (a / y));
	elseif (z <= 1.25e-75)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.3e-31)
		tmp = t_2;
	elseif (z <= 1.26e+57)
		tmp = t_1;
	elseif (z <= 1.45e+141)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+14], t$95$3, If[LessEqual[z, -6.5e-238], t$95$1, If[LessEqual[z, 7e-294], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-75], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-31], t$95$2, If[LessEqual[z, 1.26e+57], t$95$1, If[LessEqual[z, 1.45e+141], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.8e14 or 1.45000000000000003e141 < z

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0 41.6%

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

   4. Taylor expanded in y around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. associate-*r/ 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

      4. distribute-neg-frac 60.7%

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

   6. Simplified 60.7%

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

   if -2.8e14 < z < -6.5000000000000006e-238 or 1.29999999999999998e-31 < z < 1.26e57

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r/ 63.7%

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

   8. Simplified 63.7%

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

   if -6.5000000000000006e-238 < z < 7.00000000000000064e-294

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in t around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. associate-/l* 93.1%

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

   8. Simplified 93.1%

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

   if 7.00000000000000064e-294 < z < 1.24999999999999995e-75

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in t around inf 73.5%

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

   if 1.24999999999999995e-75 < z < 1.29999999999999998e-31 or 1.26e57 < z < 1.45000000000000003e141

   1. Initial program 78.8%

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

   3. Taylor expanded in y around -inf 61.0%

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

   4. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-294}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+57}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+141}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (* t (/ (- z) (- a z)))))
   (if (<= z -8.5e+113)
     t_2
     (if (<= z -3.8e+58)
       t_1
       (if (<= z -9.8e-40)
         (/ (* t (- z y)) z)
         (if (<= z 1.06e-55)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 3.5e+150) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -8.5e+113) {
		tmp = t_2;
	} else if (z <= -3.8e+58) {
		tmp = t_1;
	} else if (z <= -9.8e-40) {
		tmp = (t * (z - y)) / z;
	} else if (z <= 1.06e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.5e+150) {
		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 = (t - x) * (y / (a - z))
    t_2 = t * (-z / (a - z))
    if (z <= (-8.5d+113)) then
        tmp = t_2
    else if (z <= (-3.8d+58)) then
        tmp = t_1
    else if (z <= (-9.8d-40)) then
        tmp = (t * (z - y)) / z
    else if (z <= 1.06d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 3.5d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -8.5e+113) {
		tmp = t_2;
	} else if (z <= -3.8e+58) {
		tmp = t_1;
	} else if (z <= -9.8e-40) {
		tmp = (t * (z - y)) / z;
	} else if (z <= 1.06e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.5e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * (-z / (a - z))
	tmp = 0
	if z <= -8.5e+113:
		tmp = t_2
	elif z <= -3.8e+58:
		tmp = t_1
	elif z <= -9.8e-40:
		tmp = (t * (z - y)) / z
	elif z <= 1.06e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 3.5e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8.5e+113)
		tmp = t_2;
	elseif (z <= -3.8e+58)
		tmp = t_1;
	elseif (z <= -9.8e-40)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (z <= 1.06e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 3.5e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -8.5e+113)
		tmp = t_2;
	elseif (z <= -3.8e+58)
		tmp = t_1;
	elseif (z <= -9.8e-40)
		tmp = (t * (z - y)) / z;
	elseif (z <= 1.06e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 3.5e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+113], t$95$2, If[LessEqual[z, -3.8e+58], t$95$1, If[LessEqual[z, -9.8e-40], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.06e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+150], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5000000000000001e113 or 3.49999999999999984e150 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 39.6%

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

   4. Taylor expanded in y around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-*r/ 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. distribute-neg-frac 66.6%

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

   6. Simplified 66.6%

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

   if -8.5000000000000001e113 < z < -3.7999999999999999e58 or 1.06e-55 < z < 3.49999999999999984e150

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. div-sub 53.5%

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

      2. associate-*r/ 57.3%

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

      3. associate-/l* 53.3%

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

      4. associate-/r/ 57.3%

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

   5. Simplified 57.3%

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

   if -3.7999999999999999e58 < z < -9.7999999999999995e-40

   1. Initial program 72.6%

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

   3. Taylor expanded in x around 0 54.0%

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

   4. Taylor expanded in a around 0 54.3%

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

      1. associate-*r/ 54.3%

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

      2. neg-mul-1 54.3%

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

      3. *-commutative 54.3%

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

      4. distribute-rgt-neg-out 54.3%

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

   6. Simplified 54.3%

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

   if -9.7999999999999995e-40 < z < 1.06e-55

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+150}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t + t \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (+ t (* t (/ (- a y) z)))))
   (if (<= z -1.25e+84)
     t_2
     (if (<= z -4.8e+58)
       t_1
       (if (<= z -1.75e-38)
         t_2
         (if (<= z 1.36e-55)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 1.45e+151) t_1 (* t (/ (- z) (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t + (t * ((a - y) / z));
	double tmp;
	if (z <= -1.25e+84) {
		tmp = t_2;
	} else if (z <= -4.8e+58) {
		tmp = t_1;
	} else if (z <= -1.75e-38) {
		tmp = t_2;
	} else if (z <= 1.36e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.45e+151) {
		tmp = t_1;
	} else {
		tmp = t * (-z / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = t + (t * ((a - y) / z))
    if (z <= (-1.25d+84)) then
        tmp = t_2
    else if (z <= (-4.8d+58)) then
        tmp = t_1
    else if (z <= (-1.75d-38)) then
        tmp = t_2
    else if (z <= 1.36d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.45d+151) then
        tmp = t_1
    else
        tmp = t * (-z / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t + (t * ((a - y) / z));
	double tmp;
	if (z <= -1.25e+84) {
		tmp = t_2;
	} else if (z <= -4.8e+58) {
		tmp = t_1;
	} else if (z <= -1.75e-38) {
		tmp = t_2;
	} else if (z <= 1.36e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.45e+151) {
		tmp = t_1;
	} else {
		tmp = t * (-z / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t + (t * ((a - y) / z))
	tmp = 0
	if z <= -1.25e+84:
		tmp = t_2
	elif z <= -4.8e+58:
		tmp = t_1
	elif z <= -1.75e-38:
		tmp = t_2
	elif z <= 1.36e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.45e+151:
		tmp = t_1
	else:
		tmp = t * (-z / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t + Float64(t * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -1.25e+84)
		tmp = t_2;
	elseif (z <= -4.8e+58)
		tmp = t_1;
	elseif (z <= -1.75e-38)
		tmp = t_2;
	elseif (z <= 1.36e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.45e+151)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(-z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t + (t * ((a - y) / z));
	tmp = 0.0;
	if (z <= -1.25e+84)
		tmp = t_2;
	elseif (z <= -4.8e+58)
		tmp = t_1;
	elseif (z <= -1.75e-38)
		tmp = t_2;
	elseif (z <= 1.36e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.45e+151)
		tmp = t_1;
	else
		tmp = t * (-z / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(t * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+84], t$95$2, If[LessEqual[z, -4.8e+58], t$95$1, If[LessEqual[z, -1.75e-38], t$95$2, If[LessEqual[z, 1.36e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+151], t$95$1, N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e84 or -4.8e58 < z < -1.7500000000000001e-38

   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 67.4%

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

      1. associate--l+ 67.4%

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

      2. distribute-lft-out-- 67.4%

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

      3. div-sub 67.4%

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

      4. mul-1-neg 67.4%

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

      5. unsub-neg 67.4%

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

      6. distribute-rgt-out-- 67.6%

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

      7. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around inf 53.7%

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

      1. associate-*r/ 57.4%

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

   8. Simplified 57.4%

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

   if -1.25e84 < z < -4.8e58 or 1.35999999999999993e-55 < z < 1.45000000000000009e151

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf 52.4%

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

      1. div-sub 52.4%

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

      2. associate-*r/ 56.7%

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

      3. associate-/l* 52.1%

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

      4. associate-/r/ 56.7%

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

   5. Simplified 56.7%

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

   if -1.7500000000000001e-38 < z < 1.35999999999999993e-55

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 83.3%

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

   5. Simplified 83.3%

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

   if 1.45000000000000009e151 < z

   1. Initial program 59.8%

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

   3. Taylor expanded in x around 0 46.5%

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

   4. Taylor expanded in y around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-*r/ 72.6%

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

      3. distribute-rgt-neg-in 72.6%

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

      4. distribute-neg-frac 72.6%

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

   6. Simplified 72.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t + t \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;t + t \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+151}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-39} \lor \neg \left(z \leq 4.7 \cdot 10^{-87} \lor \neg \left(z \leq 6.8 \cdot 10^{-29}\right) \land z \leq 6.5 \cdot 10^{+36}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e-39)
         (not (or (<= z 4.7e-87) (and (not (<= z 6.8e-29)) (<= z 6.5e+36)))))
   (- t (/ (- t x) (/ z (- y a))))
   (+ x (/ (- t x) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e-39) || !((z <= 4.7e-87) || (!(z <= 6.8e-29) && (z <= 6.5e+36)))) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.7d-39)) .or. (.not. (z <= 4.7d-87) .or. (.not. (z <= 6.8d-29)) .and. (z <= 6.5d+36))) then
        tmp = t - ((t - x) / (z / (y - a)))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e-39) || !((z <= 4.7e-87) || (!(z <= 6.8e-29) && (z <= 6.5e+36)))) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e-39) or not ((z <= 4.7e-87) or (not (z <= 6.8e-29) and (z <= 6.5e+36))):
		tmp = t - ((t - x) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e-39) || !((z <= 4.7e-87) || (!(z <= 6.8e-29) && (z <= 6.5e+36))))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e-39) || ~(((z <= 4.7e-87) || (~((z <= 6.8e-29)) && (z <= 6.5e+36)))))
		tmp = t - ((t - x) / (z / (y - a)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e-39], N[Not[Or[LessEqual[z, 4.7e-87], And[N[Not[LessEqual[z, 6.8e-29]], $MachinePrecision], LessEqual[z, 6.5e+36]]]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000015e-39 or 4.7000000000000001e-87 < z < 6.79999999999999945e-29 or 6.4999999999999998e36 < z

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. distribute-lft-out-- 68.4%

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

      3. div-sub 68.4%

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

      4. mul-1-neg 68.4%

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

      5. unsub-neg 68.4%

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

      6. distribute-rgt-out-- 68.5%

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

      7. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   if -3.70000000000000015e-39 < z < 4.7000000000000001e-87 or 6.79999999999999945e-29 < z < 6.4999999999999998e36

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 82.5%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-39} \lor \neg \left(z \leq 4.7 \cdot 10^{-87} \lor \neg \left(z \leq 6.8 \cdot 10^{-29}\right) \land z \leq 6.5 \cdot 10^{+36}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))) (t_2 (+ t (* x (/ (- y a) z)))))
   (if (<= z -1.95e-38)
     t_2
     (if (<= z 1.7e-55)
       t_1
       (if (<= z 3.2e-31)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 7.9e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double t_2 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.95e-38) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 3.2e-31) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7.9e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    t_2 = t + (x * ((y - a) / z))
    if (z <= (-1.95d-38)) then
        tmp = t_2
    else if (z <= 1.7d-55) then
        tmp = t_1
    else if (z <= 3.2d-31) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 7.9d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double t_2 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.95e-38) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 3.2e-31) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7.9e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	t_2 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -1.95e-38:
		tmp = t_2
	elif z <= 1.7e-55:
		tmp = t_1
	elif z <= 3.2e-31:
		tmp = y / ((a - z) / (t - x))
	elif z <= 7.9e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	t_2 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -1.95e-38)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 3.2e-31)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 7.9e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	t_2 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -1.95e-38)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 3.2e-31)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 7.9e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-38], t$95$2, If[LessEqual[z, 1.7e-55], t$95$1, If[LessEqual[z, 3.2e-31], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.9e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e-38 or 7.9000000000000001e37 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

      6. distribute-rgt-out-- 67.4%

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

      7. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r/ 70.1%

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

      3. distribute-rgt-neg-in 70.1%

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

      4. distribute-neg-frac 70.1%

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

      5. neg-sub0 70.1%

         \[\leadsto t - x \cdot \frac{\color{blue}{0 - \left(y - a\right)}}{z} \]

      6. associate--r- 70.1%

         \[\leadsto t - x \cdot \frac{\color{blue}{\left(0 - y\right) + a}}{z} \]

      7. neg-sub0 70.1%

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

   8. Simplified 70.1%

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

   if -1.95e-38 < z < 1.69999999999999986e-55 or 3.20000000000000018e-31 < z < 7.9000000000000001e37

   1. Initial program 91.1%

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

   3. Taylor expanded in a around inf 80.5%

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

      1. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

   if 1.69999999999999986e-55 < z < 3.20000000000000018e-31

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 85.9%

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

      3. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (/ t (/ (- a z) (- y z)))))
   (if (<= z -6.2e-80)
     t_2
     (if (<= z 1.7e-55)
       t_1
       (if (<= z 9.4e-32)
         (/ (- y) (/ z (- t x)))
         (if (<= z 2.05e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -6.2e-80) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 9.4e-32) {
		tmp = -y / (z / (t - x));
	} else if (z <= 2.05e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t / ((a - z) / (y - z))
    if (z <= (-6.2d-80)) then
        tmp = t_2
    else if (z <= 1.7d-55) then
        tmp = t_1
    else if (z <= 9.4d-32) then
        tmp = -y / (z / (t - x))
    else if (z <= 2.05d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -6.2e-80) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 9.4e-32) {
		tmp = -y / (z / (t - x));
	} else if (z <= 2.05e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -6.2e-80:
		tmp = t_2
	elif z <= 1.7e-55:
		tmp = t_1
	elif z <= 9.4e-32:
		tmp = -y / (z / (t - x))
	elif z <= 2.05e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -6.2e-80)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 9.4e-32)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= 2.05e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -6.2e-80)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 9.4e-32)
		tmp = -y / (z / (t - x));
	elseif (z <= 2.05e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-80], t$95$2, If[LessEqual[z, 1.7e-55], t$95$1, If[LessEqual[z, 9.4e-32], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000032e-80 or 2.0499999999999999e37 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 61.6%

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

   5. Simplified 61.6%

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

   if -6.20000000000000032e-80 < z < 1.69999999999999986e-55 or 9.40000000000000039e-32 < z < 2.0499999999999999e37

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.69999999999999986e-55 < z < 9.40000000000000039e-32

   1. Initial program 99.1%

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

   3. Taylor expanded in y around -inf 85.9%

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

   4. Taylor expanded in a around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-/l* 83.8%

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

   6. Simplified 83.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+37}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (/ t (/ (- a z) (- y z)))))
   (if (<= z -7.6e-81)
     t_2
     (if (<= z 1.65e-55)
       t_1
       (if (<= z 1.25e-30)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 7e+36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -7.6e-81) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-30) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t / ((a - z) / (y - z))
    if (z <= (-7.6d-81)) then
        tmp = t_2
    else if (z <= 1.65d-55) then
        tmp = t_1
    else if (z <= 1.25d-30) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 7d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -7.6e-81) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-30) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -7.6e-81:
		tmp = t_2
	elif z <= 1.65e-55:
		tmp = t_1
	elif z <= 1.25e-30:
		tmp = y / ((a - z) / (t - x))
	elif z <= 7e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -7.6e-81)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 1.25e-30)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 7e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -7.6e-81)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 1.25e-30)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 7e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e-81], t$95$2, If[LessEqual[z, 1.65e-55], t$95$1, If[LessEqual[z, 1.25e-30], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999997e-81 or 6.9999999999999996e36 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 61.6%

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

   5. Simplified 61.6%

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

   if -7.5999999999999997e-81 < z < 1.65e-55 or 1.24999999999999993e-30 < z < 6.9999999999999996e36

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.65e-55 < z < 1.24999999999999993e-30

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 85.9%

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

      3. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+36}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+160}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -1.1e-81)
     t_1
     (if (<= z 1.75e-56)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 5.6e+89)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 6.6e+160) (+ t (/ a (/ z (- t x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -1.1e-81) {
		tmp = t_1;
	} else if (z <= 1.75e-56) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.6e+89) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 6.6e+160) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-1.1d-81)) then
        tmp = t_1
    else if (z <= 1.75d-56) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 5.6d+89) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 6.6d+160) then
        tmp = t + (a / (z / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -1.1e-81) {
		tmp = t_1;
	} else if (z <= 1.75e-56) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.6e+89) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 6.6e+160) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -1.1e-81:
		tmp = t_1
	elif z <= 1.75e-56:
		tmp = x + ((t - x) * (y / a))
	elif z <= 5.6e+89:
		tmp = y / ((a - z) / (t - x))
	elif z <= 6.6e+160:
		tmp = t + (a / (z / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -1.1e-81)
		tmp = t_1;
	elseif (z <= 1.75e-56)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 5.6e+89)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 6.6e+160)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -1.1e-81)
		tmp = t_1;
	elseif (z <= 1.75e-56)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 5.6e+89)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 6.6e+160)
		tmp = t + (a / (z / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-81], t$95$1, If[LessEqual[z, 1.75e-56], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+89], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+160], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e-81 or 6.5999999999999994e160 < z

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 43.9%

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

      1. associate-/l* 64.9%

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

   5. Simplified 64.9%

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

   if -1.1e-81 < z < 1.7499999999999999e-56

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0 80.8%

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

      1. associate-/l* 85.3%

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

      2. associate-/r/ 85.7%

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

   5. Simplified 85.7%

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

   if 1.7499999999999999e-56 < z < 5.5999999999999996e89

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. div-sub 58.7%

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

      2. associate-*r/ 58.7%

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

      3. associate-/l* 58.9%

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

   5. Simplified 58.9%

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

   if 5.5999999999999996e89 < z < 6.5999999999999994e160

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. distribute-lft-out-- 78.9%

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

      3. div-sub 78.9%

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

      4. mul-1-neg 78.9%

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

      5. unsub-neg 78.9%

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

      6. distribute-rgt-out-- 78.9%

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

      7. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+160}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -2e-38)
     t_1
     (if (<= z 1.7e-55)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 7.6e+34)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 7.5e+56) (- x (/ z (/ (- a z) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -2e-38) {
		tmp = t_1;
	} else if (z <= 1.7e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 7.6e+34) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7.5e+56) {
		tmp = x - (z / ((a - z) / 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 + (x * ((y - a) / z))
    if (z <= (-2d-38)) then
        tmp = t_1
    else if (z <= 1.7d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 7.6d+34) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 7.5d+56) then
        tmp = x - (z / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -2e-38) {
		tmp = t_1;
	} else if (z <= 1.7e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 7.6e+34) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 7.5e+56) {
		tmp = x - (z / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -2e-38:
		tmp = t_1
	elif z <= 1.7e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 7.6e+34:
		tmp = y / ((a - z) / (t - x))
	elif z <= 7.5e+56:
		tmp = x - (z / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -2e-38)
		tmp = t_1;
	elseif (z <= 1.7e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 7.6e+34)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 7.5e+56)
		tmp = Float64(x - Float64(z / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -2e-38)
		tmp = t_1;
	elseif (z <= 1.7e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 7.6e+34)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 7.5e+56)
		tmp = x - (z / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-38], t$95$1, If[LessEqual[z, 1.7e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+34], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+56], N[(x - N[(z / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9999999999999999e-38 or 7.4999999999999999e56 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. distribute-lft-out-- 67.6%

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

      3. div-sub 67.6%

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

      4. mul-1-neg 67.6%

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

      5. unsub-neg 67.6%

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

      6. distribute-rgt-out-- 67.7%

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

      7. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in t around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*r/ 71.4%

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

      3. distribute-rgt-neg-in 71.4%

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

      4. distribute-neg-frac 71.4%

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

      5. neg-sub0 71.4%

         \[\leadsto t - x \cdot \frac{\color{blue}{0 - \left(y - a\right)}}{z} \]

      6. associate--r- 71.4%

         \[\leadsto t - x \cdot \frac{\color{blue}{\left(0 - y\right) + a}}{z} \]

      7. neg-sub0 71.4%

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

   8. Simplified 71.4%

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

   if -1.9999999999999999e-38 < z < 1.69999999999999986e-55

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 83.3%

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

   5. Simplified 83.3%

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

   if 1.69999999999999986e-55 < z < 7.6000000000000003e34

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

      2. associate-*r/ 70.4%

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

      3. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   if 7.6000000000000003e34 < z < 7.4999999999999999e56

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around inf 83.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3e+14)
     t
     (if (<= z -3.4e-220)
       t_1
       (if (<= z -7.2e-238) (* t (/ y (- a z))) (if (<= z 3.5e+90) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3e+14) {
		tmp = t;
	} else if (z <= -3.4e-220) {
		tmp = t_1;
	} else if (z <= -7.2e-238) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.5e+90) {
		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 = x * (1.0d0 - (y / a))
    if (z <= (-3d+14)) then
        tmp = t
    else if (z <= (-3.4d-220)) then
        tmp = t_1
    else if (z <= (-7.2d-238)) then
        tmp = t * (y / (a - z))
    else if (z <= 3.5d+90) 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 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3e+14) {
		tmp = t;
	} else if (z <= -3.4e-220) {
		tmp = t_1;
	} else if (z <= -7.2e-238) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.5e+90) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3e+14:
		tmp = t
	elif z <= -3.4e-220:
		tmp = t_1
	elif z <= -7.2e-238:
		tmp = t * (y / (a - z))
	elif z <= 3.5e+90:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3e+14)
		tmp = t;
	elseif (z <= -3.4e-220)
		tmp = t_1;
	elseif (z <= -7.2e-238)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 3.5e+90)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3e+14)
		tmp = t;
	elseif (z <= -3.4e-220)
		tmp = t_1;
	elseif (z <= -7.2e-238)
		tmp = t * (y / (a - z));
	elseif (z <= 3.5e+90)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+14], t, If[LessEqual[z, -3.4e-220], t$95$1, If[LessEqual[z, -7.2e-238], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+90], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e14 or 3.4999999999999998e90 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 53.6%

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

   if -3e14 < z < -3.39999999999999993e-220 or -7.20000000000000021e-238 < z < 3.4999999999999998e90

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 67.3%

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

      1. associate-/l* 71.2%

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

      2. associate-/r/ 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in x around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. unsub-neg 52.5%

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

   8. Simplified 52.5%

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

   if -3.39999999999999993e-220 < z < -7.20000000000000021e-238

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 89.4%

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

   4. Taylor expanded in y around inf 89.4%

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

      1. associate-/l* 89.4%

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

   6. Simplified 89.4%

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

      1. clear-num 89.4%

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

      2. associate-/r/ 89.1%

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

      3. clear-num 89.1%

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

   8. Applied egg-rr 89.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -3e+14)
     t
     (if (<= z -2.3e-238)
       t_1
       (if (<= z 5.5e-298) (* x (- 1.0 (/ y a))) (if (<= z 2.8e+90) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3e+14) {
		tmp = t;
	} else if (z <= -2.3e-238) {
		tmp = t_1;
	} else if (z <= 5.5e-298) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.8e+90) {
		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 = x + (t * (y / a))
    if (z <= (-3d+14)) then
        tmp = t
    else if (z <= (-2.3d-238)) then
        tmp = t_1
    else if (z <= 5.5d-298) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.8d+90) 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 = x + (t * (y / a));
	double tmp;
	if (z <= -3e+14) {
		tmp = t;
	} else if (z <= -2.3e-238) {
		tmp = t_1;
	} else if (z <= 5.5e-298) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.8e+90) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -3e+14:
		tmp = t
	elif z <= -2.3e-238:
		tmp = t_1
	elif z <= 5.5e-298:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.8e+90:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -3e+14)
		tmp = t;
	elseif (z <= -2.3e-238)
		tmp = t_1;
	elseif (z <= 5.5e-298)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.8e+90)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -3e+14)
		tmp = t;
	elseif (z <= -2.3e-238)
		tmp = t_1;
	elseif (z <= 5.5e-298)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.8e+90)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+14], t, If[LessEqual[z, -2.3e-238], t$95$1, If[LessEqual[z, 5.5e-298], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+90], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e14 or 2.8e90 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 53.6%

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

   if -3e14 < z < -2.30000000000000005e-238 or 5.4999999999999996e-298 < z < 2.8e90

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 65.9%

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

      1. associate-/l* 68.7%

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

      2. associate-/r/ 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in t around inf 60.8%

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

      1. associate-*r/ 62.6%

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

   8. Simplified 62.6%

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

   if -2.30000000000000005e-238 < z < 5.4999999999999996e-298

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+14) t (if (<= z 1.85e+84) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+14) {
		tmp = t;
	} else if (z <= 1.85e+84) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d+14)) then
        tmp = t
    else if (z <= 1.85d+84) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+14) {
		tmp = t;
	} else if (z <= 1.85e+84) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+14:
		tmp = t
	elif z <= 1.85e+84:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= 1.85e+84)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= 1.85e+84)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+14], t, If[LessEqual[z, 1.85e+84], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e14 or 1.85e84 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 53.6%

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

   if -2.7e14 < z < 1.85e84

   1. Initial program 89.9%

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

   3. Taylor expanded in z around 0 67.7%

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

      1. associate-/l* 71.5%

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

      2. associate-/r/ 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in x around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

   8. Simplified 51.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+25)
   x
   (if (<= a -1.56e-46) (/ t (/ a y)) (if (<= a 3.8e-48) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+25) {
		tmp = x;
	} else if (a <= -1.56e-46) {
		tmp = t / (a / y);
	} else if (a <= 3.8e-48) {
		tmp = t;
	} 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 <= (-1.9d+25)) then
        tmp = x
    else if (a <= (-1.56d-46)) then
        tmp = t / (a / y)
    else if (a <= 3.8d-48) then
        tmp = t
    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 <= -1.9e+25) {
		tmp = x;
	} else if (a <= -1.56e-46) {
		tmp = t / (a / y);
	} else if (a <= 3.8e-48) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+25:
		tmp = x
	elif a <= -1.56e-46:
		tmp = t / (a / y)
	elif a <= 3.8e-48:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+25)
		tmp = x;
	elseif (a <= -1.56e-46)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 3.8e-48)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+25)
		tmp = x;
	elseif (a <= -1.56e-46)
		tmp = t / (a / y);
	elseif (a <= 3.8e-48)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+25], x, If[LessEqual[a, -1.56e-46], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-48], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9e25 or 3.80000000000000002e-48 < a

   1. Initial program 88.7%

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

   3. Taylor expanded in a around inf 45.6%

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

   if -1.9e25 < a < -1.55999999999999991e-46

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 56.4%

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

      1. associate-/l* 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around 0 44.8%

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

   if -1.55999999999999991e-46 < a < 3.80000000000000002e-48

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 42.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e+32)
   x
   (if (<= a -3.1e-46) (/ (- x) (/ a y)) (if (<= a 1.15e-46) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e+32) {
		tmp = x;
	} else if (a <= -3.1e-46) {
		tmp = -x / (a / y);
	} else if (a <= 1.15e-46) {
		tmp = t;
	} 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 <= (-5.7d+32)) then
        tmp = x
    else if (a <= (-3.1d-46)) then
        tmp = -x / (a / y)
    else if (a <= 1.15d-46) then
        tmp = t
    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 <= -5.7e+32) {
		tmp = x;
	} else if (a <= -3.1e-46) {
		tmp = -x / (a / y);
	} else if (a <= 1.15e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e+32:
		tmp = x
	elif a <= -3.1e-46:
		tmp = -x / (a / y)
	elif a <= 1.15e-46:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e+32)
		tmp = x;
	elseif (a <= -3.1e-46)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= 1.15e-46)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.7e+32)
		tmp = x;
	elseif (a <= -3.1e-46)
		tmp = -x / (a / y);
	elseif (a <= 1.15e-46)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e+32], x, If[LessEqual[a, -3.1e-46], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-46], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7e32 or 1.15e-46 < a

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 46.5%

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

   if -5.7e32 < a < -3.1000000000000001e-46

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 62.2%

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

      1. associate-/l* 66.4%

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

      2. associate-/r/ 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around inf 60.7%

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

   7. Taylor expanded in t around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. mul-1-neg 56.6%

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

      3. distribute-lft-neg-out 56.6%

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

      4. associate-*l/ 60.7%

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

      5. associate-*l/ 60.7%

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

      6. distribute-rgt-in 60.7%

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

      7. +-commutative 60.7%

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

      8. distribute-frac-neg 60.7%

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

      9. sub-neg 60.7%

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

      10. div-sub 60.7%

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

      11. associate-*r/ 56.6%

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

   9. Simplified 56.6%

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

   10. Taylor expanded in t around 0 33.7%

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

       1. mul-1-neg 33.7%

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

       2. associate-/l* 42.6%

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

       3. distribute-neg-frac 42.6%

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

   12. Simplified 42.6%

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

   if -3.1000000000000001e-46 < a < 1.15e-46

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 42.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+28) x (if (<= a 2.6e-47) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+28) {
		tmp = x;
	} else if (a <= 2.6e-47) {
		tmp = t;
	} 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 <= (-4.8d+28)) then
        tmp = x
    else if (a <= 2.6d-47) then
        tmp = t
    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 <= -4.8e+28) {
		tmp = x;
	} else if (a <= 2.6e-47) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+28:
		tmp = x
	elif a <= 2.6e-47:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+28)
		tmp = x;
	elseif (a <= 2.6e-47)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+28)
		tmp = x;
	elseif (a <= 2.6e-47)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+28], x, If[LessEqual[a, 2.6e-47], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.79999999999999962e28 or 2.6e-47 < a

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 46.1%

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

   if -4.79999999999999962e28 < a < 2.6e-47

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 38.5%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.0% 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 79.2%

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

3. Taylor expanded in z around inf 25.5%

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

4. Final simplification 25.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))))